smith Namespace Reference

Accelerator functionality. More...

Namespaces
	accelerator
	Namespace for methods involving accelerator-enabled builds.
	cli
	Command line functionality.
	heat_transfer
	HeatTransfer helper structs.
	input
	The input related helper functions and objects.
	mesh
	Mesh related input options.
	output
	The output related helper functions and objects.
	profiling
	profiling namespace
	solid_mechanics
	SolidMechanics helper data types.
	thermomechanics
	Thermomechanics helper data types.

Classes
class	DifferentiablePhysics
	Implementation of BasePhysics which uses FieldStates and gretl to track the computational graph, dynamically checkpoint, and back-propagate sensitivities. More...
class	DifferentiableSolver
	Abstract interface to DifferentiableSolver interface. Each differentiable solve should provide both its forward solve and an adjoint solve. More...
class	LinearDifferentiableSolver
	Implementation of the DifferentiableSolver interface for the special case of linear solves with linear adjoint solves. More...
class	NonlinearDifferentiableSolver
	Implementation of the DifferentiableSolver interface for the special case of nonlinear solves with linear adjoint solves. More...
class	DifferentiableBlockSolver
	Abstract interface to DifferentiableBlockSolver interface. Each differentiable block solve should provide both its forward solve and an adjoint solve. More...
class	LinearDifferentiableBlockSolver
	Implementation of the DifferentiableBlockSolver interface for the special case of linear solves with linear adjoint solves. More...
class	NonlinearDifferentiableBlockSolver
	Implementation of the DifferentiableBlockSolver interface for the special case of nonlinear solves with linear adjoint solves. More...
class	DirichletBoundaryConditions
	A generic class for setting Dirichlet boundary conditions on arbitrary physics. More...
struct	zero_dual_from_state
	functor which takes a std::shared_ptr<FiniteElementState>, and returns a zero-valued std::shared_ptr<FiniteElementDual> with the same space More...
struct	zero_state_from_dual
	functor which takes a std::shared_ptr<FiniteElementDual>, and returns a zero-valued std::shared_ptr<FiniteElementState> with the same space More...
struct	FieldStateWeightedSum
	temporary object to register the multiplication of a gretl::State<double> with a FieldState. Casts back More...
class	LumpedMassExplicitNewmarkStateAdvancer
	Lumped mass explicit dynamics implementation for the StateAdvancer interface. More...
class	ParaviewWriter
	Class which interactions with ParaViewDataCollection to write arbitrary field results to disk. This allows output independent of a particular BasePhysics. More...
class	SolidMechanicsStateAdvancer
	Implementation of the StateAdvancer interface for advancing the solution of solid mechanics problems. More...
class	StateAdvancer
	Base state advancer class, allows specification for quasi-static solve strategies, or time integration algorithms. More...
class	TimeDiscretizedWeakForm
class	TimeDiscretizedWeakForm< spatial_dim, OutputSpace, Parameters< InputSpaces... > >
	A time discretized weakform gets a TimeInfo object passed as arguments to q-function (lambdas which are integrated over quadrature points) so users can have access to time increments, and timestep cycle. These quantities are often valuable for time integrated PDEs. More...
class	SecondOrderTimeDiscretizedWeakForms
	A container holding the two types of weak forms useful for solving time discretized second order (in time) systems of equations. More...
class	SecondOrderTimeDiscretizedWeakForm
class	SecondOrderTimeDiscretizedWeakForm< spatial_dim, OutputSpace, Parameters< TrialInputSpace, InputSpaces... > >
	Useful for time-discretized PDEs of second order (involves for first and second derivatives of time). Users write q-functions in terns of u, u_dot, u_dot_dot, and the weak form is transformed by the ImplicitNewmarkSecondOrderTimeIntegrationRule so that is it globally a function of u, u_old, u_dot_old, u_dot_dot_old, with u as the distinct unknown for the time discretized system. More...
struct	BackwardEulerFirstOrderTimeIntegrationRule
	encodes rules for time discretizing first order odes (involving first time derivatives). When solving f(u, u_dot, t) = 0 this class provides the current discrete approximation for u and u_dot as a function of (u^{n+1}, u^n). More...
struct	ImplicitNewmarkSecondOrderTimeIntegrationRule
	encodes rules for time discretizing second order odes (involving first and second time derivatives). When solving f(u, u_dot, u_dot_dot, t) = 0 this class provides the current discrete approximation for u, u_dot, and u_dot_dot as a function of (u^{n+1},u^n,u_dot^n,u_dot_dot^n). More...
class	TimestepEstimator
	Base class interface for estimating the stable timestep given the current state and parameters. More...
class	ConstantTimeStepEstimator
	TimeStepEstimator which uses a simple and fixed timestep. More...
class	ApplicationManager
	RAII Application Manager class. Initializes MPI and other important libraries as well as automatically finalizes them upon going out of scope. More...
struct	variant_alternative
	Obtains the type at index I of a variant<T0, T1> More...
struct	variant_alternative< 0, T0, T1 >
	Obtains the type at index 0 of a variant<T0, T1> More...
struct	variant_alternative< 1, T0, T1 >
	Obtains the type at index 1 of a variant<T0, T1> More...
struct	variant
	A simple variant type that supports only two elements. More...
class	BlockDiagonalPreconditioner
	Simple block diagonal preconditioner for block systems. More...
class	BlockTriangularPreconditioner
	Simple block triangular preconditioner for block systems. More...
class	BlockSchurPreconditioner
	Simple 2x2 block Schur complement preconditioner for block systems. More...
class	NewtonSolver
	Newton solver with a 2-way line-search. Reverts to regular Newton if max_line_search_iterations is set to 0. More...
struct	TrustRegionSettings
	Internal structure for storing trust region settings. More...
struct	TrustRegionResults
	Internal structure for storing trust region stateful data. More...
class	TrustRegion
	Equation solver class based on a standard preconditioned trust-region algorithm. More...
class	EquationSolver
	This class manages the objects typically required to solve a nonlinear set of equations arising from discretization of a PDE of the form F(x) = 0. Specifically, it has. More...
class	SuperLUSolver
	A wrapper class for using the MFEM SuperLU solver with a HypreParMatrix. More...
struct	DifferentiateWRT
struct	differentiate_wrt_this
	this type exists solely as a way to signal to smith::Functional that the function smith::Functional::operator()` should differentiate w.r.t. a specific argument More...
struct	Domain
	a class for representing a geometric region that can be used for integration More...
struct	dual
	Dual number struct (value plus gradient) More...
struct	is_dual_number
	class for checking if a type is a dual number or not More...
struct	is_dual_number< dual< T > >
	class for checking if a type is a dual number or not More...
struct	ElementRestriction
struct	BlockElementRestriction
	a generalization of mfem::ElementRestriction that works with multiple kinds of element geometries. Instead of doing the "E->L" (gather) and "L->E" (scatter) operations for only one element geometry, this class does them with block "E-vectors", where each element geometry is a separate block. More...
struct	TensorProductQuadratureRule
	a convenience class for generating information about tensor product integration rules from the underlying 1D rule. More...
struct	CompileTimeValue
struct	batched_jacobian
	this struct is used to look up mfem's memory layout of the quadrature point jacobian matrices More...
struct	batched_jacobian< mfem::Geometry::CUBE, q >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	batched_jacobian< mfem::Geometry::SQUARE, q >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	batched_jacobian< mfem::Geometry::TRIANGLE, q >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	batched_jacobian< mfem::Geometry::TETRAHEDRON, q >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	batched_position
	this struct is used to look up mfem's memory layout of the quadrature point position vectors More...
struct	batched_position< mfem::Geometry::CUBE, q >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	batched_position< mfem::Geometry::SQUARE, q >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	batched_position< mfem::Geometry::TRIANGLE, q >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	batched_position< mfem::Geometry::TETRAHEDRON, q >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	batched_position< mfem::Geometry::SEGMENT, q >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	H1
	H1 elements of order p. More...
struct	Hcurl
	H(curl) elements of order p. More...
struct	L2
	Discontinuous elements of order p. More...
struct	QOI
	"Quantity of Interest" elements (i.e. elements with a single shape function, 1) More...
struct	FunctionSpace
	a small POD class for tracking function space metadata More...
struct	finite_element
	Template prototype for finite element implementations. More...
struct	DependsOn
struct	Index
	Compile-time alias for index of differentiation. More...
class	Functional< test(trials...), exec >
	Intended to be like std::function for finite element kernels. More...
struct	QoIProlongation
	this class behaves like a Prolongation operator, except is specialized for the case of a quantity of interest. The action of its MultTranspose() operator (the only thing it is used for) sums the values from different processors. More...
struct	QoIElementRestriction
	this class behaves like a Restriction operator, except is specialized for the case of a quantity of interest. The action of its ScatterAdd() operator (the only thing it is used for) sums the values on this local processor. More...
class	Functional< double(trials...), exec >
	a partial template specialization of Functional with test == double, implying "quantity of interest" More...
struct	GeometricFactors
	a class that computes and stores positions and jacobians at each quadrature point More...
struct	Dimension
	Compile-time alias for a dimension. More...
struct	Integral
	a class for representing a Integral calculations and their derivatives More...
struct	isotropic_tensor
	an object representing a highly symmetric kind of tensor, that is interoperable with smith::tensor, but uses less memory and performs less calculation than its dense counterpart More...
struct	isotropic_tensor< T, n >
	there is no such thing as a rank-1 isotropic tensor, but we include this specialization to help explain that to users, rather than just producing an "incomplete type" compilation error More...
struct	isotropic_tensor< T, m, m >
	a rank-2 isotropic tensor is essentially just the Identity matrix, with a constant of proportionality More...
struct	isotropic_tensor< T, 3, 3, 3 >
	the only rank-3 isotropic tensor we suport is the alternating tensor (levi-civita symbol) More...
struct	isotropic_tensor< T, m, m, m, m >
	there are 3 independent rank-4 isotropic tensors (dilatational, symmetric, antisymmetric), so this object represents a linear combination of them More...
struct	QuadratureRule
	A rule for numerical quadrature (set of points and weights) Can be thought of as a compile-time analogue of mfem::IntegrationRule. More...
struct	Nothing
	these classes are a little confusing. These two special types represent the similar (but different) cases of: More...
struct	Empty
	see Nothing for a complete description of this class and when to use it More...
struct	QuadratureData
	A class for storing and access user-defined types at quadrature points. More...
class	ShapeAwareFunctional< shape, test(trials...), exec >
	This is a small wrapper around smith::Functional for shape-displaced domains of integration. More...
struct	tensor
	Arbitrary-rank tensor class. More...
struct	zero
	A sentinel struct for eliding no-op tensor operations. More...
struct	is_zero
	checks if a type is zero More...
struct	is_zero< zero >
struct	LuFactorization
	Representation of an LU factorization. More...
struct	tuple
	This is a class that mimics most of std::tuple's interface, except that it is usable in CUDA kernels and admits some arithmetic operator overloads. More...
struct	tuple< T0 >
	Type that mimics std::tuple. More...
struct	tuple< T0, T1 >
	Type that mimics std::tuple. More...
struct	tuple< T0, T1, T2 >
	Type that mimics std::tuple. More...
struct	tuple< T0, T1, T2, T3 >
	Type that mimics std::tuple. More...
struct	tuple< T0, T1, T2, T3, T4 >
	Type that mimics std::tuple. More...
struct	tuple< T0, T1, T2, T3, T4, T5 >
	Type that mimics std::tuple. More...
struct	tuple< T0, T1, T2, T3, T4, T5, T6 >
	Type that mimics std::tuple. More...
struct	tuple< T0, T1, T2, T3, T4, T5, T6, T7 >
	Type that mimics std::tuple. More...
struct	tuple< T0, T1, T2, T3, T4, T5, T6, T7, T8 >
	Type that mimics std::tuple. More...
struct	tuple< T0, T1, T2, T3, T4, T5, T6, T7, T8, T9 >
	Type that mimics std::tuple. More...
struct	tuple< T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10 >
	Type that mimics std::tuple. More...
struct	tuple_size
struct	tuple_size< smith::tuple< Types... > >
struct	tuple_element
	a struct used to determine the type at index I of a tuple More...
struct	tuple_element< I, tuple< Head, Tail... > >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	tuple_element< 0, tuple< Head, Tail... > >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	is_tuple
	Trait for checking if a type is a smith::tuple. More...
struct	is_tuple< smith::tuple< T... > >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	is_tuple_of_tuples
	Trait for checking if a type if a smith::tuple containing only smith::tuple. More...
struct	is_tuple_of_tuples< smith::tuple< T... > >
	Trait for checking if a type if a smith::tuple containing only smith::tuple. More...
struct	is_tensor_of_dual_number
	class for checking if a type is a tensor of dual numbers or not More...
struct	is_tensor_of_dual_number< tensor< dual< T >, n... > >
	class for checking if a type is a tensor of dual numbers or not More...
struct	SolverStatus
	Status and diagnostics of nonlinear equation solvers. More...
struct	ScalarSolverOptions
	Settings for solve_scalar_equation. More...
struct	TimesteppingOptions
	A timestep and boundary condition enforcement method for a dynamic solver. More...
struct	AMGXOptions
	Stores the information required to configure a NVIDIA AMGX preconditioner. More...
struct	AMGFContactOptions
	Stores the configuration information for an AMGFContact preconditioner. More...
struct	LinearSolverOptions
	Parameters for an iterative linear solution scheme. More...
struct	NonlinearSolverOptions
	Nonlinear solution scheme parameters. More...
class	BasePhysics
	This is the abstract base class for a generic forward solver. More...
class	BoundaryCondition
	Boundary condition information bundle. More...
class	BoundaryConditionManager
	A container for the boundary condition information relating to a specific physics module. More...
class	Components
	A set to flag components of a vector field. More...
struct	TimeInfo
	struct storing time and timestep information More...
struct	Parameters
	a struct that is used in the physics modules to clarify which template arguments are user-controlled parameters (e.g. for design optimization) More...
class	Constraint
	Abstract constraint class. More...
struct	ContactOptions
	Stores the options for a contact pair. More...
class	ContactData
	This class stores all ContactInteractions for a problem, calls Tribol functions that act on all contact interactions, and agglomerates fields that exist over different ContactInteractions. More...
class	FunctionalObjective
class	FunctionalObjective< spatial_dim, Parameters< InputSpaces... >, std::integer_sequence< int, parameter_indices... > >
	FunctionalObjective object, implements to the ScalarFunctional interface using smith::ShapeAwareFunctional. More...
class	FunctionalWeakForm
class	FunctionalWeakForm< spatial_dim, OutputSpace, Parameters< InputSpaces... >, std::integer_sequence< int, input_indices... > >
	A nonlinear WeakForm class implemented using smith::Functional. More...
class	HeatTransfer
	An object containing the solver for a heat transfer PDE. More...
class	HeatTransfer< order, dim, Parameters< parameter_space... >, std::integer_sequence< int, parameter_indices... > >
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. More...
struct	HeatTransferInputOptions
	Stores all information held in the input file that is used to configure the solver. More...
class	HeatTransferWeakForm
class	HeatTransferWeakForm< order, dim, Parameters< InputSpaces... > >
	The weak form for heat transfer. More...
struct	HardeningInputOptions
	Contains function that defines the schema for hardening laws. More...
struct	LiquidCrystElastomerBrighenti
	Brighenti's liquid crystal elastomer model. More...
struct	LiquidCrystalElastomerBertoldi
	Bertoldi's liquid crystal elastomer model Paper: Li, S., Librandi, G., Yao, Y., Richard, A. J., Schneider‐Yamamura, A., Aizenberg, J., & Bertoldi, K. (2021). Controlling Liquid Crystal Orientations for Programmable Anisotropic Transformations in Cellular Microstructures. Advanced Materials, 33(42), 2105024. More...
struct	SolidMaterialInputOptions
	Contains function that defines the schema for solid mechanics materials. More...
struct	ThermalMaterialInputOptions
	Contains function that defines the schema for heat transfer materials. More...
class	Mesh
	Helper class for constructing a mesh consistent with Smith. More...
class	ScalarObjective
	Abstract residual class. More...
class	SolidMechanics
class	SolidMechanics< order, dim, Parameters< parameter_space... >, std::integer_sequence< int, parameter_indices... > >
	The nonlinear solid solver class. More...
class	SolidMechanicsContact
class	SolidMechanicsContact< order, dim, Parameters< parameter_space... >, std::integer_sequence< int, parameter_indices... > >
	The nonlinear solid with contact solver class. More...
struct	SolidMechanicsInputOptions
	Stores all information held in the input file that is used to configure the solver. More...
class	SolidWeakForm
class	SolidWeakForm< order, dim, Parameters< InputSpaces... > >
	The weak form for solid mechanics. More...
class	FiniteElementDual
	Class for encapsulating the dual vector space of a finite element space (i.e. the space of linear forms as applied to a specific basis set) More...
class	FiniteElementState
	Class for encapsulating the critical MFEM components of a primal finite element field. More...
class	FiniteElementVector
	Class for encapsulating the data associated with a vector derived from a MFEM finite element space. Specifically, it contains the information needed for both primal finite element state fields and dual finite element vectors. More...
class	StateManager
	Manages the lifetimes of FEState objects such that restarts are abstracted from physics modules. More...
class	Thermomechanics
	The operator-split thermal-structural solver. More...
struct	ThermomechanicsInputOptions
	Stores all information held in the input file that is used to configure the thermal structural solver. More...
class	ThermomechanicsMonolithic
class	ThermomechanicsMonolithic< order, dim, Parameters< parameter_space... >, std::integer_sequence< int, parameter_indices... > >
	The monolithic thermal-structural solver with operator-split options. More...
class	WeakForm
	Abstract WeakForm class. More...

Typedefs
using	FEFieldPtr = std::shared_ptr< FiniteElementState >
	typedef
using	FEDualPtr = std::shared_ptr< FiniteElementDual >
	typedef
using	FieldState = gretl::State< FEFieldPtr, FEDualPtr >
	typedef
using	ReactionState = gretl::State< FEDualPtr, FEFieldPtr >
	typedef
using	FieldVecState = gretl::State< std::vector< FEFieldPtr >, std::vector< FEDualPtr > >
	typedef
using	DoubleState = gretl::State< double, double >
	typedef
using	QuasiStaticFirstOrderTimeIntegrationRule = BackwardEulerFirstOrderTimeIntegrationRule
template<typename T , int dim, ExecutionSpace space>
using	ExecArray = axom::Array< T, dim, detail::execution_to_memory_v< space > >
	Alias for an Array corresponding to a particular ExecutionSpace.
template<typename T , int dim = 1>
using	CPUArray = ExecArray< T, dim, ExecutionSpace::CPU >
	Alias for an array on the CPU.
template<typename T , int dim = 1>
using	GPUArray = ExecArray< T, dim, ExecutionSpace::CPU >
	Alias for an array on the GPU.
template<typename T , int dim = 1>
using	UnifiedArray = ExecArray< T, dim, ExecutionSpace::CPU >
	Alias for an array in unified memory.
template<typename T , int dim, ExecutionSpace space>
using	ExecArrayView = axom::ArrayView< T, dim, detail::execution_to_memory_v< space > >
	Alias for an ArrayView corresponding to a particular ExecutionSpace.
template<typename T , int dim = 1>
using	CPUArrayView = ExecArrayView< T, dim, ExecutionSpace::CPU >
	Alias for an array view on the CPU.
using	BlockOverride = std::pair< int, std::unique_ptr< const mfem::Operator > >
	Optional override for a diagonal block operator. More...
using	vec2 = tensor< double, 2 >
	statically sized vector of 2 doubles
using	vec3 = tensor< double, 3 >
	statically sized vector of 3 doubles
using	mat2 = tensor< double, 2, 2 >
	statically sized 2x2 matrix of doubles
using	mat3 = tensor< double, 3, 3 >
	statically sized 3x3 matrix of doubles
template<typename T , int n1, int n2 = 1>
using	reduced_tensor = std::conditional_t<(n1==1 &&n2==1), double, std::conditional_t< n1==1, tensor< T, n2 >, std::conditional_t< n2==1, tensor< T, n1 >, tensor< T, n1, n2 > >> >
	Removes 1s from tensor dimensions For example, a tensor<T, 1, 10> is equivalent to a tensor<T, 10> More...
template<typename T1 , typename T2 >
using	outer_product_t = typename detail::outer_prod< T1, T2 >::type
	a type function that returns the tensor type of an outer product of two tensors More...
template<int i, int n, typename T >
using	one_hot_t = typename one_hot< i, n, T >::type
	a tuple type with n entries, all of which are of type smith::zero, except for the i^{th} entry, which is of type T More...
using	FieldPtr = FiniteElementState *
	using
using	DualFieldPtr = FiniteElementDual *
	using
using	ConstFieldPtr = FiniteElementState const *
	using
using	ConstDualFieldPtr = FiniteElementDual const *
	using
using	var_hardening_t = std::variant< solid_mechanics::LinearHardening, solid_mechanics::PowerLawHardening, solid_mechanics::VoceHardening >
	Holds all possible isotropic hardening laws that can be utilized in our input file.
using	var_solid_material_t = std::variant< solid_mechanics::NeoHookean, solid_mechanics::LinearIsotropic, solid_mechanics::J2SmallStrain< solid_mechanics::LinearHardening >, solid_mechanics::J2SmallStrain< solid_mechanics::PowerLawHardening >, solid_mechanics::J2SmallStrain< solid_mechanics::VoceHardening > >
	All possible solid mechanics materials that can be utilized in our input file.
using	var_thermal_material_t = std::variant< heat_transfer::LinearIsotropicConductor, heat_transfer::LinearConductor< 2 >, heat_transfer::LinearConductor< 3 > >
	Holds all possible heat transfer materials that can be utilized in our Input Deck.
using	GeneralCoefficient = variant< std::shared_ptr< mfem::Coefficient >, std::shared_ptr< mfem::VectorCoefficient > >
	A sum type for encapsulating either a scalar or vector coeffient.
using	QuadratureField = double
	This is a placeholder for quadrature fields.
using	QuadratureFieldPtr = double *
	This is a placeholder for quadrature field pointers.
using	ConstQuadratureFieldPtr = const double *
	This is a placeholder for const quadrature field pointers.

Enumerations
enum class	ExecutionSpace { CPU , GPU , Dynamic }
	enum used for signalling whether or not to perform certain calculations on the CPU or GPU
enum class	BlockTriangularType { Lower , Upper , Symmetric }
	Selects the block triangular sweep used by BlockTriangularPreconditioner. More...
enum class	BlockSchurType { Diagonal , Lower , Upper , Full }
	Selects the block Schur preconditioner variant. More...
enum class	SchurApproxType { DiagInv , A22Only , Custom }
	Selects how the (1,1) Schur operator is approximated. More...
enum class	Family {   QOI , H1 , HCURL , HDIV ,   L2 }
	Element conformity. More...
enum class	TimestepMethod {   QuasiStatic , BackwardEuler , SDIRK33 , ForwardEuler ,   RK2 , RK3SSP , RK4 , GeneralizedAlpha ,   ImplicitMidpoint , SDIRK23 , SDIRK34 , Newmark ,   HHTAlpha , WBZAlpha , AverageAcceleration , LinearAcceleration ,   CentralDifference , FoxGoodwin }
	Timestep method of a solver. More...
enum class	DirichletEnforcementMethod { DirectControl , RateControl , FullControl }
	this enum describes which way to enforce the time-varying constraint u(t) == U(t) More...
enum class	LinearSolver {   CG , GMRES , SuperLU , Strumpack ,   PetscCG , PetscGMRES }
	Linear solution method indicator. More...
enum class	NonlinearSolver {   Newton , LBFGS , NewtonLineSearch , TrustRegion ,   KINFullStep , KINBacktrackingLineSearch , KINPicard , PetscNewton ,   PetscNewtonBacktracking , PetscNewtonCriticalPoint , PetscTrustRegion }
	Nonlinear solver method indicator. More...
enum class	AMGXSolver {   AMG , PCGF , CG , PCG ,   PBICGSTAB , BICGSTAB , FGMRES , JACOBI_L1 ,   GS , POLYNOMIAL , KPZ_POLYNOMIAL , BLOCK_JACOBI ,   MULTICOLOR_GS , MULTICOLOR_DILU }
	Solver types supported by AMGX. More...
enum class	PetscPCType {   JACOBI , JACOBI_L1 , JACOBI_ROWSUM , JACOBI_ROWMAX ,   PBJACOBI , BJACOBI , LU , ILU ,   CHOLESKY , SVD , ASM , GASM ,   GAMG , HMG , NONE }
	Preconditioner types supported by PETSc. More...
enum class	Preconditioner {   HypreJacobi , HypreL1Jacobi , HypreGaussSeidel , HypreAMG ,   HypreILU , AMGX , Petsc , AMGFContact ,   None }
	The type of preconditioner to be used. More...
enum	SubSpaceOptions { NEVER , WHEN_INDEFINITE , WHEN_INDEFINITE_OR_BOUNDARY , ALWAYS }
	Enumerated options for when to use trust-region subspace solver.
enum class	Component : size_t { X = 0b001 , Y = 0b010 , Z = 0b100 , ALL = 0b111 }
	Type giving vector components meaningful names and restricting inputs to Components class to meaningful values.
enum class	ContactMethod { SingleMortar }
	Methodology for enforcing contact constraints (i.e. how you form the constraint equations) More...
enum class	ContactEnforcement { Penalty , LagrangeMultiplier }
	Describes how to enforce the contact constraint equations. More...
enum class	ContactType { TiedNormal , Frictionless }
	Mechanical constraint type on contact surfaces. More...
enum class	ContactJacobian { Approximate , Exact }
	Method for computing Jacobian of contact terms. More...
enum class	ElementType { H1 , HCURL , HDIV , L2 }
	The type of a finite element basis function. More...

Functions
void	defineInputFileSchema (axom::inlet::Inlet &inlet)
	Define the input file structure for the driver code. More...
gretl::State< int >	make_milestone (const std::vector< FieldState > &states)
	gretl-function to create a dummy-state which records all states and params of interest to the mechanics. This is used to inject additional adjoint loads and evaluate individual timestep sensitivities for the BasePhysics interface.
template<int dim, typename ShapeDispSpace , typename VectorSpace , typename... ParamSpaces>
auto	buildSolidMechanics (std::shared_ptr< smith::Mesh > mesh, std::shared_ptr< DifferentiableSolver > d_solid_nonlinear_solver, smith::ImplicitNewmarkSecondOrderTimeIntegrationRule time_rule, size_t num_checkpoints, std::string physics_name, const std::vector< std::string > &param_names={})
	Helper function to generate the base-physics for solid mechanics. More...
double	matrixNorm (std::unique_ptr< mfem::HypreParMatrix > &K)
	Utility to compute the matrix norm.
double	skewMatrixNorm (std::unique_ptr< mfem::HypreParMatrix > &K)
	Utility to compute 0.5*norm(K-K.T)
void	initializeSolver (mfem::Solver *mfem_solver, const smith::FiniteElementState &u)
	Initialize mfem solver if near-nullspace is needed.
std::shared_ptr< LinearDifferentiableSolver >	buildDifferentiableLinearSolver (LinearSolverOptions linear_opts, const smith::Mesh &mesh)
	Create a differentiable linear solver. More...
std::shared_ptr< NonlinearDifferentiableSolver >	buildDifferentiableNonlinearSolver (NonlinearSolverOptions nonlinear_opts, LinearSolverOptions linear_opts, const smith::Mesh &mesh)
	Create a differentiable nonlinear solver. More...
std::shared_ptr< NonlinearDifferentiableBlockSolver >	buildDifferentiableNonlinearBlockSolver (NonlinearSolverOptions nonlinear_opts, LinearSolverOptions linear_opts, const smith::Mesh &mesh)
	Create a differentiable nonlinear block solver. More...
template<typename DispSpace , typename DensitySpace >
auto	createKineticEnergyIntegrator (smith::Domain &domain, const mfem::ParFiniteElementSpace &velocity_space, const mfem::ParFiniteElementSpace &density_space)
	Utility function to construct a smith::functional which evaluates the total kinetic energy.
template<typename DispSpace , typename DensitySpace >
gretl::State< double >	computeKineticEnergy (const std::shared_ptr< smith::Functional< double(DispSpace, DispSpace, DensitySpace)>> &energy_func, smith::FieldState disp, smith::FieldState velo, smith::FieldState density, double scaling)
	Utility function which computes the kinetic energy and returns it as a gretl state (with its vjp defined)
auto	checkGradients (const gretl::State< double > &objectiveState, FieldState &inputState, FiniteElementDual &inputDual, double objectiveBase, gretl::DataStore &dataStore, double eps)
	testing utility to confirm order of convergence of the finite differences relative to the backprop gradient
auto	checkGradients (const gretl::State< double > &objectiveState, gretl::State< double, double > &inputState, double &inputDual, double objectiveBase, gretl::DataStore &dataStore, double eps)
	testing utility to confirm order of convergence of the finite differences relative to the backprop gradient
double	checkGradWrt (const gretl::State< double > &objective, smith::FieldState &input, double eps, size_t num_fd_steps=4, bool printmore=false)
	Testing utility function which runs a gretl graph num_fd_steps (with increasingly smaller finite difference steps) to check if the computed graph gradients are converging to the finite differenced gradients at the expected rate.
double	checkGradWrt (const gretl::State< double > &objective, gretl::State< double, double > &input, double eps, size_t num_fd_steps=4, bool printmore=false)
	Testing utility function which runs a gretl graph num_fd_steps (with increasingly smaller finite difference steps) to check if the computed graph gradients are converging to the finite differenced gradients at the expected rate.
DoubleState	evaluateObjective (const ScalarObjective &objective, const FieldState &shape_disp, const std::vector< FieldState > &inputs, const TimeInfo &time_info=TimeInfo(0.0, 1.0, 0))
	Evaluates a DoubleState using a provided ScalarObjective reference, and the input arguments to that objective. This operation is tracked on the gretl graph.
FieldState	computeLumpedMass (const WeakForm *mass_residual_eval, const FieldState &shape_u, const FieldState &lumped_field, const FieldState &rho)
	gretl-function implementation to compute lumped mass vectors from shape_displacements FieldState and a density field FieldState. A lumped_field is also passed to communicate the intended dimension of the lumped mass. For example, as scalar lumped field will result in a single lumped mass per node, while a vector lumped field will give a nodal lumped field, where every component of the lumped vector per node has the full mass lumped value (the sum of all lumped masses will be dim * total_mass)
FieldState	diagInverse (const FieldState &x)
	gretl-function implementation to compute invert the values for every entry in a FieldState.
FieldState	evalResidual (const WeakForm *residual_eval, FieldState shape_disp, const std::vector< FieldState > &states, const std::vector< FieldState > &params, TimeInfo time_info, size_t inertial_index)
	gretl-function implementation which evaluates the residual force (which is minus the mechanical force) given shape displacement, states and params. The inertial index denotes which index in the state corresponds to the highest time derivative term (e.g., acceleration for solid mechanics).
FieldState	componentWiseMult (const FieldState &x, const FieldState &y, const BoundaryConditionManager *bc_manager)
	gretl-function implementation which multiplies x and y component-wise to create a new FieldState. The bc_manager is used to zero the constrained dofs of the output Field.
FieldState	negativeComponentWiseMult (const FieldState &x, const FieldState &y, const BoundaryConditionManager *bc_manager)
	gretl-function implementation which multiplies and then negates x and y component-wise to create a new FieldState. The bc_manager is used to zero the constrained dofs of the output Field. The intended use-case here is explicit dynamics, where the residual is the negative of the force, and the inverse of the mass is strictly positive. The negative component-wise multiplication of these gives the nodal accelerations.
FieldState	square (const FieldState &state)
	gretl-function to square (x^2) every component of the Field
gretl::State< double >	innerProduct (const FieldState &a, const FieldState &b)
	gretl-function to compute the inner product (vector l2-norm) of a and b
gretl::State< double >	innerProduct (const ReactionState &a, const ReactionState &b)
	gretl-function to compute the inner product (vector l2-norm) of a and b
FieldState	axpby (double a, const FieldState &x, double b, const FieldState &y)
	gretl-function to compute a*x + b*y
FieldState	zeroCopy (const FieldState &x)
	gretl-function to make a deep-copy of a FieldState and initialize it to 0.
FieldState	axpby (const gretl::State< double > &a, const FieldState &x, const gretl::State< double > &b, const FieldState &y)
	axpby using State<double> and FieldState
FieldState	weighted_sum (const std::vector< double > &weights, const std::vector< FieldState > &weighted_fields, const std::vector< gretl::State< double >> &differentiable_weights, const std::vector< FieldState > &differentiably_weighted_fields, const std::vector< double > &differentiable_scale_factors)
	compute the differentiable weighted sum of fields, weighted by both double weights, and also gret::State<double> differentiable weights. The differentiable_scale_factors are applied to the differentiable weights to enable negation and scalar muliplication of weights.
FieldStateWeightedSum	operator* (double a, const FieldState &b)
	multiply scalar by a FieldState to get a temporary FieldStateWeightedSum which can cast back to a FieldState
FieldStateWeightedSum	operator* (const FieldState &b, double a)
	multiply scalar by a FieldState to get a temporary FieldStateWeightedSum which can cast back to a FieldState
FieldStateWeightedSum	operator* (double a, const FieldStateWeightedSum &b)
	multiply scalar by a FieldStateWeightedSum to get a temporary FieldStateWeightedSum which can cast back to a FieldState
FieldStateWeightedSum	operator* (const FieldStateWeightedSum &b, double a)
	multiply scalar by a FieldStateWeightedSum to get a temporary FieldStateWeightedSum which can cast back to a FieldState
FieldStateWeightedSum	operator* (const gretl::State< double > &a, const FieldState &b)
	multiply scalar by a FieldState to get a temporary FieldStateWeightedSum which can cast back to a FieldState
FieldStateWeightedSum	operator* (const FieldState &b, const gretl::State< double > &a)
	multiply scalar by a FieldState to get a temporary FieldStateWeightedSum which can cast back to a FieldState
FieldStateWeightedSum	operator+ (const FieldState &x, const FieldState &y)
	add two FieldState
FieldStateWeightedSum	operator- (const FieldState &x, const FieldState &y)
	subtract two FieldState
FieldStateWeightedSum	operator+ (const FieldStateWeightedSum &ax, const FieldStateWeightedSum &by)
	add two FieldStateWeightedSum
FieldStateWeightedSum	operator- (const FieldStateWeightedSum &ax, const FieldStateWeightedSum &by)
	subtract two FieldStateWeightedSum
FieldStateWeightedSum	operator+ (const FieldStateWeightedSum &ax, const FieldState &y)
	add FieldStateWeightedSum and FieldState
FieldStateWeightedSum	operator+ (const FieldState &y, const FieldStateWeightedSum &ax)
	add FieldStateWeightedSum and FieldState
FieldStateWeightedSum	operator- (const FieldStateWeightedSum &ax, const FieldState &by)
	subtract FieldState from FieldStateWeightedSum
FieldStateWeightedSum	operator- (const FieldState &ax, const FieldStateWeightedSum &by)
	subtract FieldStateWeightedSum from FieldState
FieldState	createFieldState (gretl::DataStore &dataStore, const smith::FEFieldPtr &s)
	initialize on the gretl::DataStore a FieldState with values from s
template<typename function_space >
FieldState	createFieldState (gretl::DataStore &dataStore, function_space space, const std::string &name, const std::string &mesh_tag)
	initialize on the gretl::DataStore a FieldState from a FiniteElementState of given space, name and mesh.
ReactionState	createReactionState (gretl::DataStore &dataStore, const smith::FEDualPtr &s)
	initialize on the gretl::DataStore a ReactionState with values from s
template<typename function_space >
ReactionState	createReactionState (gretl::DataStore &dataStore, function_space space, const std::string &name, const std::string &mesh_tag)
	initialize on the gretl::DataStore a ReactionState from a FiniteElementDual of given space, name and mesh.
FieldState	weighted_average (const FieldState &a, const FieldState &b, double weight)
	gretl-function to compute the weighted average a * weight + b * (1-weight)
mfem::ParFiniteElementSpace &	space (FieldState field)
	Get the space from the primal field of a field states.
std::vector< const mfem::ParFiniteElementSpace * >	spaces (const std::vector< FieldState > &states, const std::vector< FieldState > &params={})
	Get the spaces from the primal fields of a vector of field states.
std::vector< FiniteElementState * >	getFieldPointers (std::vector< FieldState > &states, std::vector< FieldState > params={})
	Get a vector of FieldPtr or DualFieldPtr from a vector of FieldState.
std::vector< const FiniteElementState * >	getConstFieldPointers (const std::vector< FieldState > &states, const std::vector< FieldState > &params={})
	Get a vector of ConstFieldPtr or ConstDualFieldPtr from a vector of FieldState.
FieldState	applyZeroBoundaryConditions (const FieldState &s, const BoundaryConditionManager *bc_manager)
	uses the constrained dofs on the bc_manager to zero the corresponding dofs in FieldState s.
template<int spatial_dim, typename LumpedFieldSpace , typename DensitySpace , typename... parameter_space>
auto	createSolidMassWeakForm (const std::string &physics_name, std::shared_ptr< smith::Mesh > &mesh, const FiniteElementState &lumped_field, const FiniteElementState &density)
	creates a lumped mass weak form
void	applyBoundaryConditions (double time, const smith::BoundaryConditionManager *bc_manager, smith::FEFieldPtr &primal_field, const smith::FEFieldPtr &bc_field_ptr)
	apply boundary conditions
FieldState	nonlinearSolve (const WeakForm *residual_eval, const FieldState &shape_disp, const std::vector< FieldState > &states, const std::vector< FieldState > &params, const std::vector< double > &state_update_weights, size_t primal_solve_state_index, size_t dirichlet_state_index, const TimeInfo &time_info, const DifferentiableSolver *solver, const BoundaryConditionManager *bc_manager, const FieldState *bc_field=nullptr)
	Solve a nonlinear system of equations as defined by the weak form. More...
FieldState	solve (const WeakForm &residual_eval, const FieldState &shape_disp, const std::vector< FieldState > &states, const std::vector< FieldState > &params, const TimeInfo &time_info, const DifferentiableSolver &solver, const DirichletBoundaryConditions &bcs, size_t unknown_state_index=0)
	Solve a nonlinear system of equations as defined by the weak form, assuming that the field indexed by unknown_index is the unknown field. More...
std::vector< FieldState >	block_solve (const std::vector< WeakForm * > &residual_evals, const std::vector< std::vector< size_t >> block_indices, const FieldState &shape_disp, const std::vector< std::vector< FieldState >> &states, const std::vector< std::vector< FieldState >> &params, const TimeInfo &time_info, const DifferentiableBlockSolver *solver, const std::vector< const BoundaryConditionManager * > &bc_managers)
	Solve a block nonlinear system of equations as defined by the vector of weak form. More...
auto	createParaviewWriter (const smith::Mesh &mesh, const std::vector< FieldState > &states, std::string output_name)
	Creates a ParaviewWriter from a mesh, vector of FieldState, and the name of the output paraview file. File will be in directory filename/filename.pvd.
auto	createParaviewWriter (const mfem::ParMesh &mesh, const std::vector< const FiniteElementState * > &states, std::string output_name)
	Creates a ParaviewWriter from an mfem::ParMesh, vector of FiniteElementState pointers, and the name of the output paraview file. File will be in directory filename/filename.pvd.
auto	evaluateWeakForm (const std::shared_ptr< WeakForm > &weak_form, const TimeInfo &time_info, FieldState shape_disp, const std::vector< FieldState > &field_states, FieldState field_for_residual_space)
	gretl-function implementation which evaluates the residual force (which is minus the mechanical force) given shape displacement, states and params. The field_for_residual_space Field is only used to set the appropriate size (mfem::ParFiniteElementSpace) for the residual field so it can be returned as a ReactionState
TimeInfo	create_time_info (DoubleState t, DoubleState dt, size_t cycle)
	creates a time info struct from gretl::State<double> More...
std::string	about ()
	Returns a string about the configuration of Smith. More...
std::string	gitSHA ()
	Returns a string for the Git SHA when the driver was built. More...
void	printRunInfo ()
	Outputs basic run information to the screen. More...
std::string	version (bool add_SHA=true)
	Returns a string for the version of Smith. More...
std::string	compiler ()
	Returns a string for the current compiler name and version. More...
std::string	buildType ()
	Returns a string for the current CMake build type (e.g. Debug, Release) More...
std::pair< int, int >	getMPIInfo (MPI_Comm comm=MPI_COMM_WORLD)
	Get MPI Info. More...
template<typename T , int dim, axom::MemorySpace space>
auto	view (axom::Array< T, dim, space > &arr)
	convenience function for creating a view of an axom::Array type
void	finalizer ()
	Destroy MPI, signal handling, logging, profiling, hypre, sundials, petsc, and slepc. Note this should not be called by or exposed to users.
template<typename T >
std::string	typeString (T &var)
	Return string of given parameter's type. More...
template<typename T >
void	writeToFile (std::vector< T > v, std::string filename)
	write an array of values out to file, in a space-separated format More...
void	writeToFile (mfem::Vector v, std::string filename)
	write an array of doubles out to file, in a space-separated format More...
void	writeToFile (mfem::SparseMatrix A, std::string filename)
	write a sparse matrix out to file More...
std::ostream &	operator<< (std::ostream &out, DoF dof)
	stream output for DoF
template<typename T >
void	writeToFile (axom::Array< T, 2, smith::detail::host_memory_space > arr, std::string filename)
	write a 2D array of values out to file, in a space-separated format More...
template<typename T >
void	writeToFile (axom::Array< T, 3, smith::detail::host_memory_space > arr, std::string filename)
	write a 3D array of values out to file, in a mathematica-compatible format More...
template<typename T , typename T0 , typename T1 >
constexpr T &	get (variant< T0, T1 > &v)
	Returns the variant member of specified type. More...
template<typename T , typename T0 , typename T1 >
constexpr const T &	get (const variant< T0, T1 > &v)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename Visitor , typename Variant >
constexpr decltype(auto)	visit (Visitor visitor, Variant &&v)
	Applies a functor to the active variant element. More...
template<typename T , typename T0 , typename T1 >
bool	holds_alternative (const variant< T0, T1 > &v)
	Checks whether a variant's active member is of a certain type. More...
template<typename T , typename T0 , typename T1 >
T *	get_if (variant< T0, T1 > *v)
	Returns the member of requested type if it's active, otherwise nullptr. More...
template<typename T , typename T0 , typename T1 >
const T *	get_if (const variant< T0, T1 > *v)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
mfem::Mesh	buildMeshFromFile (const std::string &mesh_file)
	Constructs an MFEM mesh from a file. More...
void	squish (mfem::Mesh &mesh)
	a transformation from the unit disk/sphere (in L1 norm) to a unit disk/sphere (in L2 norm) More...
mfem::Mesh	buildDiskMesh (int approx_number_of_elements)
	Constructs a 2D MFEM mesh of a unit disk, centered at the origin. More...
mfem::Mesh	buildBallMesh (int approx_number_of_elements)
	Constructs a 3D MFEM mesh of a unit ball, centered at the origin. More...
mfem::Mesh	buildRectangleMesh (int elements_in_x, int elements_in_y, double size_x=1., double size_y=1.)
	Constructs a 2D MFEM mesh of a rectangle. More...
mfem::Mesh	buildCuboidMesh (int elements_in_x, int elements_in_y, int elements_in_z, double size_x=1., double size_y=1., double size_z=1.)
	Constructs a 3D MFEM mesh of a cuboid. More...
mfem::Mesh	buildCylinderMesh (int radial_refinement, int elements_lengthwise, double radius, double height)
	Constructs a 3D MFEM mesh of a cylinder. More...
mfem::Mesh	buildRing (int radial_refinement, double inner_radius, double outer_radius, double total_angle, int sectors)
	Constructs a 2D MFEM mesh of a ring.
mfem::Mesh	buildRingMesh (int radial_refinement, double inner_radius, double outer_radius, double total_angle=M_PI, int sectors=8)
	Constructs a 2D MFEM mesh of a ring. More...
mfem::Mesh	buildHollowCylinderMesh (int radial_refinement, int elements_lengthwise, double inner_radius, double outer_radius, double height, double total_angle=M_PI, int sectors=8)
	Constructs a 3D MFEM mesh of a hollow cylinder. More...
mfem::Mesh	build_hollow_quarter_cylinder (std::size_t radial_divisions, std::size_t angular_divisions, std::size_t vertical_divisions, double inner_radius, double outer_radius, double height)
	Constructs an MFEM mesh of a hollow cylinder restricted to the first orthant. More...
double	matrixNorm (const mfem::HypreParMatrix &K)
	Utility to compute the matrix norm.
void	printTrustRegionInfo (double realObjective, double modelObjective, size_t cgIters, double trSize, bool willAccept)
	trust region printing utility function
std::unique_ptr< mfem::HypreParMatrix >	buildMonolithicMatrix (const mfem::BlockOperator &block_operator)
	Function for building a monolithic parallel Hypre matrix from a block system of smaller Hypre matrices. More...
std::unique_ptr< mfem::NewtonSolver >	buildNonlinearSolver (NonlinearSolverOptions nonlinear_opts, const LinearSolverOptions &linear_opts, mfem::Solver &preconditioner, MPI_Comm comm=MPI_COMM_WORLD)
	Build a nonlinear solver using the nonlinear option struct. More...
std::pair< std::unique_ptr< mfem::Solver >, std::unique_ptr< mfem::Solver > >	buildLinearSolverAndPreconditioner (LinearSolverOptions linear_opts={}, MPI_Comm comm=MPI_COMM_WORLD)
	Build the linear solver and its associated preconditioner given a linear options struct. More...
std::unique_ptr< mfem::Solver >	buildPreconditioner (LinearSolverOptions linear_opts,[[maybe_unused]] MPI_Comm comm=MPI_COMM_WORLD)
	Build a preconditioner from the available options. More...
auto	differentiate_wrt (const mfem::Vector &v)
	this function is intended to only be used in combination with smith::Functional::operator(), as a way for the user to express that it should both evaluate and differentiate w.r.t. a specific argument (only 1 argument at a time) More...
template<int d>
std::vector< tensor< double, d > >	gather (const mfem::Vector &coordinates, mfem::Array< int > ids)
	gather vertex coordinates for a list of vertices More...
void	findDomainDofsOnNeighborRanks (const smith::fes_t *fes, mfem::Array< int > &local_dof_ids)
	Get local dofs that are part of a domain, but are owned by a neighboring MPI rank. More...
Domain	EntireDomain (const mesh_t &mesh)
	constructs a domain from all the elements in a mesh
Domain	EntireBoundary (const mesh_t &mesh)
	constructs a domain from all the boundary elements in a mesh
Domain	EntireInteriorBoundary (const mesh_t &mesh)
	constructs a domain from all the interior boundary elements in a mesh
template<int d>
Domain	domain_of_interior_boundaries (const mesh_t &mesh, std::function< bool(std::vector< tensor< double, d >>, int)> predicate)
	constructs a domain from some subset of the interior boundary elements in a mesh
void	zip (std::vector< int2 > &ab, const std::vector< int > &a, const std::vector< int > &b)
	combine a pair of arrays of ints into a single array of int2, see also: unzip()
void	unzip (const std::vector< int2 > &ab, std::vector< int > &a, std::vector< int > &b)
	split an array of int2 into a pair of arrays of ints, see also: zip()
template<typename T >
std::vector< T >	set_operation (SET_OPERATION op, const std::vector< T > &a, const std::vector< T > &b)
	return a std::vector that is the result of applying (a op b)
Domain	set_operation (SET_OPERATION op, const Domain &a, const Domain &b)
	return a Domain that is the result of applying (a op b)
Domain	operator| (const Domain &a, const Domain &b)
	create a new domain that is the union of a and b
Domain	operator& (const Domain &a, const Domain &b)
	create a new domain that is the intersection of a and b
Domain	operator- (const Domain &a, const Domain &b)
	create a new domain that is the set difference of a and b
template<int dim>
auto	by_attr (int value)
	convenience predicate for creating domains by attribute
template<int dim>
auto	by_attr (std::set< int > values)
	convenience predicate for creating domains by a set of attributes
std::array< uint32_t, mfem::Geometry::NUM_GEOMETRIES >	geometry_counts (const Domain &domain)
	count the number of elements of each geometry in a domain More...
template<int dim>
tensor< double, dim >	average (std::vector< tensor< double, dim >> &positions)
	convenience function for computing the arithmetic mean of some list of vectors
template<typename T >
	dual (double, T) -> dual< T >
	class template argument deduction guide for type dual. More...
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto	operator+ (dual< gradient_type > a, double b)
	addition of a dual number and a non-dual number
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto	operator+ (double a, dual< gradient_type > b)
	addition of a dual number and a non-dual number
template<typename gradient_type_a , typename gradient_type_b >
constexpr SMITH_HOST_DEVICE auto	operator+ (dual< gradient_type_a > a, dual< gradient_type_b > b)
	addition of two dual numbers
template<typename gradient_type >
constexpr auto	operator- (dual< gradient_type > x)
	unary negation of a dual number
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto	operator- (dual< gradient_type > a, double b)
	subtraction of a non-dual number from a dual number
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto	operator- (double a, dual< gradient_type > b)
	subtraction of a dual number from a non-dual number
template<typename gradient_type_a , typename gradient_type_b >
constexpr SMITH_HOST_DEVICE auto	operator- (dual< gradient_type_a > a, dual< gradient_type_b > b)
	subtraction of two dual numbers
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto	operator* (const dual< gradient_type > &a, double b)
	multiplication of a dual number and a non-dual number
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto	operator* (double a, const dual< gradient_type > &b)
	multiplication of a dual number and a non-dual number
template<typename gradient_type_a , typename gradient_type_b >
constexpr SMITH_HOST_DEVICE auto	operator* (dual< gradient_type_a > a, dual< gradient_type_b > b)
	multiplication of two dual numbers
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto	operator/ (const dual< gradient_type > &a, double b)
	division of a dual number by a non-dual number
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto	operator/ (double a, const dual< gradient_type > &b)
	division of a non-dual number by a dual number
template<typename gradient_type_a , typename gradient_type_b >
constexpr SMITH_HOST_DEVICE auto	operator/ (dual< gradient_type_a > a, dual< gradient_type_b > b)
	division of two dual numbers
	binary_comparator_overload (<)
	implement operator< for dual numbers More...
	binary_comparator_overload (<=)
	implement operator<= for dual numbers
	binary_comparator_overload (>=)
	implement operator>= for dual numbers
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto &	operator+= (dual< gradient_type > &a, const dual< gradient_type > &b)
	compound assignment (+) for dual numbers
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto &	operator-= (dual< gradient_type > &a, const dual< gradient_type > &b)
	compound assignment (-) for dual numbers
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto &	operator+= (dual< gradient_type > &a, double b)
	compound assignment (+) for dual numbers with double righthand side
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto &	operator-= (dual< gradient_type > &a, double b)
	compound assignment (-) for dual numbers with double righthand side
template<typename gradient_type >
SMITH_HOST_DEVICE auto	abs (dual< gradient_type > x)
	Implementation of absolute value function for dual numbers. More...
template<typename gradient_type >
SMITH_HOST_DEVICE auto	max (dual< gradient_type > a, double b)
	Implementation of max for dual numbers. More...
template<typename gradient_type >
SMITH_HOST_DEVICE auto	max (double a, dual< gradient_type > b)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename gradient_type >
SMITH_HOST_DEVICE auto	max (dual< gradient_type > a, dual< gradient_type > b)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename gradient_type >
SMITH_HOST_DEVICE auto	min (dual< gradient_type > a, double b)
	Implementation of min for dual numbers. More...
template<typename gradient_type >
SMITH_HOST_DEVICE auto	min (double a, dual< gradient_type > b)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename gradient_type >
SMITH_HOST_DEVICE auto	min (dual< gradient_type > a, dual< gradient_type > b)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename S , typename T >
constexpr SMITH_HOST_DEVICE auto	inner (const dual< S > &A, const dual< T > &B)
template<typename T >
constexpr SMITH_HOST_DEVICE auto	inner (double A, const dual< T > &B)
template<typename S >
constexpr SMITH_HOST_DEVICE auto	inner (const dual< S > &A, double B)
template<typename gradient_type >
SMITH_HOST_DEVICE auto	sqrt (dual< gradient_type > x)
	implementation of square root for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	cos (dual< gradient_type > a)
	implementation of cosine for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	sin (dual< gradient_type > a)
	implementation of sine for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	atan (dual< gradient_type > a)
	implementation of atan for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	atan2 (dual< gradient_type > y, dual< gradient_type > x)
	implementation of atan2 for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	atan2 (double y, dual< gradient_type > x)
	implementation of atan2 for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	atan2 (dual< gradient_type > y, double x)
	implementation of atan2 for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	asin (dual< gradient_type > a)
	implementation of asin for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	acos (dual< gradient_type > a)
	implementation of acos for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	exp (dual< gradient_type > a)
	implementation of exponential function for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	log (dual< gradient_type > a)
	implementation of the natural logarithm function for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	log1p (dual< gradient_type > a)
	implementation of the natural logarithm of one plus the argument function for dual numbers
template<typename gradient_type >
SMITH_HOST_DEVICE auto	pow (dual< gradient_type > a, dual< gradient_type > b)
	implementation of a (dual) raised to the b (dual) power
template<typename gradient_type >
SMITH_HOST_DEVICE auto	pow (double a, dual< gradient_type > b)
	implementation of a (non-dual) raised to the b (dual) power
template<typename gradient_type >
SMITH_HOST_DEVICE auto	pow (dual< gradient_type > a, double b)
	implementation of a (dual) raised to the b (non-dual) power
template<typename T , int... n>
auto &	operator<< (std::ostream &out, dual< T > A)
	overload of operator<< for dual to work with std::cout and other std::ostreams
constexpr SMITH_HOST_DEVICE auto	make_dual (double x)
	promote a value to a dual number of the appropriate type
template<typename T >
constexpr SMITH_HOST_DEVICE auto	get_value (const T &arg)
	return the "value" part from a given type. For non-dual types, this is just the identity function
template<typename T >
constexpr SMITH_HOST_DEVICE auto	get_value (dual< T > arg)
	return the "value" part from a dual number type
template<typename gradient_type >
constexpr SMITH_HOST_DEVICE auto	get_gradient (dual< gradient_type > arg)
	return the "gradient" part from a dual number type
template<mfem::Geometry::Type g>
constexpr SMITH_HOST_DEVICE int	elements_per_block (int q)
	this function returns information about how many elements should be processed by a single thread block in CUDA (note: the optimal values are hardware and problem specific, but these values are still significantly faster than naively allocating only 1 element / block) More...
template<Family f, typename T , int q, int dim>
SMITH_HOST_DEVICE void	parent_to_physical (tensor< T, q > &qf_input, const tensor< double, dim, dim, q > &jacobians)
	transform information in the parent space (i.e. values and derivatives w.r.t {xi, eta, zeta}) into the physical space (i.e. values and derivatives w.r.t. {x, y, z}) More...
template<Family f, typename T , int q, int dim>
SMITH_HOST_DEVICE void	physical_to_parent (tensor< T, q > &qf_output, const tensor< double, dim, dim, q > &jacobians)
	transform information in the physical space (i.e. sources and fluxes w.r.t {x, y, z}) back to the parent space (i.e. values and derivatives w.r.t. {xi, eta, zeta}). Note: this also multiplies by the outputs by the determinant of the quadrature point Jacobian. More...
template<typename... T>
constexpr uint32_t	index_of_differentiation ()
	given a list of types, this function returns the index that corresponds to the type dual_vector. More...
void	check_for_missing_nodal_gridfunc (const mfem::Mesh &mesh)
	function for verifying that the mesh has been fully initialized
void	check_for_unsupported_elements (const mfem::Mesh &mesh)
	function for verifying that there are no unsupported element types in the mesh
template<typename function_space >
std::pair< std::unique_ptr< mfem::ParFiniteElementSpace >, std::unique_ptr< mfem::FiniteElementCollection > >	generateParFiniteElementSpace (mfem::ParMesh *mesh)
	create an mfem::ParFiniteElementSpace from one of Smith's tag types: H1, Hcurl, L2 More...
void	updateFaceNbrData (const mfem::ParFiniteElementSpace *const_trial_space, mfem::ParGridFunction &trial_pgf, mfem::Vector &trial_tdof_vals)
	helper function to locally cast away const on FE space so we can update face neighbor data with ExchangeFaceNbrData. This is ok because : 1) the original trial FE space is declared without const; 2) we constrained the non-constness locally; 3) the locally owned data associated with the trial function space is NOT altered and ONLY ghost data is updated.
void	appendFaceNbrData (const mfem::ParFiniteElementSpace *trial_space, const mfem::ParGridFunction &trial_pgf, const int LSize, mfem::Vector &input_L)
	helper functional to reorder the ordering of FaceNbrData for L2 space to byVDIM and append this vector to the end of local dof vector, which will result in a vector in form [ — L — | — FND — ]
void	rearrangeFaceNbrDofGlobalIndex (const mfem::ParFiniteElementSpace *trial_space, mfem::Array< HYPRE_BigInt > &face_nbr_glob_vdof_map)
	helper functional to reorder the face_nbr_glob_dof_map for L2 space to byVDIM
template<int Q, mfem::Geometry::Type geom, typename function_space >
void	compute_geometric_factors (mfem::Vector &positions_q, mfem::Vector &jacobians_q, const mfem::Vector &positions_e, const std::vector< int > &elements)
	a kernel to compute the positions and jacobians at each quadrature point (mfem calls this "geometric factors") More...
constexpr int	num_quadrature_points (mfem::Geometry::Type g, int Q)
	return the number of quadrature points in a Gauss-Legendre rule with parameter "Q" More...
constexpr int	dimension_of (mfem::Geometry::Type g)
	Returns the dimension of an element geometry. More...
std::array< uint32_t, mfem::Geometry::NUM_GEOMETRIES >	geometry_counts (const mfem::Mesh &mesh)
	count the number of elements of each geometry in a mesh More...
std::array< uint32_t, mfem::Geometry::NUM_GEOMETRIES >	boundary_geometry_counts (const mfem::Mesh &mesh)
	count the number of boundary elements of each geometry in a mesh More...
template<mfem::Geometry::Type geom, int Q, typename test , typename... trials, typename lambda_type , typename qpt_data_type >
void	generate_kernels (FunctionSignature< test(trials...)> s, Integral &integral, const lambda_type &qf, std::shared_ptr< QuadratureData< qpt_data_type > > qdata)
	function to generate kernels held by an Integral object of type "Domain", with a specific element type More...
template<typename s , int Q, int dim, typename lambda_type , typename qpt_data_type >
Integral	MakeDomainIntegral (const Domain &domain, const lambda_type &qf, std::shared_ptr< QuadratureData< qpt_data_type > > qdata, std::vector< uint32_t > argument_indices)
	function to generate kernels held by an Integral object of type "Domain", for all element types More...
template<mfem::Geometry::Type geom, int Q, typename test , typename... trials, typename lambda_type >
void	generate_bdr_kernels (FunctionSignature< test(trials...)> s, Integral &integral, const lambda_type &qf)
	function to generate kernels held by an Integral object of type "BoundaryDomain", with a specific element type More...
template<typename s , int Q, int dim, typename lambda_type >
Integral	MakeBoundaryIntegral (const Domain &domain, const lambda_type &qf, std::vector< uint32_t > argument_indices)
	function to generate kernels held by an Integral object of type "Boundary", for all element types More...
template<mfem::Geometry::Type geom, int Q, typename test , typename... trials, typename lambda_type >
void	generate_interior_face_kernels (FunctionSignature< test(trials...)> s, Integral &integral, const lambda_type &qf)
	function to generate kernels held by an Integral object of type "InteriorFaceDomain", with a specific element type More...
template<typename s , int Q, int dim, typename lambda_type >
Integral	MakeInteriorFaceIntegral (const Domain &domain, const lambda_type &qf, std::vector< uint32_t > argument_indices)
	function to generate kernels held by an Integral object of type "Boundary", for all element types More...
template<int m>
constexpr SMITH_HOST_DEVICE isotropic_tensor< double, m, m >	Identity ()
	return the identity matrix of the specified size More...
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator* (S scale, isotropic_tensor< T, m, m > I)
	scalar multiplication More...
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator* (isotropic_tensor< T, m, m > I, S scale)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator+ (isotropic_tensor< S, m, m > I1, isotropic_tensor< T, m, m > I2)
	addition of isotropic tensors More...
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator- (isotropic_tensor< S, m, m > I1, isotropic_tensor< T, m, m > I2)
	difference of isotropic tensors More...
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator+ (const isotropic_tensor< S, m, m > &I, const tensor< T, m, m > &A)
	sum of isotropic and (nonisotropic) tensor More...
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator+ (const tensor< S, m, m > &A, const isotropic_tensor< T, m, m > &I)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator- (const isotropic_tensor< S, m, m > &I, const tensor< T, m, m > &A)
	difference of isotropic and (nonisotropic) tensor More...
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator- (const tensor< S, m, m > &A, const isotropic_tensor< T, m, m > &I)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename S , typename T , int m, int... n>
constexpr SMITH_HOST_DEVICE auto	dot (const isotropic_tensor< S, m, m > &I, const tensor< T, m, n... > &A)
	dot product between an isotropic and (nonisotropic) tensor More...
template<typename S , typename T , int m, int... n>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, n... > &A, isotropic_tensor< T, m, m > I)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	double_dot (const isotropic_tensor< S, m, m > &I, const tensor< T, m, m > &A)
	double-dot product between an isotropic and (nonisotropic) tensor More...
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	sym (const isotropic_tensor< T, m, m > &I)
	return the symmetric part of an isotropic tensor More...
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	antisym (const isotropic_tensor< T, m, m > &)
	return the antisymmetric part of an isotropic tensor More...
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	tr (const isotropic_tensor< T, m, m > &I)
	calculate the trace of an isotropic tensor More...
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	transpose (const isotropic_tensor< T, m, m > &I)
	return the transpose of an isotropic tensor More...
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	inv (const isotropic_tensor< T, m, m > &I)
	return the inverse of an isotropic tensor More...
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	det (const isotropic_tensor< T, m, m > &I)
	compute the determinant of an isotropic tensor More...
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	norm (const isotropic_tensor< T, m, m > &I)
	compute the Frobenius norm (sqrt(tr(dot(transpose(I), I)))) of an isotropic tensor More...
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	squared_norm (const isotropic_tensor< T, m, m > &I)
	compute the squared Frobenius norm (tr(dot(transpose(I), I))) of an isotropic tensor More...
template<int m>
constexpr SMITH_HOST_DEVICE auto	SymmetricIdentity ()
	a helper function for creating the rank-4 isotropic tensor defined by: d(sym(A)_{ij}) / d(A_{kl}) More...
template<int m>
constexpr SMITH_HOST_DEVICE auto	AntisymmetricIdentity ()
	a helper function for creating the rank-4 isotropic tensor defined by: d(antisym(A)_{ij}) / d(A_{kl}) More...
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator* (S scale, isotropic_tensor< T, m, m, m, m > I)
	scalar multiplication More...
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator* (isotropic_tensor< S, m, m, m, m > I, T scale)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator+ (isotropic_tensor< S, m, m, m, m > I1, isotropic_tensor< T, m, m, m, m > I2)
	addition of isotropic tensors More...
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	operator- (isotropic_tensor< S, m, m, m, m > I1, isotropic_tensor< T, m, m, m, m > I2)
	difference of isotropic tensors More...
template<typename S , typename T , int m, int... n>
constexpr SMITH_HOST_DEVICE auto	double_dot (const isotropic_tensor< S, m, m, m, m > &I, const tensor< T, m, m, n... > &A)
	double-dot product between an isotropic and (nonisotropic) tensor More...
template<int n, typename T = double>
constexpr SMITH_HOST_DEVICE tensor< T, n >	GaussLobattoNodes (T a=T(0), T b=T(1))
	The positions (in 1D space) of Gauss-Lobatto points. More...
template<int n, mfem::Geometry::Type geom>
constexpr SMITH_HOST_DEVICE auto	GaussLegendreNodes ()
	The positions of Gauss-Legendre points for different geometries. More...
template<int n, mfem::Geometry::Type geom>
constexpr SMITH_HOST_DEVICE auto	GaussLegendreWeights ()
	The weights associated with each Gauss-Legendre point. More...
constexpr SMITH_HOST_DEVICE int	factorial (int n)
	compute n! More...
template<int n, typename T >
constexpr SMITH_HOST_DEVICE tensor< T, n >	powers (T x)
	compute the first n powers of x More...
template<int n, typename S >
constexpr SMITH_HOST_DEVICE tensor< S, n >	ChebyshevT (S x)
	Chebyshev polynomials of the first kind Satisfying: T_n(cos(t)) == cos(n*t) More...
template<int n, typename T >
SMITH_HOST_DEVICE tensor< T, n >	ChebyshevU (T x)
	Chebyshev polynomials of the second kind Satisfying: sin(t) U_n(cos(t)) == sin((n+1)*t) More...
template<int n, typename T >
SMITH_HOST_DEVICE tensor< T, n >	Legendre (T x)
	Legendre Polynomials, orthogonal on the domain (-1, 1) with unit weight function. More...
template<int n, typename T >
SMITH_HOST_DEVICE tensor< T, n >	Bernstein (T s)
	Bernstein Polynomials on the domain [0, 1]. More...
template<int n, typename T >
constexpr SMITH_HOST_DEVICE tensor< T, n >	GaussLobattoInterpolation ([[maybe_unused]] T x)
	Lagrange Interpolating polynomials for nodes at Gauss-Lobatto points on the interval [0, 1]. More...
template<int n, typename T >
constexpr SMITH_HOST_DEVICE tensor< T, n >	GaussLobattoInterpolationDerivative ([[maybe_unused]] T x)
	Derivatives of the Lagrange Interpolating polynomials for nodes at Gauss-Lobatto points on the interval [0, 1]. More...
template<int n, typename T >
constexpr SMITH_HOST_DEVICE tensor< T, n >	GaussLegendreInterpolation ([[maybe_unused]] T x)
	Lagrange Interpolating polynomials for nodes at Gauss-Legendre points on the interval [0, 1]. More...
template<int n, typename T >
constexpr SMITH_HOST_DEVICE tensor< T, n >	GaussLegendreInterpolationDerivative ([[maybe_unused]] T x)
	Derivatives of the Lagrange Interpolating polynomials for nodes at Gauss-Legendre points on the interval [-1, 1]. More...
template<mfem::Geometry::Type g, int Q>
constexpr SMITH_HOST_DEVICE auto	GaussQuadratureRule ()
	Returns the Gauss-Legendre quadrature rule for an element and order. More...
template<typename T , int n1>
	tensor (const T(&data)[n1]) -> tensor< T, n1 >
	class template argument deduction guide for type tensor. More...
template<typename T , int n1, int n2>
	tensor (const T(&data)[n1][n2]) -> tensor< T, n1, n2 >
	class template argument deduction guide for type tensor. More...
constexpr SMITH_HOST_DEVICE auto	operator+ (zero, zero)
	the sum of two zeros is zero
template<typename T >
constexpr SMITH_HOST_DEVICE auto	operator+ (zero, T other)
	the sum of zero with something non-zero just returns the other value
template<typename T >
constexpr SMITH_HOST_DEVICE auto	operator+ (T other, zero)
	the sum of zero with something non-zero just returns the other value
constexpr SMITH_HOST_DEVICE auto	operator- (zero)
	the unary negation of zero is zero
constexpr SMITH_HOST_DEVICE auto	operator- (zero, zero)
	the difference of two zeros is zero
template<typename T >
constexpr SMITH_HOST_DEVICE auto	operator- (zero, T other)
	the difference of zero with something else is the unary negation of the other thing
template<typename T >
constexpr SMITH_HOST_DEVICE auto	operator- (T other, zero)
	the difference of something else with zero is the other thing itself
constexpr SMITH_HOST_DEVICE auto	operator* (zero, zero)
	the product of two zeros is zero
template<typename T >
constexpr SMITH_HOST_DEVICE auto	operator* (zero, T)
	the product zero with something else is also zero
template<typename T >
constexpr SMITH_HOST_DEVICE auto	operator* (T, zero)
	the product zero with something else is also zero
template<typename T >
constexpr SMITH_HOST_DEVICE auto	operator/ (zero, T)
	zero divided by something is zero
template<typename T >
void	operator/ (T, zero)
	Get a human-readable compiler error when you try to divide by zero.
constexpr SMITH_HOST_DEVICE auto	operator+= (zero, zero)
	zero plus zero is zero
constexpr SMITH_HOST_DEVICE auto	operator-= (zero, zero)
	zero minus zero is zero
template<int i>
SMITH_HOST_DEVICE zero &	get (zero &x)
	let zero be accessed like a tuple
template<int i>
SMITH_HOST_DEVICE zero	get (const zero &)
	let zero be accessed like a tuple
template<typename T >
constexpr SMITH_HOST_DEVICE zero	dot (const T &, zero)
	the dot product of anything with zero is zero
template<typename T >
constexpr SMITH_HOST_DEVICE zero	dot (zero, const T &)
	the dot product of anything with zero is zero
template<typename T , int m, int... n>
SMITH_HOST_DEVICE consteval int	first_dim (const tensor< T, m, n... > &)
	return the size of the leftmost tensor dimension
template<typename T , int... n>
constexpr SMITH_HOST_DEVICE auto	tensor_with_shape (std::integer_sequence< int, n... >)
	Creates a tensor given the dimensions in a std::integer_sequence. More...
template<typename lambda_type >
SMITH_SUPPRESS_NVCC_HOSTDEVICE_WARNING constexpr SMITH_HOST_DEVICE auto	make_tensor (lambda_type f)
	Creates a tensor of requested dimension by subsequent calls to a functor Can be thought of as analogous to std::transform in that the set of possible indices for dimensions n are transformed into the values of the tensor by f. More...
template<int n1, typename lambda_type >
SMITH_SUPPRESS_NVCC_HOSTDEVICE_WARNING constexpr SMITH_HOST_DEVICE auto	make_tensor (lambda_type f)
	Creates a tensor of requested dimension by subsequent calls to a functor. More...
template<int n1, int n2, typename lambda_type >
SMITH_SUPPRESS_NVCC_HOSTDEVICE_WARNING constexpr SMITH_HOST_DEVICE auto	make_tensor (lambda_type f)
	Creates a tensor of requested dimension by subsequent calls to a functor. More...
template<int n1, int n2, int n3, typename lambda_type >
SMITH_SUPPRESS_NVCC_HOSTDEVICE_WARNING constexpr SMITH_HOST_DEVICE auto	make_tensor (lambda_type f)
	Creates a tensor of requested dimension by subsequent calls to a functor. More...
template<int n1, int n2, int n3, int n4, typename lambda_type >
SMITH_SUPPRESS_NVCC_HOSTDEVICE_WARNING constexpr SMITH_HOST_DEVICE auto	make_tensor (lambda_type f)
	Creates a tensor of requested dimension by subsequent calls to a functor. More...
template<typename S , typename T , int m, int... n>
constexpr SMITH_HOST_DEVICE auto	operator+ (const tensor< S, m, n... > &A, const tensor< T, m, n... > &B)
	return the sum of two tensors More...
template<typename T , int m, int... n>
constexpr SMITH_HOST_DEVICE auto	operator- (const tensor< T, m, n... > &A)
	return the unary negation of a tensor More...
template<typename S , typename T , int m, int... n>
constexpr SMITH_HOST_DEVICE auto	operator- (const tensor< S, m, n... > &A, const tensor< T, m, n... > &B)
	return the difference of two tensors More...
template<typename S , typename T , int m, int... n>
constexpr SMITH_HOST_DEVICE auto &	operator+= (tensor< S, m, n... > &A, const tensor< T, m, n... > &B)
	compound assignment (+) on tensors More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto &	operator+= (tensor< T, n, 1 > &A, const tensor< T, n > &B)
	compound assignment (+) on tensors More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto &	operator+= (tensor< T, 1, n > &A, const tensor< T, n > &B)
	compound assignment (+) on tensors More...
template<typename T >
constexpr SMITH_HOST_DEVICE auto &	operator+= (tensor< T, 1 > &A, const T &B)
	compound assignment (+) on tensors More...
template<typename T >
constexpr SMITH_HOST_DEVICE auto &	operator+= (tensor< T, 1, 1 > &A, const T &B)
	compound assignment (+) on tensors More...
template<typename T , int... n>
constexpr SMITH_HOST_DEVICE auto &	operator+= (tensor< T, n... > &A, zero)
	compound assignment (+) between a tensor and zero (no-op) More...
template<typename S , typename T , int m, int... n>
constexpr SMITH_HOST_DEVICE auto &	operator-= (tensor< S, m, n... > &A, const tensor< T, m, n... > &B)
	compound assignment (-) on tensors More...
template<typename T , int... n>
constexpr SMITH_HOST_DEVICE auto &	operator-= (tensor< T, n... > &A, zero)
	compound assignment (-) between a tensor and zero (no-op) More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	outer (double A, tensor< T, n > B)
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	outer (const tensor< T, m > &A, double B)
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	outer (zero, const tensor< T, n > &)
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	outer (const tensor< T, n > &, zero)
template<typename S , typename T , int m, int n>
constexpr SMITH_HOST_DEVICE auto	outer (const tensor< S, m > &A, const tensor< T, n > &B)
template<typename S , typename T , int m, int n>
constexpr SMITH_HOST_DEVICE auto	inner (const tensor< S, m, n > &A, const tensor< T, m, n > &B)
	this function contracts over all indices of the two tensor arguments More...
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	inner (const tensor< S, m > &A, const tensor< T, m > &B)
constexpr SMITH_HOST_DEVICE auto	inner (double A, double B)
template<typename S , int m, int n>
constexpr SMITH_HOST_DEVICE auto	inner (const tensor< S, m, n > &, zero)
	this function contracts over all indices of the two tensor arguments More...
template<typename S , int m>
constexpr SMITH_HOST_DEVICE auto	inner (const tensor< S, m > &, zero)
constexpr SMITH_HOST_DEVICE auto	inner (double, zero)
template<typename T , int m, int n>
constexpr SMITH_HOST_DEVICE auto	inner (zero, const tensor< T, m, n > &)
	this function contracts over all indices of the two tensor arguments More...
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	inner (zero, const tensor< T, m > &)
constexpr SMITH_HOST_DEVICE auto	inner (zero, double)
template<typename S , typename T , int m, int n, int p>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m, n > &A, const tensor< T, n, p > &B)
	this function contracts over the "middle" index of the two tensor arguments More...
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< T, m > &A, double B)
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	dot (double B, const tensor< T, m > &A)
template<typename S , typename T , int m>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m > &A, const tensor< T, m > &B)
template<typename S , typename T , int m, int n>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m > &A, const tensor< T, m, n > &B)
template<typename S , typename T , int m, int n, int p>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m > &A, const tensor< T, m, n, p > &B)
template<typename S , typename T , int m, int n, int p, int q>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m > &A, const tensor< T, m, n, p, q > &B)
template<typename S , typename T , int m, int n>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m, n > &A, const tensor< T, n > &B)
template<typename S , typename T , int m, int n, int p, int q, int r>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m, n > &A, const tensor< T, n, p, q, r > &B)
template<typename S , typename T , int m, int n, int p, int q>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m, n > &A, const tensor< T, n, p, q > &B)
template<typename S , typename T , int m, int n, int p>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m, n, p > &A, const tensor< T, p > &B)
template<typename S , typename T , typename U , int m, int n>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m > &u, const tensor< T, m, n > &A, const tensor< U, n > &v)
template<typename S , typename T , int m, int n, int p, int q>
constexpr SMITH_HOST_DEVICE auto	dot (const tensor< S, m, n, p, q > &A, const tensor< T, q > &B)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename T >
SMITH_HOST_DEVICE auto	cross (const tensor< T, 3, 2 > &A)
	compute the cross product of the columns of A: A(:,1) x A(:,2)
template<typename T >
SMITH_HOST_DEVICE auto	cross (const tensor< T, 2, 1 > &v)
	return the in-plane components of the cross product of {v[0], v[1], 0} x {0, 0, 1}
template<typename T >
SMITH_HOST_DEVICE auto	cross (const tensor< T, 2 > &v)
	return the in-plane components of the cross product of {v[0], v[1], 0} x {0, 0, 1}
template<typename S , typename T >
SMITH_HOST_DEVICE auto	cross (const tensor< S, 3 > &u, const tensor< T, 3 > &v)
	compute the (right handed) cross product of two 3-vectors
template<typename S , typename T , int m, int n, int p, int q>
constexpr SMITH_HOST_DEVICE auto	double_dot (const tensor< S, m, n, p, q > &A, const tensor< T, p, q > &B)
	double dot product, contracting over the two "middle" indices More...
template<typename S , typename T , int m, int n, int p>
constexpr SMITH_HOST_DEVICE auto	double_dot (const tensor< S, m, n, p > &A, const tensor< T, n, p > &B)
template<typename S , typename T , int m, int n>
constexpr auto	double_dot (const tensor< S, m, n > &A, const tensor< T, m, n > &B)
template<typename S , typename T , int... m, int... n>
constexpr SMITH_HOST_DEVICE auto	operator* (const tensor< S, m... > &A, const tensor< T, n... > &B)
	this is a shorthand for dot(A, B)
template<typename T , int m>
constexpr SMITH_HOST_DEVICE auto	squared_norm (const tensor< T, m > &A)
	Returns the squared Frobenius norm of the tensor. More...
template<typename T , int m, int n>
constexpr SMITH_HOST_DEVICE auto	squared_norm (const tensor< T, m, n > &A)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename T , int... n>
constexpr SMITH_HOST_DEVICE auto	squared_norm (const tensor< T, n... > &A)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename T , int... n>
SMITH_HOST_DEVICE auto	norm (const tensor< T, n... > &A)
	Returns the Frobenius norm of the tensor. More...
constexpr SMITH_HOST_DEVICE auto	norm (zero)
	overload of Frobenius norm for zero type
template<typename T , int... n>
SMITH_HOST_DEVICE auto	normalize (const tensor< T, n... > &A)
	Normalizes the tensor Each element is divided by the Frobenius norm of the tensor,. More...
template<typename T >
SMITH_HOST_DEVICE tensor< T, 3, 3 >	to_3x3 (const tensor< T, 2, 2 > &A)
	promotes a 2x2 matrix to a 3x3 matrix, by populating the upper left block, leaving zeroes in the third row / column More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	tr (const tensor< T, n, n > &A)
	Returns the trace of a square matrix. More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	sym (const tensor< T, n, n > &A)
	Returns the symmetric part of a square matrix. More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	antisym (const tensor< T, n, n > &A)
	Returns the antisymmetric part of a square matrix. More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	dev (const tensor< T, n, n > &A)
	Calculates the deviator of a matrix (rank-2 tensor) More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	diagonal_matrix (const tensor< T, n, n > &A)
	Returns a square matrix (rank-2 tensor) containing the diagonal entries of the input square matrix with zeros in the off-diagonal positions. More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE tensor< T, n, n >	diag (const tensor< T, n > &d)
	Returns a square diagonal matrix by specifying the diagonal entries. More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE tensor< T, n >	diag (const tensor< T, n, n > &D)
	Returns an array containing the diagonal entries of a square matrix. More...
template<int dim>
constexpr SMITH_HOST_DEVICE tensor< double, dim, dim >	DenseIdentity ()
	Obtains the identity matrix of the specified dimension. More...
template<typename T , int m, int n>
constexpr SMITH_HOST_DEVICE auto	transpose (const tensor< T, m, n > &A)
	Returns the transpose of the matrix. More...
template<typename T >
constexpr SMITH_HOST_DEVICE auto	I2 (const tensor< T, 3, 3 > &A)
	Returns the second invariant of a 3x3 matrix. More...
template<typename T >
constexpr SMITH_HOST_DEVICE auto	det (const tensor< T, 2, 2 > &A)
	Returns the determinant of a matrix. More...
template<typename T >
constexpr SMITH_HOST_DEVICE auto	det (const tensor< T, 3, 3 > &A)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename T >
constexpr SMITH_HOST_DEVICE auto	detApIm1 (const tensor< T, 2, 2 > &A)
	computes det(A + I) - 1, where precision is not lost when the entries A_{ij} << 1 More...
template<typename T >
constexpr SMITH_HOST_DEVICE auto	detApIm1 (const tensor< T, 3, 3 > &A)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename T , int dim>
auto	matrix_sqrt (const tensor< T, dim, dim > &A)
	compute the matrix square root of a square, real-valued, symmetric matrix i.e. given A, find B such that A = dot(B, B) More...
template<int i1, int i2, typename S , int m, int... n, typename T , int p, int q>
SMITH_HOST_DEVICE auto	contract (const tensor< S, m, n... > &A, const tensor< T, p, q > &B)
	a convenience function that computes a dot product between two tensor, but that allows the user to specify which indices should be summed over. For example: More...
template<int i1, int i2, typename T >
SMITH_HOST_DEVICE auto	contract (const zero &, const T &)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename T , int... n>
double	relative_error (tensor< T, n... > A, tensor< T, n... > B)
	computes the relative error (in the frobenius norm) between two tensors of the same shape More...
template<int n>
SMITH_HOST_DEVICE bool	is_symmetric (tensor< double, n, n > A, double tolerance=1.0e-8)
	Return whether a square rank 2 tensor is symmetric. More...
SMITH_HOST_DEVICE bool	is_symmetric_and_positive_definite (tensor< double, 2, 2 > A)
	Return whether a matrix is symmetric and positive definite This check uses Sylvester's criterion, checking that each upper left subtensor has a determinant greater than zero. More...
SMITH_HOST_DEVICE bool	is_symmetric_and_positive_definite (tensor< double, 3, 3 > A)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename T , int n, int... m>
constexpr SMITH_HOST_DEVICE auto	solve_lower_triangular (const tensor< T, n, n > &L, const tensor< T, n, m... > &b, const tensor< int, n > &P)
	Solves a lower triangular system Ly = b. More...
template<typename T , int n, int... m>
constexpr SMITH_HOST_DEVICE auto	solve_lower_triangular (const tensor< T, n, n > &L, const tensor< T, n, m... > &b)
template<typename T , int n, int... m>
constexpr SMITH_HOST_DEVICE auto	solve_upper_triangular (const tensor< T, n, n > &U, const tensor< T, n, m... > &y)
	Solves an upper triangular system Ux = y. More...
template<typename S , typename T , int n, int... m>
constexpr SMITH_HOST_DEVICE auto	linear_solve (const LuFactorization< S, n > &lu_factors, const tensor< T, n, m... > &b)
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	linear_solve (const LuFactorization< T, n > &, const zero)
constexpr SMITH_HOST_DEVICE tensor< double, 2, 2 >	inv (const tensor< double, 2, 2 > &A)
	Inverts a matrix. More...
constexpr SMITH_HOST_DEVICE tensor< double, 3, 3 >	inv (const tensor< double, 3, 3 > &A)
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	inv (const tensor< T, n, n > &A)
template<typename T , int m, int... n>
auto &	operator<< (std::ostream &out, const tensor< T, m, n... > &A)
	recursively serialize the entries in a tensor to an ostream. Output format uses braces and comma separators to mimic C syntax for multidimensional array initialization. More...
auto &	operator<< (std::ostream &out, zero)
	Write a zero out to an output stream. More...
SMITH_HOST_DEVICE void	print (double value)
	print a double using printf, so that it is suitable for use inside cuda kernels. (used in final recursion of printf(tensor<...>)) More...
template<int m, int... n>
SMITH_HOST_DEVICE void	print (const tensor< double, m, n... > &A)
	print a tensor using printf, so that it is suitable for use inside cuda kernels. More...
template<int n>
constexpr SMITH_HOST_DEVICE auto	chop (const tensor< double, n > &A)
	replace all entries in a tensor satisfying |x| < 1.0e-10 by literal zero More...
template<int m, int n>
constexpr SMITH_HOST_DEVICE auto	chop (const tensor< double, m, n > &A)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
SMITH_HOST_DEVICE auto	get_gradient (double)
	Retrieves the gradient component of a double (which is nothing) More...
template<int... n>
constexpr SMITH_HOST_DEVICE auto	get_gradient (const tensor< double, n... > &)
	get the gradient of type tensor (note: since its stored type is not a dual number, the derivative term is identically zero) More...
constexpr SMITH_HOST_DEVICE auto	chain_rule (const zero, const zero)
	evaluate the change (to first order) in a function, f, given a small change in the input argument, dx.
template<typename T >
constexpr SMITH_HOST_DEVICE auto	chain_rule (const zero, const T)
template<typename T >
constexpr SMITH_HOST_DEVICE auto	chain_rule (const T, const zero)
constexpr SMITH_HOST_DEVICE auto	chain_rule (const double df_dx, const double dx)
template<int... n>
constexpr SMITH_HOST_DEVICE auto	chain_rule (const tensor< double, n... > &df_dx, const double dx)
template<int... n>
constexpr SMITH_HOST_DEVICE auto	chain_rule (const tensor< double, n... > &df_dx, const tensor< double, n... > &dx)
template<int m, int... n>
constexpr SMITH_HOST_DEVICE auto	chain_rule (const tensor< double, m, n... > &df_dx, const tensor< double, n... > &dx)
template<int m, int n, int... p>
SMITH_HOST_DEVICE auto	chain_rule (const tensor< double, m, n, p... > &df_dx, const tensor< double, p... > &dx)
template<typename T , int... n>
constexpr SMITH_HOST_DEVICE int	size (const tensor< T, n... > &)
	returns the total number of stored values in a tensor More...
constexpr SMITH_HOST_DEVICE int	size (const double &)
	overload of size() for double, we say a double "stores" 1 value More...
constexpr SMITH_HOST_DEVICE int	size (zero)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<int i, typename T , int... n>
constexpr SMITH_HOST_DEVICE int	dimension (const tensor< T, n... > &)
	a function for querying the ith dimension of a tensor More...
template<typename T , int m, int... n>
constexpr SMITH_HOST_DEVICE int	leading_dimension (tensor< T, m, n... >)
	a function for querying the first dimension of a tensor More...
template<typename T , int... n>
bool	isnan (const tensor< T, n... > &A)
	returns true if any entry of a tensor is nan
bool	isnan (const zero &)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename... T>
	tuple (T...) -> tuple< T... >
	Class template argument deduction rule for tuples. More...
template<typename... T>
SMITH_HOST_DEVICE tuple< T... >	make_tuple (const T &... args)
	helper function for combining a list of values into a tuple More...
template<int i, typename... T>
constexpr SMITH_HOST_DEVICE auto &	get (tuple< T... > &values)
	return a reference to the ith tuple entry More...
template<int i, typename... T>
constexpr SMITH_HOST_DEVICE const auto &	get (const tuple< T... > &values)
	return a copy of the ith tuple entry More...
template<int i, typename... T>
constexpr SMITH_HOST_DEVICE auto	type (const tuple< T... > &values)
	a function intended to be used for extracting the ith type from a tuple. More...
template<typename... S, typename... T, int... i>
constexpr SMITH_HOST_DEVICE auto	plus_helper (const tuple< S... > &x, const tuple< T... > &y, std::integer_sequence< int, i... >)
	A helper function for the + operator of tuples. More...
template<typename... S, typename... T>
constexpr SMITH_HOST_DEVICE auto	operator+ (const tuple< S... > &x, const tuple< T... > &y)
	return a tuple of values defined by elementwise sum of x and y More...
template<typename... T, int... i>
constexpr SMITH_HOST_DEVICE void	plus_equals_helper (tuple< T... > &x, const tuple< T... > &y, std::integer_sequence< int, i... >)
	A helper function for the += operator of tuples. More...
template<typename... T>
constexpr SMITH_HOST_DEVICE auto	operator+= (tuple< T... > &x, const tuple< T... > &y)
	add values contained in y, to the tuple x More...
template<typename... T, int... i>
constexpr SMITH_HOST_DEVICE void	minus_equals_helper (tuple< T... > &x, const tuple< T... > &y, std::integer_sequence< int, i... >)
	A helper function for the -= operator of tuples. More...
template<typename... T>
constexpr SMITH_HOST_DEVICE auto	operator-= (tuple< T... > &x, const tuple< T... > &y)
	add values contained in y, to the tuple x More...
template<typename... S, typename... T, int... i>
constexpr SMITH_HOST_DEVICE auto	minus_helper (const tuple< S... > &x, const tuple< T... > &y, std::integer_sequence< int, i... >)
	A helper function for the - operator of tuples. More...
template<typename... S, typename... T>
constexpr SMITH_HOST_DEVICE auto	operator- (const tuple< S... > &x, const tuple< T... > &y)
	return a tuple of values defined by elementwise difference of x and y More...
template<typename... T, int... i>
constexpr SMITH_HOST_DEVICE auto	unary_minus_helper (const tuple< T... > &x, std::integer_sequence< int, i... >)
	A helper function for the - operator of tuples. More...
template<typename... T>
constexpr SMITH_HOST_DEVICE auto	operator- (const tuple< T... > &x)
	return a tuple of values defined by applying the unary minus operator to each element of x More...
template<typename... S, typename... T, int... i>
constexpr SMITH_HOST_DEVICE auto	div_helper (const tuple< S... > &x, const tuple< T... > &y, std::integer_sequence< int, i... >)
	A helper function for the / operator of tuples. More...
template<typename... S, typename... T>
constexpr SMITH_HOST_DEVICE auto	operator/ (const tuple< S... > &x, const tuple< T... > &y)
	return a tuple of values defined by elementwise division of x by y More...
template<typename... T, int... i>
constexpr SMITH_HOST_DEVICE auto	div_helper (const double a, const tuple< T... > &x, std::integer_sequence< int, i... >)
	A helper function for the / operator of tuples. More...
template<typename... T, int... i>
constexpr SMITH_HOST_DEVICE auto	div_helper (const tuple< T... > &x, const double a, std::integer_sequence< int, i... >)
	A helper function for the / operator of tuples. More...
template<typename... T>
constexpr SMITH_HOST_DEVICE auto	operator/ (const double a, const tuple< T... > &x)
	return a tuple of values defined by division of a by the elements of x More...
template<typename... T>
constexpr SMITH_HOST_DEVICE auto	operator/ (const tuple< T... > &x, const double a)
	return a tuple of values defined by elementwise division of x by a More...
template<typename... S, typename... T, int... i>
constexpr SMITH_HOST_DEVICE auto	mult_helper (const tuple< S... > &x, const tuple< T... > &y, std::integer_sequence< int, i... >)
	A helper function for the * operator of tuples. More...
template<typename... S, typename... T>
constexpr SMITH_HOST_DEVICE auto	operator* (const tuple< S... > &x, const tuple< T... > &y)
	return a tuple of values defined by elementwise multiplication of x and y More...
template<typename... T, int... i>
constexpr SMITH_HOST_DEVICE auto	mult_helper (const double a, const tuple< T... > &x, std::integer_sequence< int, i... >)
	A helper function for the * operator of tuples. More...
template<typename... T, int... i>
constexpr SMITH_HOST_DEVICE auto	mult_helper (const tuple< T... > &x, const double a, std::integer_sequence< int, i... >)
	A helper function for the * operator of tuples. More...
template<typename... T>
constexpr SMITH_HOST_DEVICE auto	operator* (const double a, const tuple< T... > &x)
	multiply each component of x by the value a on the left More...
template<typename... T>
constexpr SMITH_HOST_DEVICE auto	operator* (const tuple< T... > &x, const double a)
	multiply each component of x by the value a on the right More...
template<typename... T, std::size_t... i>
auto &	print_helper (std::ostream &out, const smith::tuple< T... > &A, std::integer_sequence< size_t, i... >)
	helper used to implement printing a tuple of values More...
template<typename... T>
auto &	operator<< (std::ostream &out, const smith::tuple< T... > &A)
	print a tuple of values More...
template<typename lambda , typename... T, int... i>
SMITH_HOST_DEVICE auto	apply_helper (lambda f, tuple< T... > &args, std::integer_sequence< int, i... >)
	A helper to apply a lambda to a tuple. More...
template<typename lambda , typename... T>
SMITH_HOST_DEVICE auto	apply (lambda f, tuple< T... > &args)
	a way of passing an n-tuple to a function that expects n separate arguments More...
template<typename lambda , typename... T, int... i>
SMITH_HOST_DEVICE auto	apply_helper (lambda f, const tuple< T... > &args, std::integer_sequence< int, i... >)
template<typename lambda , typename... T>
SMITH_HOST_DEVICE auto	apply (lambda f, const tuple< T... > &args)
	a way of passing an n-tuple to a function that expects n separate arguments More...
template<typename S , typename T , int m, int... n, typename = std::enable_if_t<std::is_arithmetic_v<S> || is_dual_number<S>::value>>
constexpr SMITH_HOST_DEVICE auto	operator* (S scale, const tensor< T, m, n... > &A)
	multiply a tensor by a scalar value More...
template<typename S , typename T , int m, int... n, typename = std::enable_if_t<std::is_arithmetic_v<S> || is_dual_number<S>::value>>
constexpr SMITH_HOST_DEVICE auto	operator* (const tensor< T, m, n... > &A, S scale)
	multiply a tensor by a scalar value More...
template<typename S , typename T , int m, int... n, typename = std::enable_if_t<std::is_arithmetic_v<S> || is_dual_number<S>::value>>
constexpr SMITH_HOST_DEVICE auto	operator/ (S scale, const tensor< T, m, n... > &A)
	divide a scalar by each element in a tensor More...
template<typename S , typename T , int m, int... n, typename = std::enable_if_t<std::is_arithmetic_v<S> || is_dual_number<S>::value>>
constexpr SMITH_HOST_DEVICE auto	operator/ (const tensor< T, m, n... > &A, S scale)
	divide a tensor by a scalar More...
template<int i, int N>
constexpr SMITH_HOST_DEVICE auto	make_dual_helper (zero)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<int i, int N>
constexpr SMITH_HOST_DEVICE auto	make_dual_helper (double arg)
	promote a double value to dual number with a one_hot_t< i, N, double > gradient type More...
template<int i, int N, typename T , int... n>
constexpr SMITH_HOST_DEVICE auto	make_dual_helper (const tensor< T, n... > &arg)
	promote a tensor value to dual number with a one_hot_t< i, N, tensor > gradient type More...
template<typename T0 , typename T1 >
constexpr SMITH_HOST_DEVICE auto	make_dual (const tuple< T0, T1 > &args)
	Promote a tuple of values to their corresponding dual types. More...
template<typename T0 , typename T1 , typename T2 >
constexpr SMITH_HOST_DEVICE auto	make_dual (const tuple< T0, T1, T2 > &args)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<bool dualify, typename T >
SMITH_HOST_DEVICE auto	promote_to_dual_when (const T &x)
	a function that optionally (decided at compile time) converts a value to its dual type More...
template<bool dualify, typename T , int n>
SMITH_HOST_DEVICE auto	promote_each_to_dual_when (const tensor< T, n > &x)
	a function that optionally (decided at compile time) converts a list of values to their dual types More...
template<int n, typename... T, int... i>
constexpr SMITH_HOST_DEVICE auto	make_dual_helper (const smith::tuple< T... > &args, std::integer_sequence< int, i... >)
	layer of indirection required to implement make_dual_wrt
template<int n, typename... T>
constexpr auto	make_dual_wrt (const smith::tuple< T... > &args)
	take a tuple of values, and promote the nth one to a one-hot dual number of the appropriate type More...
template<typename T1 , typename T2 , int n>
SMITH_HOST_DEVICE auto	get_value (const tensor< tuple< T1, T2 >, n > &input)
	Extracts all of the values from a tensor of dual numbers. More...
template<typename... T>
SMITH_HOST_DEVICE auto	get_value (const smith::tuple< T... > &tuple_of_values)
	Retrieves the value components of a set of (possibly dual) numbers. More...
template<typename... T>
SMITH_HOST_DEVICE auto	get_gradient (dual< smith::tuple< T... >> arg)
	Retrieves the gradient components of a set of dual numbers. More...
template<typename... T, int... n>
SMITH_HOST_DEVICE auto	get_gradient (const tensor< dual< smith::tuple< T... >>, n... > &arg)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename... T>
SMITH_HOST_DEVICE auto	get_gradient (smith::tuple< T... > tuple_of_values)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<int... n>
constexpr SMITH_HOST_DEVICE auto	make_dual (const tensor< double, n... > &A)
	Constructs a tensor of dual numbers from a tensor of values. More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE LuFactorization< T, n >	factorize_lu (const tensor< T, n, n > &A)
	Compute LU factorization of a matrix with partial pivoting. More...
template<typename S , typename T , int n, int... m>
constexpr SMITH_HOST_DEVICE auto	linear_solve (const tensor< S, n, n > &A, const tensor< T, n, m... > &b)
	Solves Ax = b for x using Gaussian elimination with partial pivoting. More...
template<typename T , int n>
constexpr SMITH_HOST_DEVICE auto	make_dual (const tensor< T, n > &x, const tensor< T, n > &dx)
	Create a tensor of dual numbers with specified seed.
template<typename T , int m, int n>
constexpr SMITH_HOST_DEVICE auto	make_dual (const tensor< T, m, n > &x, const tensor< T, m, n > &dx)
	Create a tensor of dual numbers with specified seed.
template<typename gradient_type , int n>
constexpr SMITH_HOST_DEVICE auto	inv (tensor< dual< gradient_type >, n, n > A)
template<typename T , int... n>
SMITH_HOST_DEVICE auto	get_value (const tensor< dual< T >, n... > &arg)
	Retrieves a value tensor from a tensor of dual numbers. More...
template<int... n>
constexpr SMITH_HOST_DEVICE auto	get_gradient (const tensor< dual< double >, n... > &arg)
	Retrieves a gradient tensor from a tensor of dual numbers. More...
template<int... n, int... m>
constexpr SMITH_HOST_DEVICE auto	get_gradient (const tensor< dual< tensor< double, m... >>, n... > &arg)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename function , typename... ParamTypes>
auto	solve_scalar_equation (const function &f, double x0, double lower_bound, double upper_bound, ScalarSolverOptions options, ParamTypes... params)
	Solves a nonlinear scalar-valued equation and gives derivatives of solution to parameters. More...
template<typename function , int n>
auto	find_root (const function &f, tensor< double, n > x0)
	Finds a root of a vector-valued nonlinear function. More...
template<typename T , int size>
auto	eigenvalues (const smith::tensor< T, size, size > &A)
	compute the eigenvalues of a symmetric matrix A More...
template<typename T >
int	sgn (T val)
	Signum, returns sign of input. More...
template<typename T >
SMITH_HOST_DEVICE tensor< int, 3 >	argsort (const tensor< T, 3 > &v)
	Find indices that would sort a 3-vector. More...
SMITH_HOST_DEVICE tuple< vec3, mat3 >	eig_symm (const mat3 &A)
template<typename T , typename Function , typename EigvalSecantFunction >
auto	symmetric_mat3_function (tensor< T, 3, 3 > A, const Function &f, const EigvalSecantFunction &g)
	Constructs an isotropic tensor-valued function of a symmetric 3x3 tensor from a scalar function. More...
template<typename Gradient , typename Function >
constexpr SMITH_HOST_DEVICE auto	symmetric_mat3_function_with_derivative (tensor< dual< Gradient >, 3, 3 > A, tensor< double, 3, 3 > f_A, vec3 lambda, mat3 Q, const Function &g)
	Helper function for defining the derivative.
template<typename T >
auto	log_symm (tensor< T, 3, 3 > A)
	Logarithm of a symmetric matrix. More...
template<typename T >
auto	exp_symm (tensor< T, 3, 3 > A)
	Exponential of a symmetric matrix. More...
template<typename T >
auto	sqrt_symm (tensor< T, 3, 3 > A)
	Square root of a symmetric matrix. More...
std::string	linearName (const LinearSolver &s)
	Convert linear solver enums to their string names.
std::ostream &	operator<< (std::ostream &os, LinearSolver s)
	output linear solver string representation to a stream
std::string	nonlinearName (const NonlinearSolver &s)
	Convert nonlinear linear solver enums to their string names.
std::ostream &	operator<< (std::ostream &os, NonlinearSolver s)
	output nonlinear solver string representation to a stream
std::string	petscPCName (const PetscPCType &s)
	Convert Petsc preconditioner enums to their string names.
std::ostream &	operator<< (std::ostream &os, PetscPCType s)
	output PETSc preconditioner string representation to a stream
std::string	preconditionerName (Preconditioner p)
	Convert preconditioner enums to their string names.
std::ostream &	operator<< (std::ostream &os, Preconditioner p)
	output preconditioner string representation to a stream
Components	operator+ (Component i, Component j)
	Construct a Components object from the sum of individual vector components. More...
Components	operator+ (Component i, Components c)
	Add an additional component to the set of flagged Components. More...
template<typename T >
auto	getFieldPointers (std::vector< std::shared_ptr< T >> &states, std::vector< std::shared_ptr< T >> &params)
	Get a vector of FieldPtr or DualFieldPtr from a vector of shared_pointers to FiniteElementState or FiniteElementDual.
template<typename T >
auto	getFieldPointers (std::vector< std::shared_ptr< T >> &states)
	Get a vector of FieldPtr or DualFieldPtr from a vector of shared_pointers to FiniteElementState or FiniteElementDual.
template<typename T >
auto	getFieldPointers (std::vector< T > &states, std::vector< T > &params)
	Get a vector of FieldPtr or DualFieldPtr from a vector of FiniteElementState or FiniteElementDual.
template<typename T >
auto	getFieldPointers (std::vector< T > &states)
	Get a vector of FieldPtr or DualFieldPtr from a vector of FiniteElementState or FiniteElementDual.
template<typename T >
auto	getFieldPointers (std::shared_ptr< T > &state)
	Get a vector of FieldPtr or DualFieldPtr from a single shared_ptr<FiniteElementState> or shared_ptr<FiniteElementDual>
template<typename T >
auto	getFieldPointers (T &state)
	Get a vector of FieldPtr or DualFieldPtr from a single FiniteElementState or FiniteElementDual.
template<typename T >
auto	getConstFieldPointers (const std::vector< std::shared_ptr< T >> &states, const std::vector< std::shared_ptr< T >> &params={})
	Get a vector of ConstFieldPtr or ConstDualFieldPtr from a vector of shared_pointers to FiniteElementState or FiniteElementDual.
template<typename T >
auto	getConstFieldPointers (const std::vector< T * > &states, const std::vector< T * > &params={})
	Get a vector of ConstFieldPtr or ConstDualFieldPtr from a vector of shared_pointers to FiniteElementState or FiniteElementDual.
template<typename T >
auto	getConstFieldPointers (const std::vector< T > &states, const std::vector< T > &params={})
	Get a vector of ConstFieldPtr or ConstDualFieldPtr from a vector of FiniteElementState or FiniteElementDual.
template<typename T >
auto	getConstFieldPointers (const std::shared_ptr< T > &state)
	Get a vector of ConstFieldPtr or ConstDualFieldPtr from a single shared_ptr<FiniteElementState> or shared_ptr<FiniteElementDual>
template<typename T >
auto	getConstFieldPointers (const T &state)
	Get a vector of ConstFieldPtr or ConstDualFieldPtr from a single FiniteElementState or FiniteElementDual.
template<int dim, typename signature , int... n, typename func , typename... T>
FiniteElementState	fit (func f, mfem::ParMesh &pmesh, const T &... solution_fields)
	determine field parameters to approximate the output of a user-provided q-function More...
std::vector< const mfem::ParFiniteElementSpace * >	getSpaces (const std::vector< smith::FiniteElementState > &states)
	Helper function to construct vector of spaces from an existing vector of FiniteElementState. More...
template<typename MaterialType , typename StateType , typename... parameter_types>
auto	uniaxial_stress_test (double t_max, size_t num_steps, const MaterialType material, const StateType initial_state, std::function< double(double)> epsilon_xx, const parameter_types... parameter_functions)
	Drive the material model thorugh a uniaxial tension experiment. More...
template<typename MaterialType , typename StateType , typename... parameter_types>
auto	uniaxial_stress_test_rate_dependent (double t_max, size_t num_steps, const MaterialType material, const StateType initial_state, std::function< double(double)> epsilon_xx, const parameter_types... parameter_functions)
	Drive a rate-dependent material model thorugh a uniaxial tension experiment. More...
template<typename MaterialType , typename StateType , typename... functions>
auto	single_quadrature_point_test (double t_max, size_t num_steps, const MaterialType material, const StateType initial_state, const functions... f)
	This function takes a material model (and associate state variables), subjects it to a time history of stimuli, described by functions ... f, and returns the outputs at each step. This is intended to be used for testing materials, to ensure their response is in agreement with known data (analytic or experimental). More...
template<int order, int dim, typename... ParameterSpaces>
auto	create_solid_weak_form (const std::string &physics_name, std::shared_ptr< smith::Mesh > mesh, const std::vector< const smith::FiniteElementState * > &states, const std::vector< const smith::FiniteElementState * > &params)
	Utility function for creating a shared_ptr<SolidWeakForm<>> More...
double	norm (const FiniteElementState &state, const double p=2)
	Find the Lp norm of a finite element state across all dofs. More...
double	computeL2Error (const FiniteElementState &state, mfem::VectorCoefficient &exact_solution)
	Find the L2 norm of the error of a vector-valued finite element state with respect to an exact solution. More...
double	computeL2Error (const FiniteElementState &state, mfem::Coefficient &exact_solution)
	Find the L2 norm of the error of a scalar-valued finite element state with respect to an exact solution. More...
bool	is_scalar_valued (const GeneralCoefficient &coef)
	convenience function for querying the type stored in a GeneralCoefficient
bool	is_vector_valued (const GeneralCoefficient &coef)
	convenience function for querying the type stored in a GeneralCoefficient
bool	sameFiniteElementSpace (const mfem::FiniteElementSpace &left, const mfem::FiniteElementSpace &right)
	Check if two finite element spaces are the same. More...
double	avg (const FiniteElementVector &fe_vector)
	Find the average value of a finite element vector across all dofs. More...
double	max (const FiniteElementVector &fe_vector)
	Find the max value of a finite element vector across all dofs. More...
double	min (const FiniteElementVector &fe_vector)
	Find the min value of a finite element vector across all dofs. More...
double	innerProduct (const FiniteElementVector &vec1, const FiniteElementVector &vec2)
	Find the inner prodcut between two finite element vectors across all dofs. More...
void	checkMesh (const mfem::ParMesh &pmesh, bool is_restart=false)
	Check that a mesh satisfies our required properties.

Variables
constexpr ExecutionSpace	default_execution_space = ExecutionSpace::CPU
	The default execution space for Smith builds.
std::shared_ptr< QuadratureData< Nothing > >	NoQData = ::std::make_shared<QuadratureData<Nothing>>()
	a single instance of a QuadratureData container of Nothings, since they are all interchangeable More...
std::shared_ptr< QuadratureData< Empty > >	EmptyQData = ::std::make_shared<QuadratureData<Empty>>()
	a single instance of a QuadratureData container of Emptys, since they are all interchangeable
const ScalarSolverOptions	default_solver_options {.xtol = 1e-8, .rtol = 0, .max_iter = 25}
	Default options for solve_scalar_equation.
std::map< std::string, LinearSolver >	linearSolverMap
	string->value matching for optionally entering options as string in command line More...
std::map< std::string, NonlinearSolver >	nonlinearSolverMap
	string->value matching for optionally entering options as string in command line More...
std::map< std::string, Preconditioner >	preconditionerMap
	string->value matching for optionally entering options as string in command line More...
constexpr int	SHAPE_ORDER = 1
	Polynomial order used to discretize the shape displacement field.
constexpr H1< SHAPE_ORDER, 2 >	SHAPE_DIM_2
	Function space for shape displacement on dimension 2 meshes.
constexpr H1< SHAPE_ORDER, 3 >	SHAPE_DIM_3
	Function space for shape displacement on dimension 2 meshes.

Detailed Description

Accelerator functionality.

Typedef Documentation

BlockOverride

using smith::BlockOverride = typedef std::pair<int, std::unique_ptr<const mfem::Operator> >

Optional override for a diagonal block operator.

The integer is the block index i and the operator replaces the Jacobian block A_ii (or, for 2x2 Schur systems, the block used to build/approximate the (1,1) Schur operator).

Ownership of the operator is transferred to the preconditioner.

Definition at line 18 of file block_preconditioner.hpp.

one_hot_t

template<int i, int n, typename T >

using smith::one_hot_t = typedef typename one_hot<i, n, T>::type

a tuple type with n entries, all of which are of type smith::zero, except for the i^{th} entry, which is of type T

e.g. one_hot_t< 2, 4, T > == tuple<zero, zero, T, zero>

Definition at line 125 of file tuple_tensor_dual_functions.hpp.

outer_product_t

template<typename T1 , typename T2 >

using smith::outer_product_t = typedef typename detail::outer_prod<T1, T2>::type

a type function that returns the tensor type of an outer product of two tensors

Template Parameters

T1	the first argument to the outer product
T2	the second argument to the outer product

Definition at line 1829 of file tensor.hpp.

QuasiStaticFirstOrderTimeIntegrationRule

using smith::QuasiStaticFirstOrderTimeIntegrationRule = typedef BackwardEulerFirstOrderTimeIntegrationRule

Alternative name for Backward Euler which makes sense when restricting what are typically second order odes, for example transient solid mechanics, to the quasi-static approximation. It happens that the implementation is identical to backward-Euler applied to first order systems as we want to be able to capture current velocity dependencies.

Definition at line 47 of file time_integration_rule.hpp.

reduced_tensor

template<typename T , int n1, int n2 = 1>

using smith::reduced_tensor = typedef std::conditional_t< (n1 == 1 && n2 == 1), double, std::conditional_t<n1 == 1, tensor<T, n2>, std::conditional_t<n2 == 1, tensor<T, n1>, tensor<T, n1, n2> >> >

Removes 1s from tensor dimensions For example, a tensor<T, 1, 10> is equivalent to a tensor<T, 10>

Template Parameters

T	The scalar type of the tensor
n1	The first dimension
n2	The second dimension

Definition at line 277 of file tensor.hpp.

Enumeration Type Documentation

AMGXSolver

enum smith::AMGXSolver

strong

Solver types supported by AMGX.

Enumerator
AMG	GPU Algebraic Multigrid
PCGF	GPU PCGF
CG	GPU CG
PCG	GPU PCG
PBICGSTAB	GPU PBICGSTAB
BICGSTAB	GPU BICGSTAB
FGMRES	GPU FGMRES
JACOBI_L1	GPU JACOBI_L1
GS	GPU GS
POLYNOMIAL	GPU POLYNOMIAL
KPZ_POLYNOMIAL	GPU KPZ_POLYNOMIAL
BLOCK_JACOBI	GPU BLOCK_JACOBI
MULTICOLOR_GS	GPU MULTICOLOR_GS
MULTICOLOR_DILU	GPU MULTICOLOR_DILU

Definition at line 217 of file solver_config.hpp.

BlockSchurType

enum smith::BlockSchurType

strong

Selects the block Schur preconditioner variant.

Enumerator
Diagonal	Block diagonal: apply $ A_{11}^{-1} $ and $ S^{-1} $ only.
Lower	Lower factor form.
Upper	Upper factor form.
Full	Full factor form (lower, diagonal, upper).

Definition at line 173 of file block_preconditioner.hpp.

BlockTriangularType

enum smith::BlockTriangularType

strong

Selects the block triangular sweep used by BlockTriangularPreconditioner.

Enumerator
Lower	Forward (lower triangular) sweep.
Upper	Backward (upper triangular) sweep.
Symmetric	Apply a symmetric combination of lower and upper sweeps.

Definition at line 84 of file block_preconditioner.hpp.

ContactEnforcement

enum smith::ContactEnforcement

strong

Describes how to enforce the contact constraint equations.

Enumerator
Penalty	Equal penalty applied to all constrained dofs
LagrangeMultiplier	Solve for exact pressures to satisfy constraints

Definition at line 28 of file contact_config.hpp.

ContactJacobian

enum smith::ContactJacobian

strong

Method for computing Jacobian of contact terms.

Enumerator
Approximate	Ignore higher order contributions to the Jacobian
Exact	Compute exact Jacobian (needed for quadratic convergence with Newton)

Definition at line 46 of file contact_config.hpp.

ContactMethod

enum smith::ContactMethod

strong

Methodology for enforcing contact constraints (i.e. how you form the constraint equations)

Enumerator
SingleMortar	Puso and Laursen 2004

Definition at line 20 of file contact_config.hpp.

ContactType

enum smith::ContactType

strong

Mechanical constraint type on contact surfaces.

Enumerator
TiedNormal	Tied contact in the normal direction, no friction
Frictionless	Enforce gap >= 0, pressure <= 0, gap * pressure = 0 in the normal direction

Definition at line 37 of file contact_config.hpp.

DirichletEnforcementMethod

enum smith::DirichletEnforcementMethod

strong

this enum describes which way to enforce the time-varying constraint u(t) == U(t)

Enumerator
DirectControl	Satisfies u(t+dt) == U(t+dt) This method imposes additional stability criteria for the case of second order differential equations
RateControl	(default value) Satisfies dudt(t+dt) == dUdt(t+dt) This method does not impose any additional stability criteria for the case of second order differential equations.
FullControl	satisfies u(t+dt) == U(t+dt), dudt(t+dt) == dUdt(t+dt), (and d2udt2(t+dt) == d2Udt2(t+dt), for a second order ODE) Empirically, this method tends to be the most accurate for small timesteps (by a constant factor), but is more expensive to evaluate

Definition at line 60 of file solver_config.hpp.

ElementType

enum smith::ElementType

strong

The type of a finite element basis function.

Note

TODO This class is used instead of the Family class from functional due to incompatibilities with Vector expression templates and the dual number class.

Enumerator
H1	Nodal scalar-valued basis functions.
HCURL	Nedelec (continuous tangent) vector-valued basis functions.
HDIV	Raviart-Thomas (continuous normal) vector-valued basis functions.
L2	Discontinuous scalar-valued basis functions.

Definition at line 38 of file finite_element_vector.hpp.

Family

enum smith::Family

strong

Element conformity.

QOI denotes a "quantity of interest", implying integration with the test function "1" H1 denotes a function space where values are continuous across element boundaries HCURL denotes a vector-valued function space where only the tangential component is continuous across element boundaries HDIV denotes a vector-valued function space where only the normal component is continuous across element boundaries L2 denotes a function space where values are discontinuous across element boundaries

Definition at line 180 of file finite_element.hpp.

LinearSolver

enum smith::LinearSolver

strong

Linear solution method indicator.

Enumerator
CG	Conjugate gradient
GMRES	Generalized minimal residual method
SuperLU	SuperLU MPI-enabled direct nodal solver
Strumpack	Strumpack MPI-enabled direct frontal solver
PetscCG	PETSc MPI-enabled conjugate gradient solver
PetscGMRES	PETSc MPI-enabled generalize minimal residual solver

Definition at line 102 of file solver_config.hpp.

NonlinearSolver

enum smith::NonlinearSolver

strong

Nonlinear solver method indicator.

Enumerator
Newton	MFEM-native Newton-Raphson
LBFGS	MFEM-native Limited memory BFGS
NewtonLineSearch	Custom solver using preconditioned earch direction with backtracking line search
TrustRegion	Custom solver using a trust region solver
KINFullStep	KINSOL Full Newton (Sundials must be enabled)
KINBacktrackingLineSearch	KINSOL Newton with Backtracking Line Search (Sundials must be enabled)
KINPicard	KINSOL Picard (Sundials must be enabled)
PetscNewton	PETSc Full Newton
PetscNewtonBacktracking	PETSc Newton with backtracking line search
PetscNewtonCriticalPoint	PETSc Newton with critical point line search
PetscTrustRegion	PETSc trust region solver

Definition at line 149 of file solver_config.hpp.

PetscPCType

enum smith::PetscPCType

strong

Preconditioner types supported by PETSc.

Enumerator
JACOBI	Jacobi with diagonal scaling
JACOBI_L1	Jacobi with row-wise L1 norm scaling
JACOBI_ROWSUM	Jacobi with row sum (no absolute value) scaling
JACOBI_ROWMAX	Jacobi with L-infinity norm scaling
PBJACOBI	Point-block Jacobi with LU factorization on sub-blocks
BJACOBI	Block Jacobi with LU factorization on sub-blocks, set number of blocks with -pc_bjacobi_blocks
LU	Direct solver based on LU factorization
ILU	Incomplete LU factorization
CHOLESKY	Cholesky factorization
SVD	LAPACK xGESVD SVD decomposition, fully redundant (SLOW for MPI)
ASM	Additive Schwarz method, each block is solved with its own KSP object, blocks cannot be shared between MPI processes. Set total number of blocks with -pc_asm_blocks N
GASM	Additive Schwarz method, each block is solved with its own KSP object, blocks can be shared between MPI processes. Set total number of blocks with -pc_gasm_total_subdomains N
GAMG	PETSc built-in AMG preconditioner
HMG	Hierarchical AMG for multi-component PDE problems
NONE	No preconditioner, or type set via -pc_type CLI flag

Definition at line 271 of file solver_config.hpp.

Preconditioner

enum smith::Preconditioner

strong

The type of preconditioner to be used.

Enumerator
HypreJacobi	Hypre-based Jacobi
HypreL1Jacobi	Hypre-based L1-scaled Jacobi
HypreGaussSeidel	Hypre-based Gauss-Seidel
HypreAMG	Hypre's BoomerAMG algebraic multi-grid
HypreILU	Hypre's Incomplete LU
AMGX	NVIDIA's AMGX GPU-enabled algebraic multi-grid, GPU builds only
Petsc	PETSc preconditioner,
AMGFContact	MFEM-based AMG with filtering (AMGF), contact problems only
None	No preconditioner used

Definition at line 336 of file solver_config.hpp.

SchurApproxType

enum smith::SchurApproxType

strong

Selects how the (1,1) Schur operator is approximated.

Enumerator
DiagInv	Use assembled \( S \approx A_{22} - A_{21} \\mathrm{diag}(A_{11})^{-1} A_{12} \).
A22Only	Use \( S \approx A_{22} \).
Custom	Use a custom operator provided via the overrides list for block index 1.

Definition at line 185 of file block_preconditioner.hpp.

TimestepMethod

enum smith::TimestepMethod

strong

Timestep method of a solver.

Enumerator
QuasiStatic	Quasistatic
BackwardEuler	FirstOrderODE option
SDIRK33	FirstOrderODE option
ForwardEuler	FirstOrderODE option
RK2	FirstOrderODE option
RK3SSP	FirstOrderODE option
RK4	FirstOrderODE option
GeneralizedAlpha	FirstOrderODE option
ImplicitMidpoint	FirstOrderODE option
SDIRK23	FirstOrderODE option
SDIRK34	FirstOrderODE option
Newmark	SecondOrderODE option
HHTAlpha	SecondOrderODE option
WBZAlpha	SecondOrderODE option
AverageAcceleration	SecondOrderODE option
LinearAcceleration	SecondOrderODE option
CentralDifference	SecondOrderODE option
FoxGoodwin	SecondOrderODE option

Definition at line 25 of file solver_config.hpp.

Function Documentation

about()

std::string smith::about

(

)

Returns a string about the configuration of Smith.

Returns

string containing various configuration information about Smith

Definition at line 56 of file about.cpp.

abs()

template<typename gradient_type >

SMITH_HOST_DEVICE auto smith::abs

(

dual< gradient_type >

x

)

Implementation of absolute value function for dual numbers.

Note

This is not differentiable at x = 0.0. At that point, the gradient is calculated as the gradient of x.

Definition at line 219 of file dual.hpp.

antisym() [1/2]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::antisym ( const isotropic_tensor< T, m, m > &  )

constexpr

return the antisymmetric part of an isotropic tensor

Template Parameters

T	the types stored in the isotropic tensor
m	the number of rows and columns in I

Returns

zero (isotropic matrices are symmetric, so the antisymmetric part is identically zero)

Definition at line 256 of file isotropic_tensor.hpp.

antisym() [2/2]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto smith::antisym ( const tensor< T, n, n > &  A )

constexpr

Returns the antisymmetric part of a square matrix.

Parameters

[in]

A

The matrix to obtain the antisymmetric part of

Returns

(1/2) * (A - A^T)

Definition at line 1181 of file tensor.hpp.

AntisymmetricIdentity()

template<int m>

constexpr SMITH_HOST_DEVICE auto smith::AntisymmetricIdentity ( )

constexpr

a helper function for creating the rank-4 isotropic tensor defined by: d(antisym(A)_{ij}) / d(A_{kl})

Template Parameters

m	the dimension

Definition at line 394 of file isotropic_tensor.hpp.

apply() [1/2]

template<typename lambda , typename... T>

SMITH_HOST_DEVICE auto smith::apply	(	lambda	f,
		const tuple< T... > &	args
	)

a way of passing an n-tuple to a function that expects n separate arguments

Template Parameters

lambda	a callable type
T	the types of arguments to be passed in to f

Parameters

f	the callable object
args	a tuple of arguments

e.g. foo(bar, baz) is equivalent to apply(foo, smith::tuple(bar,baz));

Definition at line 803 of file tuple.hpp.

apply() [2/2]

template<typename lambda , typename... T>

SMITH_HOST_DEVICE auto smith::apply	(	lambda	f,
		tuple< T... > &	args
	)

a way of passing an n-tuple to a function that expects n separate arguments

Template Parameters

lambda	a callable type
T	the types of arguments to be passed in to f

Parameters

f	the callable object
args	a tuple of arguments

e.g. foo(bar, baz) is equivalent to apply(foo, smith::tuple(bar,baz));

Definition at line 779 of file tuple.hpp.

apply_helper() [1/2]

template<typename lambda , typename... T, int... i>

SMITH_HOST_DEVICE auto smith::apply_helper	(	lambda	f,
		const tuple< T... > &	args,
		std::integer_sequence< int, i... >
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 788 of file tuple.hpp.

apply_helper() [2/2]

template<typename lambda , typename... T, int... i>

SMITH_HOST_DEVICE auto smith::apply_helper	(	lambda	f,
		tuple< T... > &	args,
		std::integer_sequence< int, i... >
	)

A helper to apply a lambda to a tuple.

Template Parameters

lambda	The functor type
T	The tuple types
i	The integer sequence to i

Parameters

f	The functor to apply to the tuple
args	The input tuple

Returns

The functor output

Definition at line 764 of file tuple.hpp.

argsort()

template<typename T >

SMITH_HOST_DEVICE tensor<int, 3> smith::argsort

(

const tensor< T, 3 > &

v

)

Find indices that would sort a 3-vector.

Parameters

v	3-vector to sort.

Returns

3-vector of indices that would sort v in ascending order.

Definition at line 783 of file tuple_tensor_dual_functions.hpp.

avg()

double smith::avg

(

const FiniteElementVector &

fe_vector

)

Find the average value of a finite element vector across all dofs.

Parameters

fe_vector

The state variable to compute the average of

Returns

The average value

Note

This acts on the actual scalar degree of freedom values, not the interpolated shape function values. This implies these may or may not be nodal averages depending on the choice of finite element basis.

Definition at line 117 of file finite_element_vector.cpp.

Bernstein()

template<int n, typename T >

SMITH_HOST_DEVICE tensor<T, n> smith::Bernstein

(

T

s

)

Bernstein Polynomials on the domain [0, 1].

Template Parameters

n	how many entries to compute

Parameters

[in]

s

where to evaluate the polynomials

Definition at line 467 of file polynomials.hpp.

binary_comparator_overload()

smith::binary_comparator_overload

(

)

implement operator< for dual numbers

implement operator> for dual numbers

implement operator== for dual numbers

block_solve()

std::vector< FieldState > smith::block_solve	(	const std::vector< WeakForm * > &	residual_evals,
		const std::vector< std::vector< size_t >>	block_indices,
		const FieldState &	shape_disp,
		const std::vector< std::vector< FieldState >> &	states,
		const std::vector< std::vector< FieldState >> &	params,
		const TimeInfo &	time_info,
		const DifferentiableBlockSolver *	solver,
		const std::vector< const BoundaryConditionManager * > &	bc_managers
	)

Solve a block nonlinear system of equations as defined by the vector of weak form.

Parameters

residual_evals	Vector of weak forms which define the equations to be solved
block_indices	Matrix of index arguments specifying where in each WeakForm the unknown fields are passed in. Example: for a 2 weak-form system, with weak-forms, r1, r2 r1(a,b,c) r2(b,d,e,a)
shape_disp	The mesh-morphed shape displacement
states	The time varying states as inputs to the weak form
params	The fixed field parameters as inputs to the weak form
time_info	Timestep information (time, dt, cycle)
solver	The differentiable, potentially nonlinear, equation solver used to solve the system of equations
bc_managers	Holds information about which degrees of freedom (DOFS)

Returns

Vector of field solutions satisfying the weak forms

Definition at line 270 of file nonlinear_solve.cpp.

boundary_geometry_counts()

std::array<uint32_t, mfem::Geometry::NUM_GEOMETRIES> smith::boundary_geometry_counts ( const mfem::Mesh &  mesh )

inline

count the number of boundary elements of each geometry in a mesh

Parameters

mesh	the mesh to count

Definition at line 89 of file geometry.hpp.

build_hollow_quarter_cylinder()

mfem::Mesh smith::build_hollow_quarter_cylinder	(	std::size_t	radial_divisions,
		std::size_t	angular_divisions,
		std::size_t	vertical_divisions,
		double	inner_radius,
		double	outer_radius,
		double	height
	)

Constructs an MFEM mesh of a hollow cylinder restricted to the first orthant.

Parameters

radial_divisions	number of elements in the radial direction
angular_divisions	number of elements in the theta direction
vertical_divisions	number of elements in the z-direction
inner_radius	the radius of the inner wall of the cylinder
outer_radius	the radius of the outer wall of the cylinder
height	the height of the top surface of the cylinder

Note

the cylinder's axis of symmetry is along the z-direction

Definition at line 370 of file mesh_utils.cpp.

buildBallMesh()

mfem::Mesh smith::buildBallMesh

(

int

approx_number_of_elements

)

Constructs a 3D MFEM mesh of a unit ball, centered at the origin.

This routine creates a mesh by refining a coarse ball mesh until the number of elements is as close as possible to the user-specified number of elements

Parameters

[in]

approx_number_of_elements

Approximate number of elements

Returns

The constructed mesh

Definition at line 113 of file mesh_utils.cpp.

buildCuboidMesh()

mfem::Mesh smith::buildCuboidMesh	(	int	elements_in_x,
		int	elements_in_y,
		int	elements_in_z,
		double	size_x = 1.,
		double	size_y = 1.,
		double	size_z = 1.
	)

Constructs a 3D MFEM mesh of a cuboid.

Parameters

[in]	elements_in_x	the number of elements in the x-direction
[in]	elements_in_y	the number of elements in the y-direction
[in]	elements_in_z	the number of elements in the z-direction
[in]	size_x	Overall size in the x-direction
[in]	size_y	Overall size in the y-direction
[in]	size_z	Overall size in the z-direction

Returns

The constructed serial mesh

Definition at line 155 of file mesh_utils.cpp.

buildCylinderMesh()

mfem::Mesh smith::buildCylinderMesh	(	int	radial_refinement,
		int	elements_lengthwise,
		double	radius,
		double	height
	)

Constructs a 3D MFEM mesh of a cylinder.

Parameters

[in]	radial_refinement	the number of times to apply uniform mesh refinement to the cross section
[in]	elements_lengthwise	the number of elements in the z-direction
[in]	radius	the radius of the cylinder
[in]	height	the number of elements in the z-direction

Returns

The constructed mesh

Definition at line 162 of file mesh_utils.cpp.

buildDifferentiableLinearSolver()

std::shared_ptr< LinearDifferentiableSolver > smith::buildDifferentiableLinearSolver	(	LinearSolverOptions	linear_opts,
		const smith::Mesh &	mesh
	)

Create a differentiable linear solver.

Parameters

linear_opts	linear options struct
mesh	mesh

Definition at line 396 of file differentiable_solver.cpp.

buildDifferentiableNonlinearBlockSolver()

std::shared_ptr< NonlinearDifferentiableBlockSolver > smith::buildDifferentiableNonlinearBlockSolver	(	NonlinearSolverOptions	nonlinear_opts,
		LinearSolverOptions	linear_opts,
		const smith::Mesh &	mesh
	)

Create a differentiable nonlinear block solver.

Parameters

nonlinear_opts	nonlinear options struct
linear_opts	linear options struct
mesh	mesh

Definition at line 411 of file differentiable_solver.cpp.

buildDifferentiableNonlinearSolver()

std::shared_ptr< NonlinearDifferentiableSolver > smith::buildDifferentiableNonlinearSolver	(	NonlinearSolverOptions	nonlinear_opts,
		LinearSolverOptions	linear_opts,
		const smith::Mesh &	mesh
	)

Create a differentiable nonlinear solver.

Parameters

nonlinear_opts	nonlinear options struct
linear_opts	linear options struct
mesh	mesh

Definition at line 403 of file differentiable_solver.cpp.

buildDiskMesh()

mfem::Mesh smith::buildDiskMesh

(

int

approx_number_of_elements

)

Constructs a 2D MFEM mesh of a unit disk, centered at the origin.

This routine creates a mesh by refining a coarse disk mesh until the number of elements is as close as possible to the user-specified number of elements

Parameters

[in]

approx_number_of_elements

The appoximate number of elements

Returns

The constructed mesh

Definition at line 80 of file mesh_utils.cpp.

buildHollowCylinderMesh()

mfem::Mesh smith::buildHollowCylinderMesh	(	int	radial_refinement,
		int	elements_lengthwise,
		double	inner_radius,
		double	outer_radius,
		double	height,
		double	total_angle = M_PI,
		int	sectors = 8
	)

Constructs a 3D MFEM mesh of a hollow cylinder.

Parameters

[in]	radial_refinement	the number of times to apply uniform mesh refinement to the cross section
[in]	elements_lengthwise	the number of elements in the z-direction
[in]	inner_radius	inner radius the radius of the cylindrical shell
[in]	outer_radius	ouer radius the radius of the cylindrical shell
[in]	height	the number of elements in the z-direction
[in]	total_angle	the angle in radians over which to generate the portion of an extruded cylinder
[in]	sectors	the number of starting sectors in the hollow cylinder

Returns

The constructed mesh

Definition at line 359 of file mesh_utils.cpp.

buildLinearSolverAndPreconditioner()

std::pair< std::unique_ptr< mfem::Solver >, std::unique_ptr< mfem::Solver > > smith::buildLinearSolverAndPreconditioner	(	LinearSolverOptions	linear_opts = {},
		MPI_Comm	comm = MPI_COMM_WORLD
	)

Build the linear solver and its associated preconditioner given a linear options struct.

Parameters

linear_opts	The options to configure the linear solver and preconditioner
comm	The MPI communicator for the supplied HypreParMatrix and HypreParVectors

Returns

A pair containing the constructed linear solver and preconditioner objects

Definition at line 1097 of file equation_solver.cpp.

buildMeshFromFile()

mfem::Mesh smith::buildMeshFromFile

(

const std::string &

mesh_file

)

Constructs an MFEM mesh from a file.

This opens and reads an external mesh file and constructs a serial MFEM Mesh object.

Parameters

[in]

mesh_file

The mesh file to open

Returns

A serial mesh object

Definition at line 25 of file mesh_utils.cpp.

buildMonolithicMatrix()

std::unique_ptr< mfem::HypreParMatrix > smith::buildMonolithicMatrix

(

const mfem::BlockOperator &

block_operator

)

Function for building a monolithic parallel Hypre matrix from a block system of smaller Hypre matrices.

Parameters

block_operator

The block system of HypreParMatrices

Returns

The assembled monolithic HypreParMatrix

Precondition

block_operator must have assembled HypreParMatrices for its sub-blocks

Definition at line 941 of file equation_solver.cpp.

buildNonlinearSolver()

std::unique_ptr< mfem::NewtonSolver > smith::buildNonlinearSolver	(	NonlinearSolverOptions	nonlinear_opts,
		const LinearSolverOptions &	linear_opts,
		mfem::Solver &	preconditioner,
		MPI_Comm	comm = MPI_COMM_WORLD
	)

Build a nonlinear solver using the nonlinear option struct.

Parameters

nonlinear_opts	The options to configure the nonlinear solution scheme
linear_opts	The options to configure the linear solution scheme
preconditioner	A preconditioner to help with either linear or nonlinear solves
comm	The MPI communicator for the supplied nonlinear operators and HypreParVectors

Returns

The constructed nonlinear solver

Definition at line 1026 of file equation_solver.cpp.

buildPreconditioner()

std::unique_ptr< mfem::Solver > smith::buildPreconditioner	(	LinearSolverOptions	linear_opts,
		[[maybe_unused] ] MPI_Comm	comm = MPI_COMM_WORLD
	)

Build a preconditioner from the available options.

Parameters

linear_opts	The options to configure the linear solver and preconditioner
comm	The communicator for the underlying operator and HypreParVectors

Returns

A constructed preconditioner based on the input option

Definition at line 1211 of file equation_solver.cpp.

buildRectangleMesh()

mfem::Mesh smith::buildRectangleMesh	(	int	elements_in_x,
		int	elements_in_y,
		double	size_x = 1.,
		double	size_y = 1.
	)

Constructs a 2D MFEM mesh of a rectangle.

Parameters

[in]	elements_in_x	the number of elements in the x-direction
[in]	elements_in_y	the number of elements in the y-direction
[in]	size_x	Overall size in the x-direction
[in]	size_y	Overall size in the y-direction

Returns

The constructed serial mesh

Definition at line 150 of file mesh_utils.cpp.

buildRingMesh()

mfem::Mesh smith::buildRingMesh	(	int	radial_refinement,
		double	inner_radius,
		double	outer_radius,
		double	total_angle = M_PI,
		int	sectors = 8
	)

Constructs a 2D MFEM mesh of a ring.

Parameters

[in]	radial_refinement	the number of times to apply uniform mesh refinement to the cross section
[in]	inner_radius	inner radius the radius of the cylindrical shell
[in]	outer_radius	ouer radius the radius of the cylindrical shell
[in]	total_angle	the angle in radians over which to generate the portion of an extruded cylinder
[in]	sectors	the number of starting sectors in the hollow cylinder

Returns

A unique_ptr containing the constructed mesh

Definition at line 353 of file mesh_utils.cpp.

buildSolidMechanics()

template<int dim, typename ShapeDispSpace , typename VectorSpace , typename... ParamSpaces>

auto smith::buildSolidMechanics	(	std::shared_ptr< smith::Mesh >	mesh,
		std::shared_ptr< DifferentiableSolver >	d_solid_nonlinear_solver,
		smith::ImplicitNewmarkSecondOrderTimeIntegrationRule	time_rule,
		size_t	num_checkpoints,
		std::string	physics_name,
		const std::vector< std::string > &	param_names = {}
	)

Helper function to generate the base-physics for solid mechanics.

Template Parameters

ShapeDispSpace	Space for shape displacement, must be H1<1, dim> in most cases
VectorSpace	Space for displacement, velocity, acceleration field, typically H1<order, dim>
...ParamSpaces	Additional parameter spaces, either H1<param_order, param_dim> or L1<param_order, param_dim>
dim	Spatial dimension

Parameters

mesh	smith::Mesh
d_solid_nonlinear_solver	Abstract differentiable solver
time_rule	Time integration rule for second order systems. Likely either quasi-static or implicit Newmark
num_checkpoints	Number of checkpointed states for gretl to store for reverse mode derivatives
physics_name	Name of the physics/WeakForm
param_names	Names for the parameter fields with a one-to-one correspondence with the templated ParamSpaces

Returns

tuple of shared pointers to the: BasePhysics, WeakForm, and DirichetBoundaryConditions

Note

Only the BasePhysics needs to stay in scope. The others are returned to the user so they can define the WeakForm integrals, and to specify space and time varying boundary conditions

Definition at line 37 of file differentiable_solid_mechanics.hpp.

buildType()

std::string smith::buildType

(

)

Returns a string for the current CMake build type (e.g. Debug, Release)

Returns

string value of the build type

Definition at line 228 of file about.cpp.

chain_rule() [1/7]

constexpr SMITH_HOST_DEVICE auto smith::chain_rule ( const double  df_dx, const double  dx  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for a scalar-valued function of a scalar, the chain rule is just multiplication

Definition at line 1877 of file tensor.hpp.

chain_rule() [2/7]

template<typename T >

constexpr SMITH_HOST_DEVICE auto smith::chain_rule ( const  T, const  zero  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

this overload implements a no-op for the case where the small change is indentically zero

Definition at line 1868 of file tensor.hpp.

chain_rule() [3/7]

template<int m, int n, int... p>

SMITH_HOST_DEVICE auto smith::chain_rule	(	const tensor< double, m, n, p... > &	df_dx,
		const tensor< double, p... > &	dx
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for a matrix-valued function of a tensor, the chain rule contracts over all indices of dx

Definition at line 1920 of file tensor.hpp.

chain_rule() [4/7]

template<int m, int... n>

constexpr SMITH_HOST_DEVICE auto smith::chain_rule ( const tensor< double, m, n... > &  df_dx, const tensor< double, n... > &  dx  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for a vector-valued function of a tensor, the chain rule contracts over all indices of dx

Definition at line 1906 of file tensor.hpp.

chain_rule() [5/7]

template<int... n>

constexpr SMITH_HOST_DEVICE auto smith::chain_rule ( const tensor< double, n... > &  df_dx, const double  dx  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for a tensor-valued function of a scalar, the chain rule is just scalar multiplication

Definition at line 1884 of file tensor.hpp.

chain_rule() [6/7]

template<int... n>

constexpr SMITH_HOST_DEVICE auto smith::chain_rule ( const tensor< double, n... > &  df_dx, const tensor< double, n... > &  dx  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for a scalar-valued function of a tensor, the chain rule is the inner product

Definition at line 1894 of file tensor.hpp.

chain_rule() [7/7]

template<typename T >

constexpr SMITH_HOST_DEVICE auto smith::chain_rule ( const  zero, const  T  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

this overload implements a no-op for the case where the gradient w.r.t. an input argument is identically zero

Definition at line 1858 of file tensor.hpp.

ChebyshevT()

template<int n, typename S >

constexpr SMITH_HOST_DEVICE tensor<S, n> smith::ChebyshevT ( S  x )

constexpr

Chebyshev polynomials of the first kind Satisfying: T_n(cos(t)) == cos(n*t)

Template Parameters

n	how many entries to compute

Parameters

[in]

x

where to evaluate the polynomials

Definition at line 407 of file polynomials.hpp.

ChebyshevU()

template<int n, typename T >

SMITH_HOST_DEVICE tensor<T, n> smith::ChebyshevU

(

T

x

)

Chebyshev polynomials of the second kind Satisfying: sin(t) U_n(cos(t)) == sin((n+1)*t)

Template Parameters

n	how many entries to compute

Parameters

[in]

x

where to evaluate the polynomials

Definition at line 428 of file polynomials.hpp.

chop()

template<int n>

constexpr SMITH_HOST_DEVICE auto smith::chop ( const tensor< double, n > &  A )

constexpr

replace all entries in a tensor satisfying |x| < 1.0e-10 by literal zero

Parameters

[in]

A

The tensor to "chop"

Definition at line 1758 of file tensor.hpp.

compiler()

std::string smith::compiler

(

)

Returns a string for the current compiler name and version.

Returns

string value of the current compiler name and version

Definition at line 226 of file about.cpp.

compute_geometric_factors()

template<int Q, mfem::Geometry::Type geom, typename function_space >

void smith::compute_geometric_factors	(	mfem::Vector &	positions_q,
		mfem::Vector &	jacobians_q,
		const mfem::Vector &	positions_e,
		const std::vector< int > &	elements
	)

a kernel to compute the positions and jacobians at each quadrature point (mfem calls this "geometric factors")

Template Parameters

Q	a parameter controlling the number of quadrature points an element
function_space	the polynomial order and kind of function space used to interpolate
geom	the element geometry

Parameters

positions_q	(output) the positions for each quadrature point
jacobians_q	(output) the jacobians for each quadrature point
positions_e	(input) the "e-vector" of position data
elements	(input) the list of element indices that are part of this domain

Definition at line 27 of file geometric_factors.cpp.

computeL2Error() [1/2]

double smith::computeL2Error	(	const FiniteElementState &	state,
		mfem::Coefficient &	exact_solution
	)

Find the L2 norm of the error of a scalar-valued finite element state with respect to an exact solution.

Parameters

state	The numerical solution
exact_solution	The exact solution to measure error against

Returns

The L2 norm of the difference between state and exact_solution

Definition at line 122 of file finite_element_state.cpp.

computeL2Error() [2/2]

double smith::computeL2Error	(	const FiniteElementState &	state,
		mfem::VectorCoefficient &	exact_solution
	)

Find the L2 norm of the error of a vector-valued finite element state with respect to an exact solution.

Parameters

state	The numerical solution
exact_solution	The exact solution to measure error against

Returns

The L2 norm of the difference between state and exact_solution

Definition at line 117 of file finite_element_state.cpp.

contract()

template<int i1, int i2, typename S , int m, int... n, typename T , int p, int q>

SMITH_HOST_DEVICE auto smith::contract	(	const tensor< S, m, n... > &	A,
		const tensor< T, p, q > &	B
	)

a convenience function that computes a dot product between two tensor, but that allows the user to specify which indices should be summed over. For example:

tensor< double, 4, 4, 4 > A = ...;
tensor< double, 4, 4 > B = ...;
tensor< double, 4, 4, 4 > C = contract<1, 0>(A, B);
 
//                 sum over index 1 for A
//                          V
// C(i, j, k) = \sum_l A(i, l, j) * B(l, k)
//                                    ^
//                          sum over index 0 for B

Template Parameters

i1	the index of contraction for the left operand
i2	the index of contraction for the right operand
S	the datatype stored in the left operand
m	leading dimension of the left operand
n	the trailing dimensions of the left operand
T	the datatype stored in the right operand
p	the number of rows in the right operand
q	the number of columns in the right operand

Parameters

A	the left operand
B	the right operand

Definition at line 1405 of file tensor.hpp.

create_solid_weak_form()

template<int order, int dim, typename... ParameterSpaces>

auto smith::create_solid_weak_form	(	const std::string &	physics_name,
		std::shared_ptr< smith::Mesh >	mesh,
		const std::vector< const smith::FiniteElementState * > &	states,
		const std::vector< const smith::FiniteElementState * > &	params
	)

Utility function for creating a shared_ptr<SolidWeakForm<>>

Local enum to better document the expected indexing order to states

Definition at line 347 of file solid_weak_form.hpp.

create_time_info()

TimeInfo smith::create_time_info ( DoubleState  t, DoubleState  dt, size_t  cycle  )

inline

creates a time info struct from gretl::State<double>

Parameters

t	time
dt	timestep
cycle	iteration

Returns

Definition at line 50 of file state_advancer.hpp.

defineInputFileSchema()

void smith::defineInputFileSchema

(

axom::inlet::Inlet &

inlet

)

Define the input file structure for the driver code.

Parameters

[in]

inlet

The inlet instance

Definition at line 43 of file smith.cpp.

DenseIdentity()

template<int dim>

constexpr SMITH_HOST_DEVICE tensor<double, dim, dim> smith::DenseIdentity ( )

constexpr

Obtains the identity matrix of the specified dimension.

Returns

I_dim

Definition at line 1259 of file tensor.hpp.

det() [1/2]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::det ( const isotropic_tensor< T, m, m > &  I )

constexpr

compute the determinant of an isotropic tensor

Template Parameters

T	the types stored in the isotropic tensor
m	the number of rows and columns in I

Parameters

I	the isotropic tensor to compute the determinant of

Definition at line 311 of file isotropic_tensor.hpp.

det() [2/2]

template<typename T >

constexpr SMITH_HOST_DEVICE auto smith::det ( const tensor< T, 2, 2 > &  A )

constexpr

Returns the determinant of a matrix.

Parameters

[in]

A

The matrix to obtain the determinant of

Definition at line 1302 of file tensor.hpp.

detApIm1()

template<typename T >

constexpr SMITH_HOST_DEVICE auto smith::detApIm1 ( const tensor< T, 2, 2 > &  A )

constexpr

computes det(A + I) - 1, where precision is not lost when the entries A_{ij} << 1

detApIm1(A) = det(A + I) - 1 When the entries of A are small compared to unity, computing det(A + I) - 1 directly will suffer from catastrophic cancellation.

Parameters

A	Input matrix

Returns

det(A + I) - 1, where I is the identity matrix

Definition at line 1326 of file tensor.hpp.

dev()

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto smith::dev ( const tensor< T, n, n > &  A )

constexpr

Calculates the deviator of a matrix (rank-2 tensor)

Parameters

[in]

A

The matrix to calculate the deviator of In the context of stress tensors, the deviator is obtained by subtracting the mean stress (average of main diagonal elements) from each element on the main diagonal

Definition at line 1200 of file tensor.hpp.

diag() [1/2]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE tensor<T, n, n> smith::diag ( const tensor< T, n > &  d )

constexpr

Returns a square diagonal matrix by specifying the diagonal entries.

Parameters

[in]

d

a list of diagonal entries

Definition at line 1231 of file tensor.hpp.

diag() [2/2]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE tensor<T, n> smith::diag ( const tensor< T, n, n > &  D )

constexpr

Returns an array containing the diagonal entries of a square matrix.

Parameters

[in]

D

the matrix to extract the diagonal entries from

Definition at line 1245 of file tensor.hpp.

diagonal_matrix()

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto smith::diagonal_matrix ( const tensor< T, n, n > &  A )

constexpr

Returns a square matrix (rank-2 tensor) containing the diagonal entries of the input square matrix with zeros in the off-diagonal positions.

Parameters

[in]

A

The input square matrix This operation is used to compute a term in the constitutive response of a linear, cubic solid material

Definition at line 1217 of file tensor.hpp.

differentiate_wrt()

auto smith::differentiate_wrt ( const mfem::Vector &  v )

inline

this function is intended to only be used in combination with smith::Functional::operator(), as a way for the user to express that it should both evaluate and differentiate w.r.t. a specific argument (only 1 argument at a time)

For example:

mfem::Vector arg0 = ...;
mfem::Vector arg1 = ...;
mfem::Vector just_the_value = my_functional(arg0, arg1);
auto [value, gradient_wrt_arg1] = my_functional(arg0, differentiate_wrt(arg1));

Definition at line 41 of file differentiate_wrt.hpp.

dimension()

template<int i, typename T , int... n>

constexpr SMITH_HOST_DEVICE int smith::dimension ( const tensor< T, n... > &  )

constexpr

a function for querying the ith dimension of a tensor

Template Parameters

i	which dimension to query
T	the datatype stored in the tensor
n	the tensor extents

Returns

the ith dimension

Definition at line 1962 of file tensor.hpp.

dimension_of()

constexpr int smith::dimension_of ( mfem::Geometry::Type  g )

constexpr

Returns the dimension of an element geometry.

Parameters

[in]

g

The Geometry to retrieve the dimension of

Definition at line 55 of file geometry.hpp.

div_helper() [1/3]

template<typename... T, int... i>

constexpr SMITH_HOST_DEVICE auto smith::div_helper ( const double  a, const tuple< T... > &  x, std::integer_sequence< int, i... >    )

constexpr

A helper function for the / operator of tuples.

Template Parameters

T	the types stored in the tuple y
i	The integer sequence to i

Parameters

x	tuple of values
a	the constant numerator

Returns

the returned tuple ratio

Definition at line 596 of file tuple.hpp.

div_helper() [2/3]

template<typename... S, typename... T, int... i>

constexpr SMITH_HOST_DEVICE auto smith::div_helper ( const tuple< S... > &  x, const tuple< T... > &  y, std::integer_sequence< int, i... >    )

constexpr

A helper function for the / operator of tuples.

Template Parameters

S	the types stored in the tuple x
T	the types stored in the tuple y
i	The integer sequence to i

Parameters

x	tuple of values
y	tuple of values

Returns

the returned tuple ratio

Definition at line 566 of file tuple.hpp.

div_helper() [3/3]

template<typename... T, int... i>

constexpr SMITH_HOST_DEVICE auto smith::div_helper ( const tuple< T... > &  x, const double  a, std::integer_sequence< int, i... >    )

constexpr

A helper function for the / operator of tuples.

Template Parameters

T	the types stored in the tuple y
i	The integer sequence to i

Parameters

x	tuple of values
a	the constant denomenator

Returns

the returned tuple ratio

Definition at line 611 of file tuple.hpp.

dot() [1/13]

template<typename S , typename T , int m, int... n>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const isotropic_tensor< S, m, m > &  I, const tensor< T, m, n... > &  A  )

constexpr

dot product between an isotropic and (nonisotropic) tensor

Template Parameters

S	the types stored in isotropic tensor
T	the types stored in tensor
m	the number of rows and columns in I
n	the trailing dimensions of A

Parameters

I	the left operand
A	the (full) right operand

Returns

a new tensor equal to the index notation expression: output(i,...) := I(i,j) * A(j,...)

Definition at line 203 of file isotropic_tensor.hpp.

dot() [2/13]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< S, m > &  A, const tensor< T, m > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

vector . vector

Definition at line 806 of file tensor.hpp.

dot() [3/13]

template<typename S , typename T , int m, int n>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< S, m > &  A, const tensor< T, m, n > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

vector . matrix

Definition at line 820 of file tensor.hpp.

dot() [4/13]

template<typename S , typename T , int m, int n, int p>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< S, m > &  A, const tensor< T, m, n, p > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

vector . tensor3D

Definition at line 836 of file tensor.hpp.

dot() [5/13]

template<typename S , typename T , int m, int n, int p, int q>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< S, m > &  A, const tensor< T, m, n, p, q > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

vector . tensor4D

this overload, and others of the form dot(vector, tensor), can be implemented more succinctly as a single variadic function, but for some reason gcc-11 (but not gcc-10 or gcc-12) seemed to break when compiling that compact implementation, so we're manually writing out some of the different dot product overloads in order to support that compiler and version

Definition at line 856 of file tensor.hpp.

dot() [6/13]

template<typename S , typename T , typename U , int m, int n>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< S, m > &  u, const tensor< T, m, n > &  A, const tensor< U, n > &  v  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

vector . matrix . vector

Definition at line 936 of file tensor.hpp.

dot() [7/13]

template<typename S , typename T , int m, int n>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< S, m, n > &  A, const tensor< T, n > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

matrix . vector

Definition at line 870 of file tensor.hpp.

dot() [8/13]

template<typename S , typename T , int m, int n, int p>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< S, m, n > &  A, const tensor< T, n, p > &  B  )

constexpr

this function contracts over the "middle" index of the two tensor arguments

Template Parameters

S	the underlying type of the tensor (lefthand) argument
T	the underlying type of the tensor (righthand) argument
n	integers describing the tensor shape

Parameters

[in]	A	The lefthand tensor
[in]	B	The righthand tensor

Definition at line 768 of file tensor.hpp.

dot() [9/13]

template<typename S , typename T , int m, int n, int p, int q>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< S, m, n > &  A, const tensor< T, n, p, q > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

matrix . tensor

Definition at line 902 of file tensor.hpp.

dot() [10/13]

template<typename S , typename T , int m, int n, int p, int q, int r>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< S, m, n > &  A, const tensor< T, n, p, q, r > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

matrix . tensor

Definition at line 886 of file tensor.hpp.

dot() [11/13]

template<typename S , typename T , int m, int n, int p>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< S, m, n, p > &  A, const tensor< T, p > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

3rd-order-tensor . vector

Definition at line 918 of file tensor.hpp.

dot() [12/13]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::dot ( const tensor< T, m > &  A, double  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

vector . scalar

Definition at line 786 of file tensor.hpp.

dot() [13/13]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::dot ( double  B, const tensor< T, m > &  A  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

scalar * vector

Definition at line 796 of file tensor.hpp.

double_dot() [1/5]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::double_dot ( const isotropic_tensor< S, m, m > &  I, const tensor< T, m, m > &  A  )

constexpr

double-dot product between an isotropic and (nonisotropic) tensor

Template Parameters

S	the types stored in isotropic tensor
T	the types stored in tensor
m	the number of rows and columns in I, A

Parameters

I	the left operand
A	the (full) right operand

Returns

a new tensor equal to the index notation expression: output := I(i,j) * A(i,j) \(\propto\) tr(A)

Definition at line 229 of file isotropic_tensor.hpp.

double_dot() [2/5]

template<typename S , typename T , int m, int... n>

constexpr SMITH_HOST_DEVICE auto smith::double_dot ( const isotropic_tensor< S, m, m, m, m > &  I, const tensor< T, m, m, n... > &  A  )

constexpr

double-dot product between an isotropic and (nonisotropic) tensor

Template Parameters

S	the types stored in isotropic tensor
T	the types stored in tensor
m	the dimension of each extent of I

Parameters

I	the left operand
A	the (full) right operand

Returns

a new tensor equal to the index notation expression: output(...) := I(i,j) * A(i,j,...)

Definition at line 466 of file isotropic_tensor.hpp.

double_dot() [3/5]

template<typename S , typename T , int m, int n>

constexpr auto smith::double_dot ( const tensor< S, m, n > &  A, const tensor< T, m, n > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

2nd-order-tensor : 2nd-order-tensor, like inner()

Definition at line 1044 of file tensor.hpp.

double_dot() [4/5]

template<typename S , typename T , int m, int n, int p>

constexpr SMITH_HOST_DEVICE auto smith::double_dot ( const tensor< S, m, n, p > &  A, const tensor< T, n, p > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

3rd-order-tensor : 2nd-order-tensor

Definition at line 1026 of file tensor.hpp.

double_dot() [5/5]

template<typename S , typename T , int m, int n, int p, int q>

constexpr SMITH_HOST_DEVICE auto smith::double_dot ( const tensor< S, m, n, p, q > &  A, const tensor< T, p, q > &  B  )

constexpr

double dot product, contracting over the two "middle" indices

Template Parameters

S	the underlying type of the tensor (lefthand) argument
T	the underlying type of the tensor (righthand) argument
m	first dimension of A
n	second dimension of A
p	third dimension of A, first dimensions of B
q	fourth dimension of A, second dimensions of B

Parameters

[in]	A	The lefthand tensor
[in]	B	The righthand tensor

Definition at line 1006 of file tensor.hpp.

dual()

template<typename T >

smith::dual	(	double	,
		T
	)		-> dual< T >

class template argument deduction guide for type dual.

Note

this lets users write

dual something{my_value, my_gradient}; 

instead of explicitly writing the template parameter

dual< decltype(my_gradient) > something{my_value, my_gradient}; 

eig_symm()

SMITH_HOST_DEVICE tuple<vec3, mat3> smith::eig_symm ( const mat3 &  A )

inline

Eigendecomposition for a symmetric 3x3 matrix

Parameters

A	Matrix for which the eigendecomposition will be computed. Must be symmetric, this is not checked.

Returns

tuple with the eigenvalues in the first element, and the matrix of eigenvectors (columnwise) in the second element.

Note

based on "A robust algorithm for finding the eigenvalues and eigenvectors of 3x3 symmetric matrices", by Scherzinger & Dohrmann

Definition at line 807 of file tuple_tensor_dual_functions.hpp.

eigenvalues()

template<typename T , int size>

auto smith::eigenvalues

(

const smith::tensor< T, size, size > &

A

)

compute the eigenvalues of a symmetric matrix A

Template Parameters

T	either double or a smith::dual type
size	the dimensions of the matrix

Parameters

A	the matrix

Returns

a vector of the eigenvalues of A (and their derivatives, if A contains dual numbers)

Definition at line 727 of file tuple_tensor_dual_functions.hpp.

elements_per_block()

template<mfem::Geometry::Type g>

constexpr SMITH_HOST_DEVICE int smith::elements_per_block ( int  q )

constexpr

this function returns information about how many elements should be processed by a single thread block in CUDA (note: the optimal values are hardware and problem specific, but these values are still significantly faster than naively allocating only 1 element / block)

Template Parameters

g	the element geometry

Parameters

q	the number of quadrature points per dimension

Returns

how many elements each thread block should process

Definition at line 140 of file finite_element.hpp.

exp_symm()

template<typename T >

auto smith::exp_symm

(

tensor< T, 3, 3 >

A

)

Exponential of a symmetric matrix.

Parameters

A	Matrix to operate on. Must be symmetric. This is not checked.

Returns

Exponential mapping of A.

Definition at line 1033 of file tuple_tensor_dual_functions.hpp.

factorial()

constexpr SMITH_HOST_DEVICE int smith::factorial ( int  n )

constexpr

compute n!

Parameters

[in]

n

Definition at line 374 of file polynomials.hpp.

factorize_lu()

template<typename T , int n>

constexpr SMITH_HOST_DEVICE LuFactorization<T, n> smith::factorize_lu ( const tensor< T, n, n > &  A )

constexpr

Compute LU factorization of a matrix with partial pivoting.

The convention followed is to place ones on the diagonal of the lower triangular factor.

Parameters

[in]

A

The matrix to factorize

Returns

An LuFactorization object

See also

LuFactorization

Definition at line 364 of file tuple_tensor_dual_functions.hpp.

find_root()

template<typename function , int n>

auto smith::find_root	(	const function &	f,
		tensor< double, n >	x0
	)

Finds a root of a vector-valued nonlinear function.

Uses Newton-Raphson iteration.

Template Parameters

function	Type for the functor object
n	Vector dimension of the equation

Parameters

f	A callable representing the function of which a root is sought. Must take an n-vector argument and return an n-vector
x0	Initial guess for root. Must be an n-vector.

Returns

A root of f.

Definition at line 697 of file tuple_tensor_dual_functions.hpp.

findDomainDofsOnNeighborRanks()

void smith::findDomainDofsOnNeighborRanks	(	const smith::fes_t *	fes,
		mfem::Array< int > &	local_dof_ids
	)

Get local dofs that are part of a domain, but are owned by a neighboring MPI rank.

This is necessary for situations like this: Mesh before parallel partition: 3 -----— 2 | /| | / | | / | | / | <– Edge we want in Domain | / | | / | | / | |/ | Node 0 -----— 1

Possible mesh after partition into two ranks:

RANK 0 RANK 1

3 -----— 2 2 o | / /| | / / | | / / | | / / | <– Edge we want in Domain | / / | | / / | | / / | |/ / | 0 * 0 o-----—* 1

*: locally owned node o: node owned by a neighbor rank

We create a domain containing the right vertical edge, and then ask for its local dofs. The dof list returned for Rank 1 will be correct, containing the local indices for nodes 1 and 2. However, the dof list on rank 0 will not be correct without parallel communication. It will see that it doesn't own the edge in question, so when it then goes to fetch the local dofs on the domain, it will be an empty list.

This function corrects for that, flagging the dofs we want on the domain on each rank (using the local_dof_ids list), and then exchanging this info with neighboring ranks, so that rank 0 will be told that its local dof for node 2 should be added to the list of dofs on the domain.

Before findDomainDofsOnNeighborRanks(): dof list on Rank 0: {} dof list on Rank 1: {1, 2}

After: dof list on Rank 0: {2} dof list on Rank 1: {1, 2}

Note: the sets will actually contain the ldof indices corresponding to the global (tdof) indices in the sets above.

This function operates on the local_dof_ids data in place.

Definition at line 436 of file domain.cpp.

fit()

template<int dim, typename signature , int... n, typename func , typename... T>

FiniteElementState smith::fit	(	func	f,
		mfem::ParMesh &	pmesh,
		const T &...	solution_fields
	)

determine field parameters to approximate the output of a user-provided q-function

Parameters

[in]	f	the user-provided function to approximate
[in]	pmesh	the region over which to approximate the function f
[in]	solution_fields	[optional] any auxiliary field quantities needed to evaluate f

Note

: mesh is passed by non-const ref because mfem mutates the mesh when creating ParGridFunctions

Definition at line 76 of file fit.hpp.

gather()

template<int d>

std::vector<tensor<double, d> > smith::gather	(	const mfem::Vector &	coordinates,
		mfem::Array< int >	ids
	)

gather vertex coordinates for a list of vertices

Parameters

coordinates	mfem's 1D list of vertex coordinates
ids	the list of vertex indices to gather

Definition at line 47 of file domain.cpp.

GaussLegendreInterpolation()

template<int n, typename T >

constexpr SMITH_HOST_DEVICE tensor<T, n> smith::GaussLegendreInterpolation ( [[maybe_unused] ] T  x )

constexpr

Lagrange Interpolating polynomials for nodes at Gauss-Legendre points on the interval [0, 1].

Do[xi = GaussianQuadratureWeights[n, 0, 1, 30][[All, 1]]; Print["if constexpr (n == " <> ToString[n] <> ") return " <> ToString[CForm /@ HornerForm /@ (InterpolatingPolynomial[Transpose[{xi, #}], x] & /@ IdentityMatrix[n])] <> ";"], {n, 1, 4} ]

note: the quadratic (n == 2) and cubic (n == 3) versions of this function only satisfied the kronecker delta property to an error of ~1.0e-13 and keeping more than 16 significant figures seems to help bring that error down to machine epsilon again.

Template Parameters

n	how many entries to compute

Parameters

[in]

x

where to evaluate the polynomials

Definition at line 558 of file polynomials.hpp.

GaussLegendreInterpolationDerivative()

template<int n, typename T >

constexpr SMITH_HOST_DEVICE tensor<T, n> smith::GaussLegendreInterpolationDerivative ( [[maybe_unused] ] T  x )

constexpr

Derivatives of the Lagrange Interpolating polynomials for nodes at Gauss-Legendre points on the interval [-1, 1].

Mathematica/Wolfram Language code to generate more entries in the table: Do[xi = GaussianQuadratureWeights[n, 0, 1, 30][[All, 1]]; Print["if constexpr (n == " <> ToString[n] <> ") return " <> ToString[CForm /@ HornerForm /@ (D[InterpolatingPolynomial[Transpose[{xi, #}], x], x] & /@ IdentityMatrix[n])] <> ";"], {n, 1, 4} ]

Template Parameters

n	how many entries to compute

Parameters

[in]

x

where to evaluate the polynomials

Definition at line 595 of file polynomials.hpp.

GaussLegendreNodes()

template<int n, mfem::Geometry::Type geom>

constexpr SMITH_HOST_DEVICE auto smith::GaussLegendreNodes ( )

constexpr

The positions of Gauss-Legendre points for different geometries.

Template Parameters

n	The number of points per dimension

Mathematica/Wolfram Language code to generate the 1D entries in the table: Do[Print["if constexpr (n == " <> ToString[n] <> ") return " <> ToString[GaussianQuadratureWeights[n, 0, 1, 17][[All, 1]]] <> ";"], {n, 1, 8}]

Definition at line 43 of file polynomials.hpp.

GaussLegendreWeights()

template<int n, mfem::Geometry::Type geom>

constexpr SMITH_HOST_DEVICE auto smith::GaussLegendreWeights ( )

constexpr

The weights associated with each Gauss-Legendre point.

Template Parameters

n	The number of points

Mathematica/Wolfram Language code to generate more entries in the table: Do[Print["if constexpr (n == " <> ToString[n] <> ") return " <> ToString[GaussianQuadratureWeights[n, 0, 1, 17][[All, 2]]] <> ";"], {n, 1, 8}]

Definition at line 272 of file polynomials.hpp.

GaussLobattoInterpolation()

template<int n, typename T >

constexpr SMITH_HOST_DEVICE tensor<T, n> smith::GaussLobattoInterpolation ( [[maybe_unused] ] T  x )

constexpr

Lagrange Interpolating polynomials for nodes at Gauss-Lobatto points on the interval [0, 1].

Template Parameters

n	how many entries to compute

Parameters

[in]

x

where to evaluate the polynomials

Definition at line 494 of file polynomials.hpp.

GaussLobattoInterpolationDerivative()

template<int n, typename T >

constexpr SMITH_HOST_DEVICE tensor<T, n> smith::GaussLobattoInterpolationDerivative ( [[maybe_unused] ] T  x )

constexpr

Derivatives of the Lagrange Interpolating polynomials for nodes at Gauss-Lobatto points on the interval [0, 1].

Template Parameters

n	how many entries to compute

Parameters

[in]

x

where to evaluate the polynomials

Definition at line 521 of file polynomials.hpp.

GaussLobattoNodes()

template<int n, typename T = double>

constexpr SMITH_HOST_DEVICE tensor<T, n> smith::GaussLobattoNodes ( T  a = T(0), T  b = T(1)  )

constexpr

The positions (in 1D space) of Gauss-Lobatto points.

Template Parameters

n	The number of points

Parameters

[in]	a	The left endpoint of the interval
[in]	b	The right endpoint of the interval

Definition at line 28 of file polynomials.hpp.

GaussQuadratureRule()

template<mfem::Geometry::Type g, int Q>

constexpr SMITH_HOST_DEVICE auto smith::GaussQuadratureRule ( )

constexpr

Returns the Gauss-Legendre quadrature rule for an element and order.

Template Parameters

The	shape of the element to produce a quadrature rule for
Q	the number of quadrature points per dimension

Definition at line 45 of file quadrature.hpp.

generate_bdr_kernels()

template<mfem::Geometry::Type geom, int Q, typename test , typename... trials, typename lambda_type >

void smith::generate_bdr_kernels	(	FunctionSignature< test(trials...)>	s,
		Integral &	integral,
		const lambda_type &	qf
	)

function to generate kernels held by an Integral object of type "BoundaryDomain", with a specific element type

Template Parameters

geom	the element geometry
Q	a parameter that controls the number of quadrature points
test	the kind of test functions used in the integral
trials	the trial space(s) of the integral's inputs
lambda_type	a callable object that implements the q-function concept

Parameters

s	an object used to pass around test/trial information
integral	the Integral object to initialize
qf	the quadrature function

Definition at line 290 of file integral.hpp.

generate_interior_face_kernels()

template<mfem::Geometry::Type geom, int Q, typename test , typename... trials, typename lambda_type >

void smith::generate_interior_face_kernels	(	FunctionSignature< test(trials...)>	s,
		Integral &	integral,
		const lambda_type &	qf
	)

function to generate kernels held by an Integral object of type "InteriorFaceDomain", with a specific element type

Template Parameters

geom	the element geometry
Q	a parameter that controls the number of quadrature points
test	the kind of test functions used in the integral
trials	the trial space(s) of the integral's inputs
lambda_type	a callable object that implements the q-function concept

Parameters

s	an object used to pass around test/trial information
integral	the Integral object to initialize
qf	the quadrature function

Definition at line 376 of file integral.hpp.

generate_kernels()

template<mfem::Geometry::Type geom, int Q, typename test , typename... trials, typename lambda_type , typename qpt_data_type >

void smith::generate_kernels	(	FunctionSignature< test(trials...)>	s,
		Integral &	integral,
		const lambda_type &	qf,
		std::shared_ptr< QuadratureData< qpt_data_type > >	qdata
	)

function to generate kernels held by an Integral object of type "Domain", with a specific element type

Template Parameters

geom	the element geometry
Q	a parameter that controls the number of quadrature points
test	the kind of test functions used in the integral
trials	the trial space(s) of the integral's inputs
lambda_type	a callable object that implements the q-function concept
qpt_data_type	any quadrature point data needed by the material model

Parameters

s	an object used to pass around test/trial information
integral	the Integral object to initialize
qf	the quadrature function
qdata	the values of any quadrature point data for the material

Definition at line 202 of file integral.hpp.

generateParFiniteElementSpace()

template<typename function_space >

std::pair<std::unique_ptr<mfem::ParFiniteElementSpace>, std::unique_ptr<mfem::FiniteElementCollection> > smith::generateParFiniteElementSpace ( mfem::ParMesh *  mesh )

inline

create an mfem::ParFiniteElementSpace from one of Smith's tag types: H1, Hcurl, L2

Template Parameters

function_space

a tag type containing the kind of function space and polynomial order

Parameters

mesh	the mesh on which the space is defined

Returns

a pair containing the new finite element space and associated finite element collection

Definition at line 113 of file functional.hpp.

geometry_counts() [1/2]

std::array<uint32_t, mfem::Geometry::NUM_GEOMETRIES> smith::geometry_counts ( const Domain &  domain )

inline

count the number of elements of each geometry in a domain

Parameters

domain

the domain to count

Definition at line 312 of file domain.hpp.

geometry_counts() [2/2]

std::array<uint32_t, mfem::Geometry::NUM_GEOMETRIES> smith::geometry_counts ( const mfem::Mesh &  mesh )

inline

count the number of elements of each geometry in a mesh

Parameters

mesh	the mesh to count

Definition at line 76 of file geometry.hpp.

get() [1/3]

template<int i, typename... T>

constexpr SMITH_HOST_DEVICE const auto& smith::get ( const tuple< T... > &  values )

constexpr

return a copy of the ith tuple entry

Template Parameters

i	the tuple index to access
T	the types stored in the tuple

Definition at line 327 of file tuple.hpp.

get() [2/3]

template<int i, typename... T>

constexpr SMITH_HOST_DEVICE auto& smith::get ( tuple< T... > &  values )

constexpr

return a reference to the ith tuple entry

Template Parameters

i	the tuple index to access
T	the types stored in the tuple

Definition at line 283 of file tuple.hpp.

get() [3/3]

template<typename T , typename T0 , typename T1 >

constexpr T& smith::get ( variant< T0, T1 > &  v )

constexpr

Returns the variant member of specified type.

Returns the variant member at the provided index.

Template Parameters

T	The type of the element to retrieve
T0	The first member type of the variant
T1	The second member type of the variant

Parameters

[in]

v

The variant to return the element of

See also

std::variant::get

Precondition

T must be either T0 or T1

Note

If T == T0 == T1, the element at index 0 will be returned

Definition at line 338 of file variant.hpp.

get_gradient() [1/4]

template<int... n>

constexpr SMITH_HOST_DEVICE auto smith::get_gradient ( const tensor< double, n... > &  )

constexpr

get the gradient of type tensor (note: since its stored type is not a dual number, the derivative term is identically zero)

Returns

The sentinel,

See also

zero

Definition at line 1843 of file tensor.hpp.

get_gradient() [2/4]

template<int... n>

constexpr SMITH_HOST_DEVICE auto smith::get_gradient ( const tensor< dual< double >, n... > &  arg )

constexpr

Retrieves a gradient tensor from a tensor of dual numbers.

Parameters

[in]

arg

The tensor of dual numbers

Definition at line 511 of file tuple_tensor_dual_functions.hpp.

get_gradient() [3/4]

SMITH_HOST_DEVICE auto smith::get_gradient ( double  )

inline

Retrieves the gradient component of a double (which is nothing)

Returns

The sentinel,

See also

zero

Definition at line 1835 of file tensor.hpp.

get_gradient() [4/4]

template<typename... T>

SMITH_HOST_DEVICE auto smith::get_gradient

(

dual< smith::tuple< T... >>

arg

)

Retrieves the gradient components of a set of dual numbers.

Parameters

[in]

arg

The set of numbers to retrieve gradients from

Definition at line 315 of file tuple_tensor_dual_functions.hpp.

get_if()

template<typename T , typename T0 , typename T1 >

T* smith::get_if

(

variant< T0, T1 > *

v

)

Returns the member of requested type if it's active, otherwise nullptr.

Template Parameters

T	The type to check for

Parameters

[in]

v

The variant to check/retrieve from

See also

std::get_if

Definition at line 398 of file variant.hpp.

get_value() [1/3]

template<typename... T>

SMITH_HOST_DEVICE auto smith::get_value

(

const smith::tuple< T... > &

tuple_of_values

)

Retrieves the value components of a set of (possibly dual) numbers.

Parameters

[in]

tuple_of_values

The tuple of numbers to retrieve values from

Precondition

The tuple must contain only scalars or tensors of dual numbers or doubles

Definition at line 304 of file tuple_tensor_dual_functions.hpp.

get_value() [2/3]

template<typename T , int... n>

SMITH_HOST_DEVICE auto smith::get_value

(

const tensor< dual< T >, n... > &

arg

)

Retrieves a value tensor from a tensor of dual numbers.

Parameters

[in]

arg

The tensor of dual numbers

Definition at line 499 of file tuple_tensor_dual_functions.hpp.

get_value() [3/3]

template<typename T1 , typename T2 , int n>

SMITH_HOST_DEVICE auto smith::get_value

(

const tensor< tuple< T1, T2 >, n > &

input

)

Extracts all of the values from a tensor of dual numbers.

Template Parameters

T1	the first type of the tuple stored in the tensor
T2	the second type of the tuple stored in the tensor
n	the number of entries in the input argument

Parameters

[in]

input

The tensor of dual numbers

Returns

the tensor of all of the values

Definition at line 289 of file tuple_tensor_dual_functions.hpp.

getMPIInfo()

std::pair< int, int > smith::getMPIInfo

(

MPI_Comm

comm = MPI_COMM_WORLD

)

Get MPI Info.

Returns

std::pair<int, int> Pair containing the number of MPI processes and ranks

Definition at line 237 of file about.cpp.

getSpaces()

std::vector<const mfem::ParFiniteElementSpace*> smith::getSpaces ( const std::vector< smith::FiniteElementState > &  states )

inline

Helper function to construct vector of spaces from an existing vector of FiniteElementState.

Parameters

states

vector of FiniteElementState

Definition at line 447 of file functional_weak_form.hpp.

gitSHA()

std::string smith::gitSHA

(

)

Returns a string for the Git SHA when the driver was built.

Note: This will not update unless you reconfigure CMake after a commit.

Returns

string value of the Git SHA if built in a Git repo, empty if not

Definition at line 192 of file about.cpp.

holds_alternative()

template<typename T , typename T0 , typename T1 >

bool smith::holds_alternative

(

const variant< T0, T1 > &

v

)

Checks whether a variant's active member is of a certain type.

Template Parameters

T	The type to check for

Parameters

[in]

v

The variant to check

See also

std::holds_alternative

Definition at line 381 of file variant.hpp.

I2()

template<typename T >

constexpr SMITH_HOST_DEVICE auto smith::I2 ( const tensor< T, 3, 3 > &  A )

constexpr

Returns the second invariant of a 3x3 matrix.

Parameters

[in]

A

The matrix

Definition at line 1291 of file tensor.hpp.

Identity()

template<int m>

constexpr SMITH_HOST_DEVICE isotropic_tensor<double, m, m> smith::Identity ( )

constexpr

return the identity matrix of the specified size

Template Parameters

m	the number of rows and columns

Definition at line 61 of file isotropic_tensor.hpp.

index_of_differentiation()

template<typename... T>

constexpr uint32_t smith::index_of_differentiation ( )

constexpr

given a list of types, this function returns the index that corresponds to the type dual_vector.

Template Parameters

T	a list of types, containing at most 1 differentiate_wrt_this

e.g.

static_assert(index_of_dual_vector < foo, bar, differentiate_wrt_this, baz, qux >() == 2);

Definition at line 59 of file functional.hpp.

inner() [1/12]

template<typename S , typename T >

constexpr SMITH_HOST_DEVICE auto smith::inner ( const dual< S > &  A, const dual< T > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for zeroth-order tensors (scalars)

Definition at line 281 of file dual.hpp.

inner() [2/12]

template<typename S >

constexpr SMITH_HOST_DEVICE auto smith::inner ( const dual< S > &  A, double  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for zeroth-order tensors (scalars)

Definition at line 301 of file dual.hpp.

inner() [3/12]

template<typename S , int m>

constexpr SMITH_HOST_DEVICE auto smith::inner ( const tensor< S, m > &  , zero    )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for first order tensors (vectors)

Definition at line 720 of file tensor.hpp.

inner() [4/12]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::inner ( const tensor< S, m > &  A, const tensor< T, m > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for first order tensors (vectors)

Definition at line 688 of file tensor.hpp.

inner() [5/12]

template<typename S , int m, int n>

constexpr SMITH_HOST_DEVICE auto smith::inner ( const tensor< S, m, n > &  , zero    )

constexpr

this function contracts over all indices of the two tensor arguments

Template Parameters

S	the underlying type of the tensor (lefthand) argument
m	the number of rows
n	the number of columns

Definition at line 710 of file tensor.hpp.

inner() [6/12]

template<typename S , typename T , int m, int n>

constexpr SMITH_HOST_DEVICE auto smith::inner ( const tensor< S, m, n > &  A, const tensor< T, m, n > &  B  )

constexpr

this function contracts over all indices of the two tensor arguments

Template Parameters

S	the underlying type of the tensor (lefthand) argument
T	the underlying type of the tensor (righthand) argument
m	the number of rows
n	the number of columns

Parameters

[in]	A	The lefthand tensor
[in]	B	The righthand tensor

Definition at line 672 of file tensor.hpp.

inner() [7/12]

template<typename T >

constexpr SMITH_HOST_DEVICE auto smith::inner ( double  A, const dual< T > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for zeroth-order tensors (scalars)

Definition at line 291 of file dual.hpp.

inner() [8/12]

constexpr SMITH_HOST_DEVICE auto smith::inner ( double  A, double  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for zeroth-order tensors (scalars)

Definition at line 701 of file tensor.hpp.

inner() [9/12]

constexpr SMITH_HOST_DEVICE auto smith::inner ( double  , zero    )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for zeroth-order tensors (scalars)

Definition at line 729 of file tensor.hpp.

inner() [10/12]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::inner ( zero  , const tensor< T, m > &    )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for first order tensors (vectors)

Definition at line 748 of file tensor.hpp.

inner() [11/12]

template<typename T , int m, int n>

constexpr SMITH_HOST_DEVICE auto smith::inner ( zero  , const tensor< T, m, n > &    )

constexpr

this function contracts over all indices of the two tensor arguments

Template Parameters

T	the underlying type of the tensor (righthand) argument
m	the number of rows
n	the number of columns

Definition at line 738 of file tensor.hpp.

inner() [12/12]

constexpr SMITH_HOST_DEVICE auto smith::inner ( zero  , double    )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

for zeroth-order tensors (scalars)

Definition at line 757 of file tensor.hpp.

innerProduct()

double smith::innerProduct	(	const FiniteElementVector &	vec1,
		const FiniteElementVector &	vec2
	)

Find the inner prodcut between two finite element vectors across all dofs.

Parameters

vec1	The first vector
vec2	The second vector

Returns

The inner prodcut between finite element vectors

Definition at line 144 of file finite_element_vector.cpp.

inv() [1/5]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::inv ( const isotropic_tensor< T, m, m > &  I )

constexpr

return the inverse of an isotropic tensor

Template Parameters

T	the types stored in the isotropic tensor
m	the number of rows and columns in I

Parameters

I	the isotropic tensor to compute the inverse of

Returns

the inverse of I

Definition at line 298 of file isotropic_tensor.hpp.

inv() [2/5]

constexpr SMITH_HOST_DEVICE tensor<double, 2, 2> smith::inv ( const tensor< double, 2, 2 > &  A )

constexpr

Inverts a matrix.

Parameters

[in]

A

The matrix to invert

Note

Uses a shortcut for inverting a 2-by-2 matrix

Definition at line 1652 of file tensor.hpp.

inv() [3/5]

constexpr SMITH_HOST_DEVICE tensor<double, 3, 3> smith::inv ( const tensor< double, 3, 3 > &  A )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

Uses a shortcut for inverting a 3-by-3 matrix

Definition at line 1670 of file tensor.hpp.

inv() [4/5]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto smith::inv ( const tensor< T, n, n > &  A )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

For N-by-N matrices with N > 3, requires Gaussian elimination with partial pivoting

Definition at line 1694 of file tensor.hpp.

inv() [5/5]

template<typename gradient_type , int n>

constexpr SMITH_HOST_DEVICE auto smith::inv ( tensor< dual< gradient_type >, n, n >  A )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

when inverting a tensor of dual numbers, hardcode the analytic derivative of the inverse of a square matrix, rather than apply gauss elimination directly on the dual number types

TODO: compare performance of this hardcoded implementation to just using inv() directly

Definition at line 479 of file tuple_tensor_dual_functions.hpp.

is_symmetric()

template<int n>

SMITH_HOST_DEVICE bool smith::is_symmetric	(	tensor< double, n, n >	A,
		double	tolerance = 1.0e-8
	)

Return whether a square rank 2 tensor is symmetric.

Template Parameters

n	The height of the tensor

Parameters

A	The square rank 2 tensor
tolerance	The tolerance to check for symmetry

Returns

Whether the square rank 2 tensor (matrix) is symmetric

Definition at line 1492 of file tensor.hpp.

is_symmetric_and_positive_definite()

SMITH_HOST_DEVICE bool smith::is_symmetric_and_positive_definite ( tensor< double, 2, 2 >  A )

inline

Return whether a matrix is symmetric and positive definite This check uses Sylvester's criterion, checking that each upper left subtensor has a determinant greater than zero.

Parameters

A	The matrix to test for positive definiteness

Returns

Whether the matrix is positive definite

Definition at line 1512 of file tensor.hpp.

leading_dimension()

template<typename T , int m, int... n>

constexpr SMITH_HOST_DEVICE int smith::leading_dimension ( tensor< T, m, n... >  )

constexpr

a function for querying the first dimension of a tensor

Template Parameters

T	the datatype stored in the tensor
m	the first dimension of the tensor
n	the trailing dimensions of the tensor

Returns

m

Definition at line 1977 of file tensor.hpp.

Legendre()

template<int n, typename T >

SMITH_HOST_DEVICE tensor<T, n> smith::Legendre

(

T

x

)

Legendre Polynomials, orthogonal on the domain (-1, 1) with unit weight function.

Template Parameters

n	how many entries to compute

Parameters

[in]

x

where to evaluate the polynomials

Definition at line 448 of file polynomials.hpp.

linear_solve() [1/3]

template<typename S , typename T , int n, int... m>

constexpr SMITH_HOST_DEVICE auto smith::linear_solve ( const LuFactorization< S, n > &  lu_factors, const tensor< T, n, m... > &  b  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

For use with a matrix that has already been factorized

Definition at line 1626 of file tensor.hpp.

linear_solve() [2/3]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto smith::linear_solve ( const LuFactorization< T, n > &  , const  zero  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

Shortcut for case of zero rhs

Definition at line 1642 of file tensor.hpp.

linear_solve() [3/3]

template<typename S , typename T , int n, int... m>

constexpr SMITH_HOST_DEVICE auto smith::linear_solve ( const tensor< S, n, n > &  A, const tensor< T, n, m... > &  b  )

constexpr

Solves Ax = b for x using Gaussian elimination with partial pivoting.

Parameters

[in]	A	The coefficient matrix A
[in]	b	The righthand side vector b

Returns

x The solution vector

Definition at line 425 of file tuple_tensor_dual_functions.hpp.

log_symm()

template<typename T >

auto smith::log_symm

(

tensor< T, 3, 3 >

A

)

Logarithm of a symmetric matrix.

Parameters

A	Matrix to operate on. Must be SPD. This is not checked.

Returns

The logarithmic mapping of A.

Definition at line 1013 of file tuple_tensor_dual_functions.hpp.

make_dual() [1/2]

template<int... n>

constexpr SMITH_HOST_DEVICE auto smith::make_dual ( const tensor< double, n... > &  A )

constexpr

Constructs a tensor of dual numbers from a tensor of values.

Parameters

[in]

A

The tensor of values

Note

a d-order tensor's gradient will be initialized to the (2*d)-order identity tensor

Definition at line 344 of file tuple_tensor_dual_functions.hpp.

make_dual() [2/2]

template<typename T0 , typename T1 >

constexpr SMITH_HOST_DEVICE auto smith::make_dual ( const tuple< T0, T1 > &  args )

constexpr

Promote a tuple of values to their corresponding dual types.

Template Parameters

T0	the first type of the tuple argument
T1	the first type of the tuple argument

Parameters

args	the values to be promoted

example:

smith::tuple < double, tensor< double, 3 > > f{};
 
smith::tuple <
  dual < smith::tuple < double, zero > >
  tensor < dual < smith::tuple < zero, tensor< double, 3 > >, 3 >
> dual_of_f = make_dual(f);

Definition at line 188 of file tuple_tensor_dual_functions.hpp.

make_dual_helper() [1/2]

template<int i, int N, typename T , int... n>

constexpr SMITH_HOST_DEVICE auto smith::make_dual_helper ( const tensor< T, n... > &  arg )

constexpr

promote a tensor value to dual number with a one_hot_t< i, N, tensor > gradient type

Template Parameters

i	the index where the non-smith::zero derivative term appears
N	how many entries in the gradient type

Parameters

arg	the value to be promoted

Definition at line 159 of file tuple_tensor_dual_functions.hpp.

make_dual_helper() [2/2]

template<int i, int N>

constexpr SMITH_HOST_DEVICE auto smith::make_dual_helper ( double  arg )

constexpr

promote a double value to dual number with a one_hot_t< i, N, double > gradient type

Template Parameters

i	the index where the non-smith::zero derivative term appears
N	how many entries in the gradient type

Parameters

arg	the value to be promoted

Definition at line 142 of file tuple_tensor_dual_functions.hpp.

make_dual_wrt()

template<int n, typename... T>

constexpr auto smith::make_dual_wrt ( const smith::tuple< T... > &  args )

constexpr

take a tuple of values, and promote the nth one to a one-hot dual number of the appropriate type

Template Parameters

n	the index of the tuple argument to be made into a dual number
T	the types of the values in the tuple

Parameters

args	the values to be promoted

Definition at line 274 of file tuple_tensor_dual_functions.hpp.

make_tensor() [1/5]

template<typename lambda_type >

SMITH_SUPPRESS_NVCC_HOSTDEVICE_WARNING constexpr SMITH_HOST_DEVICE auto smith::make_tensor ( lambda_type  f )

constexpr

Creates a tensor of requested dimension by subsequent calls to a functor Can be thought of as analogous to std::transform in that the set of possible indices for dimensions n are transformed into the values of the tensor by f.

Template Parameters

lambda_type

The type of the functor

Parameters

[in]

f

The functor to generate the tensor values from

Note

the different cases of 0D, 1D, 2D, 3D, and 4D are implemented separately to work around a limitation in nvcc involving host device lambdas with auto parameters.

Definition at line 304 of file tensor.hpp.

make_tensor() [2/5]

template<int n1, typename lambda_type >

SMITH_SUPPRESS_NVCC_HOSTDEVICE_WARNING constexpr SMITH_HOST_DEVICE auto smith::make_tensor ( lambda_type  f )

constexpr

Creates a tensor of requested dimension by subsequent calls to a functor.

Template Parameters

n1	The dimension of the tensor
lambda_type	The type of the functor

Parameters

[in]

f

The functor to generate the tensor values from

Precondition

f must accept n1 arguments of type int

Note

the different cases of 0D, 1D, 2D, 3D, and 4D are implemented separately to work around a limitation in nvcc involving host device lambdas with auto parameters.

Definition at line 323 of file tensor.hpp.

make_tensor() [3/5]

template<int n1, int n2, typename lambda_type >

SMITH_SUPPRESS_NVCC_HOSTDEVICE_WARNING constexpr SMITH_HOST_DEVICE auto smith::make_tensor ( lambda_type  f )

constexpr

Creates a tensor of requested dimension by subsequent calls to a functor.

Template Parameters

n1	The first dimension of the tensor
n2	The second dimension of the tensor
lambda_type	The type of the functor

Parameters

[in]

f

The functor to generate the tensor values from

Precondition

f must accept n1 x n2 arguments of type int

Note

the different cases of 0D, 1D, 2D, 3D, and 4D are implemented separately to work around a limitation in nvcc involving host device lambdas with auto parameters.

Definition at line 347 of file tensor.hpp.

make_tensor() [4/5]

template<int n1, int n2, int n3, typename lambda_type >

SMITH_SUPPRESS_NVCC_HOSTDEVICE_WARNING constexpr SMITH_HOST_DEVICE auto smith::make_tensor ( lambda_type  f )

constexpr

Creates a tensor of requested dimension by subsequent calls to a functor.

Template Parameters

n1	The first dimension of the tensor
n2	The second dimension of the tensor
n3	The third dimension of the tensor
lambda_type	The type of the functor

Parameters

[in]

f

The functor to generate the tensor values from

Precondition

f must accept n1 x n2 x n3 arguments of type int

Note

the different cases of 0D, 1D, 2D, 3D, and 4D are implemented separately to work around a limitation in nvcc involving host device lambdas with auto parameters.

Definition at line 374 of file tensor.hpp.

make_tensor() [5/5]

template<int n1, int n2, int n3, int n4, typename lambda_type >

SMITH_SUPPRESS_NVCC_HOSTDEVICE_WARNING constexpr SMITH_HOST_DEVICE auto smith::make_tensor ( lambda_type  f )

constexpr

Creates a tensor of requested dimension by subsequent calls to a functor.

Template Parameters

n1	The first dimension of the tensor
n2	The second dimension of the tensor
n3	The third dimension of the tensor
n4	The fourth dimension of the tensor
lambda_type	The type of the functor

Parameters

[in]

f

The functor to generate the tensor values from

Precondition

f must accept n1 x n2 x n3 x n4 arguments of type int

Note

the different cases of 0D, 1D, 2D, 3D, and 4D are implemented separately to work around a limitation in nvcc involving host device lambdas with auto parameters.

Definition at line 404 of file tensor.hpp.

make_tuple()

template<typename... T>

SMITH_HOST_DEVICE tuple<T...> smith::make_tuple

(

const T &...

args

)

helper function for combining a list of values into a tuple

Template Parameters

T	types of the values to be tuple-d

Parameters

args	the actual values to be put into a tuple

Definition at line 266 of file tuple.hpp.

MakeBoundaryIntegral()

template<typename s , int Q, int dim, typename lambda_type >

Integral smith::MakeBoundaryIntegral	(	const Domain &	domain,
		const lambda_type &	qf,
		std::vector< uint32_t >	argument_indices
	)

function to generate kernels held by an Integral object of type "Boundary", for all element types

Template Parameters

s	a function signature type containing test/trial space informationa type containing a function signature
Q	a parameter that controls the number of quadrature points
dim	the dimension of the domain
lambda_type	a callable object that implements the q-function concept

Parameters

domain	the domain of integration
qf	the quadrature function
argument_indices	the indices of trial space arguments used in the Integral

Returns

Integral the initialized Integral object

Note

this function is not meant to be called by users

Definition at line 341 of file integral.hpp.

MakeDomainIntegral()

template<typename s , int Q, int dim, typename lambda_type , typename qpt_data_type >

Integral smith::MakeDomainIntegral	(	const Domain &	domain,
		const lambda_type &	qf,
		std::shared_ptr< QuadratureData< qpt_data_type > >	qdata,
		std::vector< uint32_t >	argument_indices
	)

function to generate kernels held by an Integral object of type "Domain", for all element types

Template Parameters

s	a function signature type containing test/trial space informationa type containing a function signature
Q	a parameter that controls the number of quadrature points
dim	the dimension of the domain
lambda_type	a callable object that implements the q-function concept
qpt_data_type	any quadrature point data needed by the material model

Parameters

domain	the domain of integration
qf	the quadrature function
qdata	the values of any quadrature point data for the material
argument_indices	the indices of trial space arguments used in the Integral

Returns

Integral the initialized Integral object

Definition at line 253 of file integral.hpp.

MakeInteriorFaceIntegral()

template<typename s , int Q, int dim, typename lambda_type >

Integral smith::MakeInteriorFaceIntegral	(	const Domain &	domain,
		const lambda_type &	qf,
		std::vector< uint32_t >	argument_indices
	)

function to generate kernels held by an Integral object of type "Boundary", for all element types

Template Parameters

s	a function signature type containing test/trial space informationa type containing a function signature
Q	a parameter that controls the number of quadrature points
dim	the dimension of the domain
lambda_type	a callable object that implements the q-function concept

Parameters

domain	the domain of integration
qf	the quadrature function
argument_indices	the indices of trial space arguments used in the Integral

Returns

Integral the initialized Integral object

Note

this function is not meant to be called by users

Definition at line 427 of file integral.hpp.

matrix_sqrt()

template<typename T , int dim>

auto smith::matrix_sqrt

(

const tensor< T, dim, dim > &

A

)

compute the matrix square root of a square, real-valued, symmetric matrix i.e. given A, find B such that A = dot(B, B)

Template Parameters

T	the data type stored in each element of the matrix

Parameters

A	the matrix to compute the square root of

Returns

a square matrix, B, of the same type as A satisfying dot(B, B) == A

Definition at line 1366 of file tensor.hpp.

max() [1/2]

double smith::max

(

const FiniteElementVector &

fe_vector

)

Find the max value of a finite element vector across all dofs.

Parameters

fe_vector

The state variable to compute a max of

Returns

The max value

Note

This acts on the actual scalar degree of freedom values, not the interpolated shape function values. This implies these may or may not be nodal averages depending on the choice of finite element basis.

Definition at line 128 of file finite_element_vector.cpp.

max() [2/2]

template<typename gradient_type >

SMITH_HOST_DEVICE auto smith::max	(	dual< gradient_type >	a,
		double	b
	)

Implementation of max for dual numbers.

Note

This is not differentiable at a == b. At that point, the gradient is calculated as the gradient of b.

Definition at line 229 of file dual.hpp.

min() [1/2]

double smith::min

(

const FiniteElementVector &

fe_vector

)

Find the min value of a finite element vector across all dofs.

Parameters

fe_vector

The state variable to compute a min of

Returns

The min value

Note

This acts on the actual scalar degree of freedom values, not the interpolated shape function values. This implies these may or may not be nodal averages depending on the choice of finite element basis.

Definition at line 136 of file finite_element_vector.cpp.

min() [2/2]

template<typename gradient_type >

SMITH_HOST_DEVICE auto smith::min	(	dual< gradient_type >	a,
		double	b
	)

Implementation of min for dual numbers.

Note

This is not differentiable at a == b. At that point, the gradient is calculated as the gradient of b.

Definition at line 255 of file dual.hpp.

minus_equals_helper()

template<typename... T, int... i>

constexpr SMITH_HOST_DEVICE void smith::minus_equals_helper ( tuple< T... > &  x, const tuple< T... > &  y, std::integer_sequence< int, i... >    )

constexpr

A helper function for the -= operator of tuples.

Template Parameters

T	the types stored in the tuples x and y
i	integer sequence used to index the tuples

Parameters

x	tuple of values to be subracted from
y	tuple of values to subtract from x

Definition at line 481 of file tuple.hpp.

minus_helper()

template<typename... S, typename... T, int... i>

constexpr SMITH_HOST_DEVICE auto smith::minus_helper ( const tuple< S... > &  x, const tuple< T... > &  y, std::integer_sequence< int, i... >    )

constexpr

A helper function for the - operator of tuples.

Template Parameters

S	the types stored in the tuple x
T	the types stored in the tuple y
i	The integer sequence to i

Parameters

x	tuple of values
y	tuple of values

Returns

the returned tuple difference

Definition at line 510 of file tuple.hpp.

mult_helper() [1/3]

template<typename... T, int... i>

constexpr SMITH_HOST_DEVICE auto smith::mult_helper ( const double  a, const tuple< T... > &  x, std::integer_sequence< int, i... >    )

constexpr

A helper function for the * operator of tuples.

Template Parameters

T	the types stored in the tuple y
i	The integer sequence to i

Parameters

x	tuple of values
a	a constant multiplier

Returns

the returned tuple product

Definition at line 681 of file tuple.hpp.

mult_helper() [2/3]

template<typename... S, typename... T, int... i>

constexpr SMITH_HOST_DEVICE auto smith::mult_helper ( const tuple< S... > &  x, const tuple< T... > &  y, std::integer_sequence< int, i... >    )

constexpr

A helper function for the * operator of tuples.

Template Parameters

S	the types stored in the tuple x
T	the types stored in the tuple y
i	The integer sequence to i

Parameters

x	tuple of values
y	tuple of values

Returns

the returned tuple product

Definition at line 651 of file tuple.hpp.

mult_helper() [3/3]

template<typename... T, int... i>

constexpr SMITH_HOST_DEVICE auto smith::mult_helper ( const tuple< T... > &  x, const double  a, std::integer_sequence< int, i... >    )

constexpr

A helper function for the * operator of tuples.

Template Parameters

T	the types stored in the tuple y
i	The integer sequence to i

Parameters

x	tuple of values
a	a constant multiplier

Returns

the returned tuple product

Definition at line 696 of file tuple.hpp.

nonlinearSolve()

FieldState smith::nonlinearSolve	(	const WeakForm *	residual_eval,
		const FieldState &	shape_disp,
		const std::vector< FieldState > &	states,
		const std::vector< FieldState > &	params,
		const std::vector< double > &	state_update_weights,
		size_t	primal_solve_state_index,
		size_t	dirichlet_state_index,
		const TimeInfo &	time_info,
		const DifferentiableSolver *	solver,
		const BoundaryConditionManager *	bc_manager,
		const FieldState *	bc_field = nullptr
	)

Solve a nonlinear system of equations as defined by the weak form.

Parameters

residual_eval	The weak form which defines the equations to be solved
shape_disp	The mesh-morphed shape displacement
states	The time varying states as inputs to the weak form
params	The fixed field parameters as inputs to the weak form
state_update_weights	Specifies how to blend the arguments of the weak form into a unique unknown. The primary unknown, p, is states[primal_solve_state_index]. However, other arguments to the weak form may also depend on this unknown. The state_update_weights specify how this is done. For a nonzero weight, the field argument i is assumed to change as states[i] + (p - p_initial) * state_update_weights[i].
primal_solve_state_index	Index specifying which of the states is the primary unknown.
dirichlet_state_index	Index specifying which field has the Dirichlet boundary conditions applied to it. Typically this will be the same as the primal_solve_state_index, but it can be different. An example is explicit dynamics, where the unknown is the acceleration, and the boundary conditions are often applied directly to the displacement field.
time_info	Timestep information (time, dt, cycle)
solver	The differentiable, potentially nonlinear, equation solver used to solve the system of equations
bc_manager	Holds information about which degrees of freedom (DOFS)
bc_field	A field which holds to desired values for the fixed degrees of freedom as specified by the bc_manager

Returns

The field solution to the weak form

Definition at line 48 of file nonlinear_solve.cpp.

norm() [1/3]

double smith::norm	(	const FiniteElementState &	state,
		const double	p = 2
	)

Find the Lp norm of a finite element state across all dofs.

Parameters

state	The state variable to compute a norm of
p	The order norm to compute

Returns

The Lp norm of the finite element state

Definition at line 104 of file finite_element_state.cpp.

norm() [2/3]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::norm ( const isotropic_tensor< T, m, m > &  I )

constexpr

compute the Frobenius norm (sqrt(tr(dot(transpose(I), I)))) of an isotropic tensor

Template Parameters

T	the types stored in the isotropic tensor
m	the number of rows and columns in I

Parameters

I	the isotropic tensor to compute the norm of

Definition at line 324 of file isotropic_tensor.hpp.

norm() [3/3]

template<typename T , int... n>

SMITH_HOST_DEVICE auto smith::norm

(

const tensor< T, n... > &

A

)

Returns the Frobenius norm of the tensor.

Parameters

[in]

A

The tensor to obtain the norm from

Definition at line 1105 of file tensor.hpp.

normalize()

template<typename T , int... n>

SMITH_HOST_DEVICE auto smith::normalize

(

const tensor< T, n... > &

A

)

Normalizes the tensor Each element is divided by the Frobenius norm of the tensor,.

See also

norm

Parameters

[in]

A

The tensor to normalize

Definition at line 1122 of file tensor.hpp.

num_quadrature_points()

constexpr int smith::num_quadrature_points ( mfem::Geometry::Type  g, int  Q  )

constexpr

return the number of quadrature points in a Gauss-Legendre rule with parameter "Q"

Template Parameters

g	the element geometry
Q	the number of quadrature points per dimension

Definition at line 31 of file geometry.hpp.

operator*() [1/7]

template<typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator* ( const double  a, const tuple< T... > &  x  )

constexpr

multiply each component of x by the value a on the left

Template Parameters

T	the types stored in the tuple

Parameters

a	a scaling factor
x	the tuple object

Definition at line 708 of file tuple.hpp.

operator*() [2/7]

template<typename S , typename T , int m, int... n, typename = std::enable_if_t<std::is_arithmetic_v<S> || is_dual_number<S>::value>>

constexpr SMITH_HOST_DEVICE auto smith::operator* ( const tensor< T, m, n... > &  A, S  scale  )

constexpr

multiply a tensor by a scalar value

Template Parameters

S	the scalar value type. Must be arithmetic (e.g. float, double, int) or a dual number
T	the underlying type of the tensor (righthand) argument
n	integers describing the tensor shape

Parameters

[in]	A	The tensor to be scaled
[in]	scale	The scaling factor

Definition at line 58 of file tuple_tensor_dual_functions.hpp.

operator*() [3/7]

template<typename... S, typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator* ( const tuple< S... > &  x, const tuple< T... > &  y  )

constexpr

return a tuple of values defined by elementwise multiplication of x and y

Template Parameters

S	the types stored in the tuple x
T	the types stored in the tuple y

Parameters

x	a tuple of values
y	a tuple of values

Definition at line 665 of file tuple.hpp.

operator*() [4/7]

template<typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator* ( const tuple< T... > &  x, const double  a  )

constexpr

multiply each component of x by the value a on the right

Template Parameters

T	the types stored in the tuple

Parameters

x	the tuple object
a	a scaling factor

Definition at line 720 of file tuple.hpp.

operator*() [5/7]

template<typename S , typename T , int m, int... n, typename = std::enable_if_t<std::is_arithmetic_v<S> || is_dual_number<S>::value>>

constexpr SMITH_HOST_DEVICE auto smith::operator* ( S  scale, const tensor< T, m, n... > &  A  )

constexpr

multiply a tensor by a scalar value

Template Parameters

S	the scalar value type. Must be arithmetic (e.g. float, double, int) or a dual number
T	the underlying type of the tensor (righthand) argument
n	integers describing the tensor shape

Parameters

[in]	scale	The scaling factor
[in]	A	The tensor to be scaled

Definition at line 39 of file tuple_tensor_dual_functions.hpp.

operator*() [6/7]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::operator* ( S  scale, isotropic_tensor< T, m, m >  I  )

constexpr

scalar multiplication

Template Parameters

S	the type of the left operand, scale
T	the type of the isotropic tensor
m	the number of rows and columns in the isotropic tensor

Parameters

scale	the value that multiplies each entry of I (from the left)
I	the isotropic tensor being scaled

Returns

a new isotropic tensor equal to the product of scale * I

Definition at line 77 of file isotropic_tensor.hpp.

operator*() [7/7]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::operator* ( S  scale, isotropic_tensor< T, m, m, m, m >  I  )

constexpr

scalar multiplication

Template Parameters

S	the type of the left operand, scale
T	the type of the isotropic tensor
m	the dimension of each rank-4 isotropic tensor

Parameters

scale	the value that multiplies each entry of I (from the left)
I	the isotropic tensor being scaled

Returns

a new isotropic tensor equal to the product of scale * I

Definition at line 410 of file isotropic_tensor.hpp.

operator+() [1/7]

Components smith::operator+ ( Component  i, Component  j  )

inline

Construct a Components object from the sum of individual vector components.

See docstring on function declaration.

Definition at line 56 of file components.hpp.

operator+() [2/7]

Components smith::operator+ ( Component  i, Components  c  )

inline

Add an additional component to the set of flagged Components.

See docstring on function definition.

Definition at line 59 of file components.hpp.

operator+() [3/7]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::operator+ ( const isotropic_tensor< S, m, m > &  I, const tensor< T, m, m > &  A  )

constexpr

sum of isotropic and (nonisotropic) tensor

Template Parameters

S	the type of the left isotropic tensor
T	the type of the right tensor
m	the number of rows and columns in each tensor

Parameters

I	the left operand
A	the (full) right operand

Returns

a new tensor equal to the sum of I and A

Definition at line 132 of file isotropic_tensor.hpp.

operator+() [4/7]

template<typename S , typename T , int m, int... n>

constexpr SMITH_HOST_DEVICE auto smith::operator+ ( const tensor< S, m, n... > &  A, const tensor< T, m, n... > &  B  )

constexpr

return the sum of two tensors

Template Parameters

S	the underlying type of the lefthand argument
T	the underlying type of the righthand argument
n	integers describing the tensor shape

Parameters

[in]	A	The lefthand operand
[in]	B	The righthand operand

Definition at line 429 of file tensor.hpp.

operator+() [5/7]

template<typename... S, typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator+ ( const tuple< S... > &  x, const tuple< T... > &  y  )

constexpr

return a tuple of values defined by elementwise sum of x and y

Template Parameters

S	the types stored in the tuple x
T	the types stored in the tuple y

Parameters

x	a tuple of values
y	a tuple of values

Definition at line 439 of file tuple.hpp.

operator+() [6/7]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::operator+ ( isotropic_tensor< S, m, m >  I1, isotropic_tensor< T, m, m >  I2  )

constexpr

addition of isotropic tensors

Template Parameters

S	the type of the left isotropic tensor
T	the type of the right isotropic tensor
m	the number of rows and columns in each isotropic tensor

Parameters

I1	the left operand
I2	the right operand

Returns

a new isotropic tensor equal to the sum of I1 and I2

Definition at line 100 of file isotropic_tensor.hpp.

operator+() [7/7]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::operator+ ( isotropic_tensor< S, m, m, m, m >  I1, isotropic_tensor< T, m, m, m, m >  I2  )

constexpr

addition of isotropic tensors

Template Parameters

S	the type of the left isotropic tensor
T	the type of the right isotropic tensor
m	the dimension of each rank-4 isotropic tensor

Parameters

I1	the left operand
I2	the right operand

Returns

a new isotropic tensor equal to the sum of I1 and I2

Definition at line 433 of file isotropic_tensor.hpp.

operator+=() [1/7]

template<typename S , typename T , int m, int... n>

constexpr SMITH_HOST_DEVICE auto& smith::operator+= ( tensor< S, m, n... > &  A, const tensor< T, m, n... > &  B  )

constexpr

compound assignment (+) on tensors

Template Parameters

S	the underlying type of the tensor (lefthand) argument
T	the underlying type of the tensor (righthand) argument
n	integers describing the tensor shape

Parameters

[in]	A	The lefthand tensor
[in]	B	The righthand tensor

Definition at line 481 of file tensor.hpp.

operator+=() [2/7]

template<typename T >

constexpr SMITH_HOST_DEVICE auto& smith::operator+= ( tensor< T, 1 > &  A, const T &  B  )

constexpr

compound assignment (+) on tensors

Template Parameters

T	the underlying type of the tensor argument

Parameters

[in]	A	The lefthand tensor
[in]	B	The righthand tensor

Definition at line 540 of file tensor.hpp.

operator+=() [3/7]

template<typename T >

constexpr SMITH_HOST_DEVICE auto& smith::operator+= ( tensor< T, 1, 1 > &  A, const T &  B  )

constexpr

compound assignment (+) on tensors

Template Parameters

T	the underlying type of the tensor argument

Parameters

[in]	A	The lefthand tensor
[in]	B	The righthand tensor

Definition at line 552 of file tensor.hpp.

operator+=() [4/7]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto& smith::operator+= ( tensor< T, 1, n > &  A, const tensor< T, n > &  B  )

constexpr

compound assignment (+) on tensors

Template Parameters

T	the underlying type of the tensor argument

Parameters

[in]	A	The lefthand tensor
[in]	B	The righthand tensor

Definition at line 525 of file tensor.hpp.

operator+=() [5/7]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto& smith::operator+= ( tensor< T, n, 1 > &  A, const tensor< T, n > &  B  )

constexpr

compound assignment (+) on tensors

Template Parameters

T	the underlying type of the tensor argument

Parameters

[in]	A	The lefthand tensor
[in]	B	The righthand tensor

Definition at line 510 of file tensor.hpp.

operator+=() [6/7]

template<typename T , int... n>

constexpr SMITH_HOST_DEVICE auto& smith::operator+= ( tensor< T, n... > &  A, zero    )

constexpr

compound assignment (+) between a tensor and zero (no-op)

Template Parameters

T	the underlying type of the tensor (righthand) argument
n	integers describing the tensor shape

Parameters

[in]

A

The lefthand tensor

Definition at line 564 of file tensor.hpp.

operator+=() [7/7]

template<typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator+= ( tuple< T... > &  x, const tuple< T... > &  y  )

constexpr

add values contained in y, to the tuple x

Template Parameters

T	the types stored in the tuples x and y

Parameters

x	a tuple of values
y	a tuple of values

Definition at line 467 of file tuple.hpp.

operator-() [1/7]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::operator- ( const isotropic_tensor< S, m, m > &  I, const tensor< T, m, m > &  A  )

constexpr

difference of isotropic and (nonisotropic) tensor

Template Parameters

S	the type of the left isotropic tensor
T	the type of the right tensor
m	the number of rows and columns in each tensor

Parameters

I	the left operand
A	the (full) right operand

Returns

a new tensor equal to the difference of I and A

Definition at line 167 of file isotropic_tensor.hpp.

operator-() [2/7]

template<typename S , typename T , int m, int... n>

constexpr SMITH_HOST_DEVICE auto smith::operator- ( const tensor< S, m, n... > &  A, const tensor< T, m, n... > &  B  )

constexpr

return the difference of two tensors

Template Parameters

S	the underlying type of the lefthand argument
T	the underlying type of the righthand argument
n	integers describing the tensor shape

Parameters

[in]	A	The lefthand operand
[in]	B	The righthand operand

Definition at line 463 of file tensor.hpp.

operator-() [3/7]

template<typename T , int m, int... n>

constexpr SMITH_HOST_DEVICE auto smith::operator- ( const tensor< T, m, n... > &  A )

constexpr

return the unary negation of a tensor

Template Parameters

T	the underlying type of the righthand argument
n	integers describing the tensor shape

Parameters

[in]

A

The tensor to negate

Definition at line 445 of file tensor.hpp.

operator-() [4/7]

template<typename... S, typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator- ( const tuple< S... > &  x, const tuple< T... > &  y  )

constexpr

return a tuple of values defined by elementwise difference of x and y

Template Parameters

S	the types stored in the tuple x
T	the types stored in the tuple y

Parameters

x	a tuple of values
y	a tuple of values

Definition at line 524 of file tuple.hpp.

operator-() [5/7]

template<typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator- ( const tuple< T... > &  x )

constexpr

return a tuple of values defined by applying the unary minus operator to each element of x

Template Parameters

T	the types stored in the tuple y

Parameters

x	a tuple of values

Definition at line 550 of file tuple.hpp.

operator-() [6/7]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::operator- ( isotropic_tensor< S, m, m >  I1, isotropic_tensor< T, m, m >  I2  )

constexpr

difference of isotropic tensors

Template Parameters

S	the type of the left isotropic tensor
T	the type of the right isotropic tensor
m	the number of rows and columns in each isotropic tensor

Parameters

I1	the left operand
I2	the right operand

Returns

a new isotropic tensor equal to the difference of I1 and I2

Definition at line 116 of file isotropic_tensor.hpp.

operator-() [7/7]

template<typename S , typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::operator- ( isotropic_tensor< S, m, m, m, m >  I1, isotropic_tensor< T, m, m, m, m >  I2  )

constexpr

difference of isotropic tensors

Template Parameters

S	the type of the left isotropic tensor
T	the type of the right isotropic tensor
m	the dimension of each rank-4 isotropic tensor

Parameters

I1	the left operand
I2	the right operand

Returns

a new isotropic tensor equal to the difference of I1 and I2

Definition at line 449 of file isotropic_tensor.hpp.

operator-=() [1/3]

template<typename S , typename T , int m, int... n>

constexpr SMITH_HOST_DEVICE auto& smith::operator-= ( tensor< S, m, n... > &  A, const tensor< T, m, n... > &  B  )

constexpr

compound assignment (-) on tensors

Template Parameters

S	the underlying type of the tensor (lefthand) argument
T	the underlying type of the tensor (righthand) argument
n	integers describing the tensor shape

Parameters

[in]	A	The lefthand tensor
[in]	B	The righthand tensor

Definition at line 578 of file tensor.hpp.

operator-=() [2/3]

template<typename T , int... n>

constexpr SMITH_HOST_DEVICE auto& smith::operator-= ( tensor< T, n... > &  A, zero    )

constexpr

compound assignment (-) between a tensor and zero (no-op)

Template Parameters

T	the underlying type of the tensor (righthand) argument
n	integers describing the tensor shape

Parameters

[in]

A

The lefthand tensor

Definition at line 593 of file tensor.hpp.

operator-=() [3/3]

template<typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator-= ( tuple< T... > &  x, const tuple< T... > &  y  )

constexpr

add values contained in y, to the tuple x

Template Parameters

T	the types stored in the tuples x and y

Parameters

x	a tuple of values
y	a tuple of values

Definition at line 494 of file tuple.hpp.

operator/() [1/5]

template<typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator/ ( const double  a, const tuple< T... > &  x  )

constexpr

return a tuple of values defined by division of a by the elements of x

Template Parameters

T	the types stored in the tuple x

Parameters

a	the numerator
x	a tuple of denominator values

Definition at line 623 of file tuple.hpp.

operator/() [2/5]

template<typename S , typename T , int m, int... n, typename = std::enable_if_t<std::is_arithmetic_v<S> || is_dual_number<S>::value>>

constexpr SMITH_HOST_DEVICE auto smith::operator/ ( const tensor< T, m, n... > &  A, S  scale  )

constexpr

divide a tensor by a scalar

Template Parameters

S	the scalar value type. Must be arithmetic (e.g. float, double, int) or a dual number
T	the underlying type of the tensor (righthand) argument
n	integers describing the tensor shape

Parameters

[in]	A	The tensor of numerators
[in]	scale	The denominator

Definition at line 96 of file tuple_tensor_dual_functions.hpp.

operator/() [3/5]

template<typename... S, typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator/ ( const tuple< S... > &  x, const tuple< T... > &  y  )

constexpr

return a tuple of values defined by elementwise division of x by y

Template Parameters

S	the types stored in the tuple x
T	the types stored in the tuple y

Parameters

x	a tuple of values
y	a tuple of values

Definition at line 580 of file tuple.hpp.

operator/() [4/5]

template<typename... T>

constexpr SMITH_HOST_DEVICE auto smith::operator/ ( const tuple< T... > &  x, const double  a  )

constexpr

return a tuple of values defined by elementwise division of x by a

Template Parameters

T	the types stored in the tuple y

Parameters

x	a tuple of numerator values
a	a denominator

Definition at line 635 of file tuple.hpp.

operator/() [5/5]

template<typename S , typename T , int m, int... n, typename = std::enable_if_t<std::is_arithmetic_v<S> || is_dual_number<S>::value>>

constexpr SMITH_HOST_DEVICE auto smith::operator/ ( S  scale, const tensor< T, m, n... > &  A  )

constexpr

divide a scalar by each element in a tensor

Template Parameters

S	the scalar value type. Must be arithmetic (e.g. float, double, int) or a dual number
T	the underlying type of the tensor (righthand) argument
n	integers describing the tensor shape

Parameters

[in]	scale	The numerator
[in]	A	The tensor of denominators

Definition at line 77 of file tuple_tensor_dual_functions.hpp.

operator<<() [1/3]

template<typename... T>

auto& smith::operator<<	(	std::ostream &	out,
		const smith::tuple< T... > &	A
	)

print a tuple of values

Template Parameters

T	the types stored in the tuple

Parameters

out	the ostream to write the output to
A	the tuple of values

Definition at line 748 of file tuple.hpp.

operator<<() [2/3]

template<typename T , int m, int... n>

auto& smith::operator<<	(	std::ostream &	out,
		const tensor< T, m, n... > &	A
	)

recursively serialize the entries in a tensor to an ostream. Output format uses braces and comma separators to mimic C syntax for multidimensional array initialization.

Parameters

[in]	out	the std::ostream to write to (e.g. std::cout or std::ofstream)
[in]	A	The tensor to write out

Definition at line 1709 of file tensor.hpp.

operator<<() [3/3]

auto& smith::operator<< ( std::ostream &  out, zero    )

inline

Write a zero out to an output stream.

Parameters

[in]

out

the std::ostream to write to (e.g. std::cout or std::ofstream)

Definition at line 1724 of file tensor.hpp.

outer() [1/5]

template<typename S , typename T , int m, int n>

constexpr SMITH_HOST_DEVICE auto smith::outer ( const tensor< S, m > &  A, const tensor< T, n > &  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

this overload implements the case where both arguments are vectors

Definition at line 651 of file tensor.hpp.

outer() [2/5]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::outer ( const tensor< T, m > &  A, double  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

this overload implements the case where the left argument is a tensor, and the right argument is a scalar

Definition at line 617 of file tensor.hpp.

outer() [3/5]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto smith::outer ( const tensor< T, n > &  , zero    )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

this overload implements the case where the left argument is a tensor, and the right argument is zero

Definition at line 641 of file tensor.hpp.

outer() [4/5]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto smith::outer ( double  A, tensor< T, n >  B  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

this overload implements the case where the left argument is a scalar, and the right argument is a tensor

Definition at line 603 of file tensor.hpp.

outer() [5/5]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto smith::outer ( zero  , const tensor< T, n > &    )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

this overload implements the case where the left argument is zero, and the right argument is a tensor

Definition at line 631 of file tensor.hpp.

parent_to_physical()

template<Family f, typename T , int q, int dim>

SMITH_HOST_DEVICE void smith::parent_to_physical	(	tensor< T, q > &	qf_input,
		const tensor< double, dim, dim, q > &	jacobians
	)

transform information in the parent space (i.e. values and derivatives w.r.t {xi, eta, zeta}) into the physical space (i.e. values and derivatives w.r.t. {x, y, z})

Template Parameters

f	the element family, used to determine which kind of transformation to apply
T	the types of quantities to be transformed
q	how many values need to be transformed
dim	the spatial dimension

Parameters

qf_input	the values to be transformed from parent to physical space
jacobians	the jacobians of the isoparametric map from parent to physical space of each quadrature point

Definition at line 267 of file finite_element.hpp.

physical_to_parent()

template<Family f, typename T , int q, int dim>

SMITH_HOST_DEVICE void smith::physical_to_parent	(	tensor< T, q > &	qf_output,
		const tensor< double, dim, dim, q > &	jacobians
	)

transform information in the physical space (i.e. sources and fluxes w.r.t {x, y, z}) back to the parent space (i.e. values and derivatives w.r.t. {xi, eta, zeta}). Note: this also multiplies by the outputs by the determinant of the quadrature point Jacobian.

Template Parameters

f	the element family, used to determine which kind of transformation to apply
T	the types of quantities to be transformed
q	how many values need to be transformed
dim	the spatial dimension

Parameters

qf_output	the values to be transformed from physical back to parent space
jacobians	the jacobians of the isoparametric map from parent to physical space of each quadrature point

Definition at line 308 of file finite_element.hpp.

plus_equals_helper()

template<typename... T, int... i>

constexpr SMITH_HOST_DEVICE void smith::plus_equals_helper ( tuple< T... > &  x, const tuple< T... > &  y, std::integer_sequence< int, i... >    )

constexpr

A helper function for the += operator of tuples.

Template Parameters

T	the types stored in the tuples x and y
i	integer sequence used to index the tuples

Parameters

x	tuple of values to be incremented
y	tuple of increment values

Definition at line 454 of file tuple.hpp.

plus_helper()

template<typename... S, typename... T, int... i>

constexpr SMITH_HOST_DEVICE auto smith::plus_helper ( const tuple< S... > &  x, const tuple< T... > &  y, std::integer_sequence< int, i... >    )

constexpr

A helper function for the + operator of tuples.

Template Parameters

S	the types stored in the tuple x
T	the types stored in the tuple y
i	The integer sequence to i

Parameters

x	tuple of values
y	tuple of values

Returns

the returned tuple sum

Definition at line 425 of file tuple.hpp.

powers()

template<int n, typename T >

constexpr SMITH_HOST_DEVICE tensor<T, n> smith::powers ( T  x )

constexpr

compute the first n powers of x

Template Parameters

n	how many powers to compute

Parameters

[in]

x

the number to be raised to varying powers

Definition at line 389 of file polynomials.hpp.

print() [1/2]

template<int m, int... n>

SMITH_HOST_DEVICE void smith::print

(

const tensor< double, m, n... > &

A

)

print a tensor using printf, so that it is suitable for use inside cuda kernels.

Parameters

[in]

A

The tensor to write out

Definition at line 1742 of file tensor.hpp.

print() [2/2]

SMITH_HOST_DEVICE void smith::print ( double  value )

inline

print a double using printf, so that it is suitable for use inside cuda kernels. (used in final recursion of printf(tensor<...>))

Parameters

[in]

value

The value to write out

Definition at line 1735 of file tensor.hpp.

print_helper()

template<typename... T, std::size_t... i>

auto& smith::print_helper	(	std::ostream &	out,
		const smith::tuple< T... > &	A,
		std::integer_sequence< size_t, i... >
	)

helper used to implement printing a tuple of values

Template Parameters

T	the types stored in the tuple
i	a list of indices used to acces each element of the tuple

Parameters

out	the ostream to write the output to
A	the tuple of values

Definition at line 733 of file tuple.hpp.

printRunInfo()

void smith::printRunInfo

(

)

Outputs basic run information to the screen.

Note: Command line options are handled in infrastructure/cli.cpp

Definition at line 194 of file about.cpp.

promote_each_to_dual_when()

template<bool dualify, typename T , int n>

SMITH_HOST_DEVICE auto smith::promote_each_to_dual_when

(

const tensor< T, n > &

x

)

a function that optionally (decided at compile time) converts a list of values to their dual types

Template Parameters

dualify	specify whether or not the input should be made into its dual type
T	the type of the values passed in
n	how many values were passed in

Parameters

x	the values to be promoted

Definition at line 228 of file tuple_tensor_dual_functions.hpp.

promote_to_dual_when()

template<bool dualify, typename T >

SMITH_HOST_DEVICE auto smith::promote_to_dual_when

(

const T &

x

)

a function that optionally (decided at compile time) converts a value to its dual type

Template Parameters

dualify	specify whether or not the value should be made into its dual type
T	the type of the value passed in

Parameters

x	the values to be promoted

Definition at line 209 of file tuple_tensor_dual_functions.hpp.

relative_error()

template<typename T , int... n>

double smith::relative_error	(	tensor< T, n... >	A,
		tensor< T, n... >	B
	)

computes the relative error (in the frobenius norm) between two tensors of the same shape

Template Parameters

T	the datatype stored in each tensor
n	the dimensions of each tensor

Parameters

A	the left argument
B	the right argument

Returns

norm(A - B) / norm(A)

Definition at line 1478 of file tensor.hpp.

sameFiniteElementSpace()

bool smith::sameFiniteElementSpace	(	const mfem::FiniteElementSpace &	left,
		const mfem::FiniteElementSpace &	right
	)

Check if two finite element spaces are the same.

Parameters

left
right

Returns

Bool which is true if the spaces are the same, otherwise false

Definition at line 25 of file finite_element_vector.cpp.

sgn()

template<typename T >

int smith::sgn

(

T

val

)

Signum, returns sign of input.

Parameters

val	Input value.

Returns

0 when input is negative, 0 when input is 0, 1 when input is positive.

Definition at line 769 of file tuple_tensor_dual_functions.hpp.

single_quadrature_point_test()

template<typename MaterialType , typename StateType , typename... functions>

auto smith::single_quadrature_point_test	(	double	t_max,
		size_t	num_steps,
		const MaterialType	material,
		const StateType	initial_state,
		const functions...	f
	)

This function takes a material model (and associate state variables), subjects it to a time history of stimuli, described by functions ... f, and returns the outputs at each step. This is intended to be used for testing materials, to ensure their response is in agreement with known data (analytic or experimental).

Template Parameters

MaterialType	the type of the material model under test
StateType	the associated state variables to be provided to the material
functions	a variadic list of callables

Parameters

t_max	the final time value for
num_steps	the number of timesteps to be
material	an instance of a material model under test
initial_state	the initial conditions for materials that exhibit hysteresis
f	the functions (e.g. std::function, lambdas, etc) that are used to generate the inputs to the material model at each timestep

Returns

a std::vector of tuples of the form: ( time, state(t), f(t) ... , output(t) ) evaluated at each step

Definition at line 124 of file material_verification_tools.hpp.

size() [1/2]

constexpr SMITH_HOST_DEVICE int smith::size ( const double &  )

constexpr

overload of size() for double, we say a double "stores" 1 value

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 1948 of file tensor.hpp.

size() [2/2]

template<typename T , int... n>

constexpr SMITH_HOST_DEVICE int smith::size ( const tensor< T, n... > &  )

constexpr

returns the total number of stored values in a tensor

Template Parameters

T	the datatype stored in the tensor
n	the extents of each dimension

Returns

the total number of values stored in the tensor

Definition at line 1939 of file tensor.hpp.

solve()

FieldState smith::solve	(	const WeakForm &	residual_eval,
		const FieldState &	shape_disp,
		const std::vector< FieldState > &	states,
		const std::vector< FieldState > &	params,
		const TimeInfo &	time_info,
		const DifferentiableSolver &	solver,
		const DirichletBoundaryConditions &	bcs,
		size_t	unknown_state_index = 0
	)

Solve a nonlinear system of equations as defined by the weak form, assuming that the field indexed by unknown_index is the unknown field.

Parameters

residual_eval	The weak form which defines the equations to be solved
shape_disp	The mesh-morphed shape displacement
states	The time varying states as inputs to the weak form
params	All fixed fields pass to the weak form
time_info	Timestep information (time, dt, cycle)
solver	The differentiable, potentially nonlinear, equation solver used to solve the system of equations
bcs	Holds information about which degrees of freedom (DOFS), and has the information about the time and space varying values for the boundary conditions
unknown_state_index

Returns

The field solution to the weak form

Definition at line 260 of file nonlinear_solve.cpp.

solve_lower_triangular() [1/2]

template<typename T , int n, int... m>

constexpr SMITH_HOST_DEVICE auto smith::solve_lower_triangular ( const tensor< T, n, n > &  L, const tensor< T, n, m... > &  b  )

constexpr

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note

For the case when no permutation of the rows is needed.

Definition at line 1587 of file tensor.hpp.

solve_lower_triangular() [2/2]

template<typename T , int n, int... m>

constexpr SMITH_HOST_DEVICE auto smith::solve_lower_triangular ( const tensor< T, n, n > &  L, const tensor< T, n, m... > &  b, const tensor< int, n > &  P  )

constexpr

Solves a lower triangular system Ly = b.

L must be lower triangular and normalized such that the diagonal entries are unity. This is not checked in the function, so failure to obey this will produce meaningless results.

Parameters

[in]	L	A lower triangular matrix
[in]	b	The right hand side
[in]	P	A list of indices to index into b in a permuted fashion.

Returns

y the solution vector

Definition at line 1568 of file tensor.hpp.

solve_scalar_equation()

template<typename function , typename... ParamTypes>

auto smith::solve_scalar_equation	(	const function &	f,
		double	x0,
		double	lower_bound,
		double	upper_bound,
		ScalarSolverOptions	options,
		ParamTypes...	params
	)

Solves a nonlinear scalar-valued equation and gives derivatives of solution to parameters.

Template Parameters

function	Function object type for the nonlinear equation to solve
...ParamTypes	Types of the (optional) parameters to the nonlinear function

Parameters

f	Nonlinear function of which a root is sought. Must have the form $f(x, p_1, p_2, ...)$, where $x$ is the independent variable, and the $p_i$ are optional parameters (scalars or tensors of arbitrary order).
x0	Initial guess of root. If x0 is outside the search interval, the initial guess will be changed to the midpoint of the search interval.
lower_bound	Lower bound of interval to search for root.
upper_bound	Upper bound of interval to search for root.
options	Options controlling behavior of solver.
...params	Optional parameters to the nonlinear function.

Returns

a tuple (x, status) where x is the root, and status is a SolverStatus object reporting the status of the solution procedure. If any of the parameters are dual number-valued, x will be dual containing the corresponding directional derivative of the root. Otherwise, x will be a double containing the root. For example, if one gives the function as $f(x, p)$, where $p$ is a dual<double> with p.gradient = 1, then the x.gradient will be $dx/dp$.

The solver uses Newton's method, safeguarded by bisection. If the Newton update would take the next iterate out of the search interval, or the absolute value of the residual is not decreasing fast enough, bisection will be used to compute the next iterate. The bounds of the search interval are updated automatically to maintain a bracket around the root. If the sign of the residual is the same at both lower_bound and upper_bound, the solver aborts.

Definition at line 576 of file tuple_tensor_dual_functions.hpp.

solve_upper_triangular()

template<typename T , int n, int... m>

constexpr SMITH_HOST_DEVICE auto smith::solve_upper_triangular ( const tensor< T, n, n > &  U, const tensor< T, n, m... > &  y  )

constexpr

Solves an upper triangular system Ux = y.

U must be upper triangular. This is not checked, so failure to obey this will produce meaningless results.

Parameters

[in]	U	An upper triangular matrix
[in]	y	The right hand side

Returns

x the solution vector

Definition at line 1608 of file tensor.hpp.

sqrt_symm()

template<typename T >

auto smith::sqrt_symm

(

tensor< T, 3, 3 >

A

)

Square root of a symmetric matrix.

Parameters

A	Matrix to operate on. Must be SPD. This is not checked.

Returns

Matrix B such that B*B = A

Definition at line 1053 of file tuple_tensor_dual_functions.hpp.

squared_norm() [1/2]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::squared_norm ( const isotropic_tensor< T, m, m > &  I )

constexpr

compute the squared Frobenius norm (tr(dot(transpose(I), I))) of an isotropic tensor

Template Parameters

T	the types stored in the isotropic tensor
m	the number of rows and columns in I

Parameters

I	the isotropic tensor to compute the squared norm of

Definition at line 337 of file isotropic_tensor.hpp.

squared_norm() [2/2]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::squared_norm ( const tensor< T, m > &  A )

constexpr

Returns the squared Frobenius norm of the tensor.

Parameters

[in]

A

The tensor to obtain the squared norm from

Definition at line 1069 of file tensor.hpp.

squish()

void smith::squish

(

mfem::Mesh &

mesh

)

a transformation from the unit disk/sphere (in L1 norm) to a unit disk/sphere (in L2 norm)

Parameters

mesh	The mesh to transform

Definition at line 56 of file mesh_utils.cpp.

sym() [1/2]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::sym ( const isotropic_tensor< T, m, m > &  I )

constexpr

return the symmetric part of an isotropic tensor

Template Parameters

T	the types stored in the isotropic tensor
m	the number of rows and columns in I

Parameters

I	the isotropic tensor to symmetrize

Returns

a copy of I (isotropic matrices are already symmetric)

Definition at line 243 of file isotropic_tensor.hpp.

sym() [2/2]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto smith::sym ( const tensor< T, n, n > &  A )

constexpr

Returns the symmetric part of a square matrix.

Parameters

[in]

A

The matrix to obtain the symmetric part of

Returns

(1/2) * (A + A^T)

Definition at line 1164 of file tensor.hpp.

symmetric_mat3_function()

template<typename T , typename Function , typename EigvalSecantFunction >

auto smith::symmetric_mat3_function	(	tensor< T, 3, 3 >	A,
		const Function &	f,
		const EigvalSecantFunction &	g
	)

Constructs an isotropic tensor-valued function of a symmetric 3x3 tensor from a scalar function.

This allows one to use a scalar-valued function of a scalar to construct an isotropic tensor-valued function of a symmetric tensor. The scalar function is applied to the principal values of the matrix, and then rotated back into the external coordinate system with the eigenvector matrix.

If A = V diag(lambda_0, lambda_1, lambda_2) V^T, then f(A) = V diag(f(lambda_0), f(lambda_1), f(lambda_2)) V^T

The function g, which we call the eigenvalue secant function, is only used if the derivative of the function is sought by having a dual number input tensor A. It must compute | df/dx, if lam1 = lam2 g(lam1, lam2) = | | ( f(lam1) - f(lam2) ) / (lam1 - lam2), otherwise

Analytically, this is a continuous function. However, in floating point arithmetic the direct implementation will often suffer from catastrophic cancellation. The presence of the g argument gives you a way to write this function in a numerically stable way (and thus preserve accuracy in the derivative of the tensor function).

Template Parameters

T	The datatype stored in the tensor
Function	Type for the functor object representing the scalar function
EigvalSecantFunction	Type for the functor object representing the secant eigenvalue function (see below)

Parameters

A	The matrix to apply the isotropic tensor function to.
f	A scalar-valued function of a scalar. This is applied to the eigenvalues of A.
g	The eigenvalue secant function

Returns

The tensor f(A).

Definition at line 968 of file tuple_tensor_dual_functions.hpp.

SymmetricIdentity()

template<int m>

constexpr SMITH_HOST_DEVICE auto smith::SymmetricIdentity ( )

constexpr

a helper function for creating the rank-4 isotropic tensor defined by: d(sym(A)_{ij}) / d(A_{kl})

Template Parameters

m	the dimension

Definition at line 383 of file isotropic_tensor.hpp.

tensor() [1/2]

template<typename T , int n1>

smith::tensor

(

const T(&)

data[n1]

)

-> tensor< T, n1 >

class template argument deduction guide for type tensor.

Note

this lets users write

tensor A = {{0.0, 1.0, 2.0}}; 

instead of explicitly writing the template parameters

tensor< double, 3 > A = {{1.0, 2.0, 3.0}}; 

tensor() [2/2]

template<typename T , int n1, int n2>

smith::tensor

(

const T(&)

data[n1][n2]

)

-> tensor< T, n1, n2 >

class template argument deduction guide for type tensor.

Note

this lets users write

tensor A = {{{1.0, 2.0, 3.0}, {4.0, 5.0, 6.0}, {7.0, 8.0, 9.0}}}; 

instead of explicitly writing the template parameters

tensor< double, 3, 3 > A = {{{1.0, 2.0, 3.0}, {4.0, 5.0, 6.0}, {7.0, 8.0, 9.0}}}; 

tensor_with_shape()

template<typename T , int... n>

constexpr SMITH_HOST_DEVICE auto smith::tensor_with_shape ( std::integer_sequence< int, n... >  )

constexpr

Creates a tensor given the dimensions in a std::integer_sequence.

See also

std::integer_sequence

Template Parameters

n	The parameter pack of integer dimensions

Definition at line 287 of file tensor.hpp.

to_3x3()

template<typename T >

SMITH_HOST_DEVICE tensor<T, 3, 3> smith::to_3x3

(

const tensor< T, 2, 2 > &

A

)

promotes a 2x2 matrix to a 3x3 matrix, by populating the upper left block, leaving zeroes in the third row / column

Parameters

[in]

A

the 2x2 matrix to be promoted to a 3x3 matrix

Definition at line 1133 of file tensor.hpp.

tr() [1/2]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::tr ( const isotropic_tensor< T, m, m > &  I )

constexpr

calculate the trace of an isotropic tensor

Template Parameters

T	the types stored in the isotropic tensor
m	the number of rows and columns in I

Parameters

I	the isotropic tensor to compute the trace of

Returns

the sum of the diagonal entries of I

Definition at line 270 of file isotropic_tensor.hpp.

tr() [2/2]

template<typename T , int n>

constexpr SMITH_HOST_DEVICE auto smith::tr ( const tensor< T, n, n > &  A )

constexpr

Returns the trace of a square matrix.

Parameters

[in]

A

The matrix to compute the trace of

Returns

The sum of the elements on the main diagonal

Definition at line 1149 of file tensor.hpp.

transpose() [1/2]

template<typename T , int m>

constexpr SMITH_HOST_DEVICE auto smith::transpose ( const isotropic_tensor< T, m, m > &  I )

constexpr

return the transpose of an isotropic tensor

Template Parameters

T	the types stored in the isotropic tensor
m	the number of rows and columns in I

Parameters

I	the isotropic tensor to compute the trace of

Returns

a copy of I (isotropic matrices are symmetric)

Definition at line 284 of file isotropic_tensor.hpp.

transpose() [2/2]

template<typename T , int m, int n>

constexpr SMITH_HOST_DEVICE auto smith::transpose ( const tensor< T, m, n > &  A )

constexpr

Returns the transpose of the matrix.

Parameters

[in]

A

The matrix to obtain the transpose of

Definition at line 1275 of file tensor.hpp.

tuple()

template<typename... T>

smith::tuple

(

T...

)

-> tuple< T... >

Class template argument deduction rule for tuples.

Template Parameters

T	The variadic template parameter for tuple types

type()

template<int i, typename... T>

constexpr SMITH_HOST_DEVICE auto smith::type ( const tuple< T... > &  values )

constexpr

a function intended to be used for extracting the ith type from a tuple.

Note

type<i>(my_tuple) returns a value, whereas get<i>(my_tuple) returns a reference

Template Parameters

i	the index of the tuple to query
T	the types stored in the tuple

Parameters

values

the tuple of values

Returns

a copy of the ith entry of the input

Definition at line 376 of file tuple.hpp.

typeString()

template<typename T >

std::string smith::typeString

(

T &

var

)

Return string of given parameter's type.

Template Parameters

T	the type to get a string name for

Parameters

[in]

var

the variable to get the type of

Returns

string representation of the type

Definition at line 36 of file debug_print.hpp.

unary_minus_helper()

template<typename... T, int... i>

constexpr SMITH_HOST_DEVICE auto smith::unary_minus_helper ( const tuple< T... > &  x, std::integer_sequence< int, i... >    )

constexpr

A helper function for the - operator of tuples.

Template Parameters

T	the types stored in the tuple y
i	The integer sequence to i

Parameters

x	tuple of values

Returns

the returned tuple difference

Definition at line 539 of file tuple.hpp.

uniaxial_stress_test()

template<typename MaterialType , typename StateType , typename... parameter_types>

auto smith::uniaxial_stress_test	(	double	t_max,
		size_t	num_steps,
		const MaterialType	material,
		const StateType	initial_state,
		std::function< double(double)>	epsilon_xx,
		const parameter_types...	parameter_functions
	)

Drive the material model thorugh a uniaxial tension experiment.

Drives material model through specified axial displacement gradient history. The time elaspses from 0 up to t_max. Currently only implemented for isotropic materials (or orthotropic materials with the principal axes aligned with the coordinate directions).

Parameters

t_max	upper limit of the time interval.
num_steps	The number of discrete time points at which the response is sampled (uniformly spaced). This is inclusive of the point at time zero.
material	The material model to use
initial_state	The state variable collection for this material, set to the desired initial condition.
epsilon_xx	A function describing the desired axial displacement gradient as a function of time. (NB axial displacement gradient is equivalent to engineering strain).
parameter_functions	Pack of functions that return each parameter as a function of time. Leave empty if the material has no parameters.

Definition at line 42 of file material_verification_tools.hpp.

uniaxial_stress_test_rate_dependent()

template<typename MaterialType , typename StateType , typename... parameter_types>

auto smith::uniaxial_stress_test_rate_dependent	(	double	t_max,
		size_t	num_steps,
		const MaterialType	material,
		const StateType	initial_state,
		std::function< double(double)>	epsilon_xx,
		const parameter_types...	parameter_functions
	)

Drive a rate-dependent material model thorugh a uniaxial tension experiment.

Drives material model through specified axial displacement gradient history. The time elapses from 0 up to t_max. Currently only implemented for isotropic materials (or orthotropic materials with the principal axes aligned with the coordinate directions).

Definition at line 92 of file material_verification_tools.hpp.

version()

std::string smith::version

(

bool

add_SHA = true

)

Returns a string for the version of Smith.

Parameters

[in]

add_SHA

boolean for whether to add the Git SHA to the version if available

Returns

string value of the version of Smith

Definition at line 214 of file about.cpp.

visit()

template<typename Visitor , typename Variant >

constexpr decltype(auto) smith::visit ( Visitor  visitor, Variant &&  v  )

constexpr

Applies a functor to the active variant element.

Parameters

[in]	visitor	The functor to apply
[in]	v	The variant to apply the functor to

See also

std::visit

Definition at line 365 of file variant.hpp.

writeToFile() [1/5]

template<typename T >

void smith::writeToFile	(	axom::Array< T, 2, smith::detail::host_memory_space >	arr,
		std::string	filename
	)

write a 2D array of values out to file, in a space-separated format

Template Parameters

T	the type of each value in the array

Parameters

arr	the array to write to file
filename	the name of the output file

Definition at line 113 of file debug_print.hpp.

writeToFile() [2/5]

template<typename T >

void smith::writeToFile	(	axom::Array< T, 3, smith::detail::host_memory_space >	arr,
		std::string	filename
	)

write a 3D array of values out to file, in a mathematica-compatible format

Template Parameters

T	the type of each value in the array

Parameters

arr	the array to write to file
filename	the name of the output file

Definition at line 136 of file debug_print.hpp.

writeToFile() [3/5]

void smith::writeToFile	(	mfem::SparseMatrix	A,
		std::string	filename
	)

write a sparse matrix out to file

Parameters

A	the matrix to write to file
filename	the name of the output file

Definition at line 90 of file debug_print.hpp.

writeToFile() [4/5]

void smith::writeToFile	(	mfem::Vector	v,
		std::string	filename
	)

write an array of doubles out to file, in a space-separated format

Parameters

v	the values to write to file
filename	the name of the output file

Definition at line 76 of file debug_print.hpp.

writeToFile() [5/5]

template<typename T >

void smith::writeToFile	(	std::vector< T >	v,
		std::string	filename
	)

write an array of values out to file, in a space-separated format

Template Parameters

T	the type of each value in the array

Parameters

v	the values to write to file
filename	the name of the output file

Definition at line 62 of file debug_print.hpp.

Variable Documentation

linearSolverMap

std::map<std::string, LinearSolver> smith::linearSolverMap

inline

Initial value:

= {
    {"CG", LinearSolver::CG},           {"GMRES", LinearSolver::GMRES},
    {"SuperLU", LinearSolver::SuperLU}, {"Strumpack", LinearSolver::Strumpack},
    {"PetscCG", LinearSolver::PetscCG}, {"PetscGMRES", LinearSolver::PetscGMRES},
}

string->value matching for optionally entering options as string in command line

Definition at line 138 of file solver_config.hpp.

nonlinearSolverMap

std::map<std::string, NonlinearSolver> smith::nonlinearSolverMap

inline

Initial value:

= {
    {"Newton", NonlinearSolver::Newton},
    {"LBFGS", NonlinearSolver::LBFGS},
    {"NewtonLineSearch", NonlinearSolver::NewtonLineSearch},
    {"TrustRegion", NonlinearSolver::TrustRegion},
    {"KINFullStep", NonlinearSolver::KINFullStep},
    {"KINBacktrackingLineSearch", NonlinearSolver::KINBacktrackingLineSearch},
    {"KINPicard", NonlinearSolver::KINPicard},
    {"PetscNewton", NonlinearSolver::PetscNewton},
    {"PetscNewtonBacktracking", NonlinearSolver::PetscNewtonBacktracking},
    {"PetscNewtonCriticalPoint", NonlinearSolver::PetscNewtonCriticalPoint},
    {"PetscTrustRegion", NonlinearSolver::PetscTrustRegion},
}

string->value matching for optionally entering options as string in command line

Definition at line 200 of file solver_config.hpp.

NoQData

std::shared_ptr< QuadratureData< Nothing > > smith::NoQData = ::std::make_shared<QuadratureData<Nothing>>()

a single instance of a QuadratureData container of Nothings, since they are all interchangeable

these values exist to serve as default arguments for materials without material state

Definition at line 18 of file quadrature_data.cpp.

preconditionerMap

std::map<std::string, Preconditioner> smith::preconditionerMap

inline

Initial value:

= {
    {"HypreJacobi", Preconditioner::HypreJacobi},
    {"HypreL1Jacobi", Preconditioner::HypreL1Jacobi},
    {"HypreGaussSeidel", Preconditioner::HypreGaussSeidel},
    {"HypreAMG", Preconditioner::HypreAMG},
    {"HypreILU", Preconditioner::HypreILU},
    {"AMGX", Preconditioner::AMGX},
    {"Petsc", Preconditioner::Petsc},
    {"AMGFContact", Preconditioner::AMGFContact},
    {"None", Preconditioner::None},
}

string->value matching for optionally entering options as string in command line

Definition at line 381 of file solver_config.hpp.