exact_solution.h

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2025 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner

// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.

// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.

// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

#ifndef LIBMESH_EXACT_SOLUTION_H
#define LIBMESH_EXACT_SOLUTION_H


// Local Includes
#include "libmesh/libmesh_common.h" // for Number

// C++ includes
#include <map>
#include <vector>
#include <memory>
#include <set>

namespace libMesh
{


// Forward Declarations
class Point;
class EquationSystems;
class Parameters;
class Mesh;
template <typename Output> class FunctionBase;
template <typename Output> class FEMFunctionBase;
enum FEMNormType : int;

// Is there any way to simplify this?
// All we need are Tensor and Gradient. - RHS
template <typename T> class TensorValue;
template <typename T> class VectorValue;
typedef TensorValue<Number> NumberTensorValue;
typedef NumberTensorValue   Tensor;
typedef VectorValue<Number> NumberVectorValue;
typedef NumberVectorValue   Gradient;

class ExactSolution
{

public:
  explicit
  ExactSolution (const EquationSystems & es);

  ExactSolution(const ExactSolution &) = delete;
  ExactSolution & operator= (const ExactSolution &) = delete;
  ExactSolution & operator= (ExactSolution &&) = delete;

  ExactSolution(ExactSolution &&);
  ~ExactSolution();

  void set_excluded_subdomains(const std::set<subdomain_id_type> & excluded);

  void attach_reference_solution (const EquationSystems * es_fine);

  void attach_exact_values (const std::vector<FunctionBase<Number> *> & f);

  void attach_exact_values (const std::vector<FEMFunctionBase<Number> *> & f);

  void attach_exact_value (unsigned int sys_num,
                           FunctionBase<Number> * f);

  void attach_exact_value (unsigned int sys_num,
                           FEMFunctionBase<Number> * f);

  typedef Number (*ValueFunctionPointer)(const Point & p,
                                         const Parameters & Parameters,
                                         const std::string & sys_name,
                                         const std::string & unknown_name);
  void attach_exact_value (ValueFunctionPointer fptr);

  void attach_exact_derivs (const std::vector<FunctionBase<Gradient> *> & g);

  void attach_exact_derivs (const std::vector<FEMFunctionBase<Gradient> *> & g);

  void attach_exact_deriv (unsigned int sys_num,
                           FunctionBase<Gradient> * g);

  void attach_exact_deriv (unsigned int sys_num,
                           FEMFunctionBase<Gradient> * g);

  typedef Gradient (*GradientFunctionPointer)(const Point & p,
                                              const Parameters & parameters,
                                              const std::string & sys_name,
                                              const std::string & unknown_name);
  void attach_exact_deriv (GradientFunctionPointer gptr);

  void attach_exact_hessians (std::vector<FunctionBase<Tensor> *> h);
  void attach_exact_hessians (std::vector<FEMFunctionBase<Tensor> *> h);

  void attach_exact_hessian (unsigned int sys_num,
                             FunctionBase<Tensor> * h);

  void attach_exact_hessian (unsigned int sys_num,
                             FEMFunctionBase<Tensor> * h);

  typedef Tensor (*HessianFunctionPointer)(const Point & p,
                                           const Parameters & parameters,
                                           const std::string & sys_name,
                                           const std::string & unknown_name);
  void attach_exact_hessian (HessianFunctionPointer hptr);

  void extra_quadrature_order (const int extraorder)
  { _extra_order = extraorder; }

  void compute_error(std::string_view sys_name,
                     std::string_view unknown_name);

  Real l2_error(std::string_view sys_name,
                std::string_view unknown_name);

  Real l1_error(std::string_view sys_name,
                std::string_view unknown_name);

  Real l_inf_error(std::string_view sys_name,
                   std::string_view unknown_name);

  Real h1_error(std::string_view sys_name,
                std::string_view unknown_name);

  Real hcurl_error(std::string_view sys_name,
                   std::string_view unknown_name);

  Real hdiv_error(std::string_view sys_name,
                  std::string_view unknown_name);

  Real h2_error(std::string_view sys_name,
                std::string_view unknown_name);

  Real error_norm(std::string_view sys_name,
                  std::string_view unknown_name,
                  const FEMNormType & norm);
private:

  template<typename OutputShape>
  void _compute_error(std::string_view sys_name,
                      std::string_view unknown_name,
                      std::vector<Real> & error_vals);

  std::vector<Real> & _check_inputs(std::string_view sys_name,
                                    std::string_view unknown_name);

  std::vector<std::unique_ptr<FEMFunctionBase<Number>>> _exact_values;

  std::vector<std::unique_ptr<FEMFunctionBase<Gradient>>> _exact_derivs;

  std::vector<std::unique_ptr<FEMFunctionBase<Tensor>>> _exact_hessians;

  typedef std::map<std::string, std::vector<Real>, std::less<>>
    SystemErrorMap;

  std::map<std::string, SystemErrorMap, std::less<>> _errors;

  const EquationSystems & _equation_systems;

  const EquationSystems * _equation_systems_fine;

  int _extra_order;

  std::set<subdomain_id_type> _excluded_subdomains;
};



} // namespace libMesh


#endif // LIBMESH_EXACT_SOLUTION_H