exact_solution.h

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2019 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
 
#ifdef LIBMESH_FORWARD_DECLARE_ENUMS
namespace libMesh
{
enum FEMNormType : int;
}
#else
#include "libmesh/enum_norm_type.h"
#endif
 
// 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;
 
// 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_value (unsigned int sys_num,
                           FunctionBase<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_deriv (unsigned int sys_num,
                           FunctionBase<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_hessian (unsigned int sys_num,
                             FunctionBase<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(const std::string & sys_name,
                     const std::string & unknown_name);
 
  Real l2_error(const std::string & sys_name,
                const std::string & unknown_name);
 
  Real l1_error(const std::string & sys_name,
                const std::string & unknown_name);
 
  Real l_inf_error(const std::string & sys_name,
                   const std::string & unknown_name);
 
  Real h1_error(const std::string & sys_name,
                const std::string & unknown_name);
 
  Real hcurl_error(const std::string & sys_name,
                   const std::string & unknown_name);
 
  Real hdiv_error(const std::string & sys_name,
                  const std::string & unknown_name);
 
  Real h2_error(const std::string & sys_name,
                const std::string & unknown_name);
 
  Real error_norm(const std::string & sys_name,
                  const std::string & unknown_name,
                  const FEMNormType & norm);
private:
 
  template<typename OutputShape>
  void _compute_error(const std::string & sys_name,
                      const std::string & unknown_name,
                      std::vector<Real> & error_vals);
 
  std::vector<Real> & _check_inputs(const std::string & sys_name,
                                    const std::string & unknown_name);
 
  std::vector<std::unique_ptr<FunctionBase<Number>>> _exact_values;
 
  std::vector<std::unique_ptr<FunctionBase<Gradient>>> _exact_derivs;
 
  std::vector<std::unique_ptr<FunctionBase<Tensor>>> _exact_hessians;
 
  typedef std::map<std::string, std::vector<Real>> SystemErrorMap;
 
  std::map<std::string, SystemErrorMap> _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