reference_cross_section.h

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// ---------------------------------------------------------------------
//
// Copyright (C) 2024 by Luca Heltai
//
// This file is part of the reduced_lagrange_multipliers application, based on
// the deal.II library.
//
// The reduced_lagrange_multipliers application is free software; you can use
// it, redistribute it, and/or modify it under the terms of the Apache-2.0
// License WITH LLVM-exception as published by the Free Software Foundation;
// either version 3.0 of the License, or (at your option) any later version. The
// full text of the license can be found in the file LICENSE.md at the top level
// of the reduced_lagrange_multipliers distribution.
//
// ---------------------------------------------------------------------

 
#ifndef rdlm_reference_inclusion
#define rdlm_reference_inclusion
 
#include <deal.II/base/parameter_acceptor.h>
#include <deal.II/base/patterns.h>
#include <deal.II/base/polynomials_p.h>
#include <deal.II/base/quadrature_lib.h>
 
#include <deal.II/dofs/dof_handler.h>
 
#include <deal.II/fe/fe.h>
#include <deal.II/fe/fe_system.h>
#include <deal.II/fe/mapping_q.h>
 
#include <deal.II/grid/tria.h>
 
#include <deal.II/lac/sparse_matrix.h>
#include <deal.II/lac/sparsity_pattern.h>
#include <deal.II/lac/vector.h>
 
#include <fstream>
 
using namespace dealii;

template <int dim, int spacedim = dim, int n_components = 1>
struct ReferenceCrossSectionParameters : public ParameterAcceptor
{
  ReferenceCrossSectionParameters();

  unsigned int refinement_level = 1;

  std::string inclusion_type = "hyper_ball";

  unsigned int inclusion_degree = 0;

  mutable std::vector<unsigned int> selected_coefficients;
};

template <int dim, int spacedim = dim, int n_components = 1>
class ReferenceCrossSection
{
public:
  ReferenceCrossSection(
    const ReferenceCrossSectionParameters<dim, spacedim, n_components> &par);

  const Quadrature<spacedim> &
  get_global_quadrature() const;

  const std::vector<Vector<double>> &
  get_basis_functions() const;

  const double &
  shape_value(const unsigned int i,
              const unsigned int q,
              const unsigned int comp) const;

  const SparseMatrix<double> &
  get_mass_matrix() const;

  unsigned int
  n_selected_basis() const;

  unsigned int
  max_n_basis() const;
 
  Quadrature<spacedim>
  get_transformed_quadrature(const Point<spacedim>     &new_origin,
                             const Tensor<1, spacedim> &new_vertical,
                             const double               scale) const;
 
  unsigned int
  n_quadrature_points() const;

 
  void
  initialize();

  double
  measure(const double scale = 1.0) const;
 
private:
  void
  make_grid();

  void
  setup_dofs();

  void
  compute_basis();

  const ReferenceCrossSectionParameters<dim, spacedim, n_components> &par;

  PolynomialsP<spacedim> polynomials;

  Triangulation<dim, spacedim> triangulation;

  QGauss<dim> quadrature_formula;

  FESystem<dim, spacedim> fe;
 
  // Mapping space for the inclusion.
  MappingQ<dim, spacedim> mapping;

  DoFHandler<dim, spacedim> dof_handler;

  std::vector<Vector<double>> basis_functions;

  std::vector<Vector<double>> selected_basis_functions;

  SparsityPattern sparsity_pattern;

  SparseMatrix<double> mass_matrix;

  Quadrature<spacedim> global_quadrature;

  double reference_measure;

  FullMatrix<double> basis_functions_on_qpoints;
};
 
#endif