Equation solver class based on a standard preconditioned trust-region algorithm. More...
Public Member Functions | |
| void | projectToBoundaryWithCoefs (mfem::Vector &z, const mfem::Vector &d, double delta, double zz, double zd, double dd) const |
| finds tau s.t. (z + tau*d)^2 = trSize^2 | |
| template<typename HessVecFunc > | |
| void | solveTheSubspaceProblem ([[maybe_unused]] mfem::Vector &z, [[maybe_unused]] const HessVecFunc &hess_vec_func, [[maybe_unused]] const std::vector< const mfem::Vector * > ds, [[maybe_unused]] const std::vector< const mfem::Vector * > Hds, [[maybe_unused]] const mfem::Vector &g, [[maybe_unused]] double delta, [[maybe_unused]] int num_leftmost) const |
| solve the exact trust-region subspace problem with directions ds, and the leftmosts | |
| void | projectToBoundaryBetweenWithCoefs (mfem::Vector &z, const mfem::Vector &y, double trSize, double zz, double zy, double yy) const |
| finds tau s.t. (z + tau*(y-z))^2 = trSize^2 | |
| void | doglegStep (const mfem::Vector &cp, const mfem::Vector &newtonP, double trSize, mfem::Vector &s) const |
| take a dogleg step in direction s, solution norm must be within trSize | |
| template<typename HessVecFunc > | |
| double | computeEnergy (const mfem::Vector &r_local, const HessVecFunc &H, const mfem::Vector &z) const |
| compute the energy of the linearized system for a given solution vector z | |
| template<typename HessVecFunc , typename PrecondFunc > | |
| void | solveTrustRegionModelProblem (const mfem::Vector &r0, mfem::Vector &rCurrent, HessVecFunc hess_vec_func, PrecondFunc precond, const TrustRegionSettings &settings, double &trSize, TrustRegionResults &results) const |
| Minimize quadratic sub-problem given residual vector, the action of the stiffness and a preconditioner. | |
| void | assembleJacobian (const mfem::Vector &x) const |
| assemble the jacobian | |
| mfem::real_t | computeResidual (const mfem::Vector &x_, mfem::Vector &r_) const |
| evaluate the nonlinear residual | |
| void | hessVec (const mfem::Vector &x_, mfem::Vector &v_) const |
| apply the action of the assembled Jacobian matrix to a vector | |
| void | precond (const mfem::Vector &x_, mfem::Vector &v_) const |
| apply trust region specific preconditioner | |
| void | Mult (const mfem::Vector &, mfem::Vector &X) const |
| This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. | |
Public Attributes | |
| size_t | num_hess_vecs = 0 |
| internal counter for hess-vecs | |
| size_t | num_preconds = 0 |
| internal counter for preconditions | |
| size_t | num_residuals = 0 |
| internal counter for residuals | |
| size_t | num_subspace_solves = 0 |
| internal counter for subspace solves | |
| size_t | num_jacobian_assembles = 0 |
| internal counter for matrix assembles | |
Protected Attributes | |
| mfem::Vector | x_pred |
| predicted solution | |
| mfem::Vector | r_pred |
| predicted residual | |
| mfem::Vector | scratch |
| scratch | |
| std::vector< std::shared_ptr< mfem::Vector > > | left_mosts |
| left most eigenvectors | |
| std::vector< std::shared_ptr< mfem::Vector > > | H_left_mosts |
| the action of the stiffness/hessian (H) on the left most eigenvectors | |
| NonlinearSolverOptions | nonlinear_options |
| nonlinear solution options | |
| LinearSolverOptions | linear_options |
| linear solution options | |
| Solver & | tr_precond |
Detailed Description
Equation solver class based on a standard preconditioned trust-region algorithm.
This is a fairly standard implementation of 'The Conjugate Gradient Method and Trust Regions in Large Scale Optimization' by T. Steihaug It is also called the Steihaug-Toint CG trust region algorithm (see also Trust Region Methods by Conn, Gould, and Toint). One important difference is we do not compute an explicit energy. Instead we rely on an incremental work approximation: 0.5 (f^n + f^{n+1}) dot (u^{n+1} - u^n). While less theoretically sound, it appears to be very effective in practice.
Definition at line 308 of file equation_solver.cpp.
Member Data Documentation
◆ tr_precond
|
protected |
handle to the preconditioner used by the trust region, it ignores the linear solver as a SPD preconditioner is currently required
Definition at line 327 of file equation_solver.cpp.
The documentation for this class was generated from the following file:
- src/serac/numerics/equation_solver.cpp
