fit.hpp

// Copyright (c) Lawrence Livermore National Security, LLC and
// other Serac Project Developers. See the top-level LICENSE file for
// details.
//
// SPDX-License-Identifier: (BSD-3-Clause)
 
#pragma once
 
#include <fstream>
#include <iostream>
#include <array>
#include <utility>
 
#include "mpi.h"
#include "mfem.hpp"
 
#include "serac/numerics/functional/functional.hpp"
#include "serac/numerics/functional/tensor.hpp"
#include "serac/physics/state/finite_element_state.hpp"
#include "serac/numerics/functional/differentiate_wrt.hpp"
#include "serac/numerics/functional/domain.hpp"
#include "serac/numerics/functional/function_signature.hpp"
#include "serac/numerics/functional/geometry.hpp"
#include "serac/numerics/functional/tuple.hpp"
 
namespace serac {
 
namespace detail {
 
template <int dim, typename signature, int... i, typename func, typename... T>
FiniteElementState fit(std::integer_sequence<int, i...>, func f, mfem::ParMesh& pmesh, const T&... solution_fields)
{
  // signature looks like return_type(arg0_type, arg1_type);
  // so this unpacks the return type
  using output_space = typename FunctionSignature<signature>::return_type;
 
  FiniteElementState fitted_field(pmesh, output_space{});
  fitted_field = 0.0;
 
  // mass term
  Domain whole_domain = EntireDomain(pmesh);
  serac::Functional<output_space(output_space)> phi_phi(&fitted_field.space(), {&fitted_field.space()});
  phi_phi.AddDomainIntegral(
      Dimension<dim>{}, DependsOn<0>{},
      [](double /*t*/, auto /*x*/, auto u) {
        return tuple{get<0>(u), zero{}};
      },
      whole_domain);
  auto M = get<1>(phi_phi(DifferentiateWRT<0>{}, 0.0 /* t */, fitted_field));
 
  // rhs
  std::array<const mfem::ParFiniteElementSpace*, sizeof...(T)> trial_spaces = {&solution_fields.space()...};
  serac::Functional<signature> phi_f(&fitted_field.space(), trial_spaces);
  phi_f.AddDomainIntegral(Dimension<dim>{}, DependsOn<i...>{}, f, whole_domain);
  mfem::Vector b = phi_f(0.0, solution_fields...);
 
  mfem::CGSolver cg(MPI_COMM_WORLD);
  cg.SetOperator(M);
  cg.SetRelTol(1e-12);
  cg.SetMaxIter(500);
  cg.SetPrintLevel(2);
  cg.Mult(b, fitted_field);
 
  return fitted_field;
}
 
}  // namespace detail
 
template <int dim, typename signature, int... n, typename func, typename... T>
FiniteElementState fit(func f, mfem::ParMesh& pmesh, const T&... solution_fields)
{
  auto iseq = std::make_integer_sequence<int, sizeof...(T)>{};
  return detail::fit<dim, signature>(iseq, f, pmesh, solution_fields...);
}
 
}  // namespace serac