libMesh::ExactSolution Class Reference

#include <exact_solution.h>

List of all members.

Public Member Functions
	ExactSolution (const EquationSystems &es)
	~ExactSolution ()
void	attach_reference_solution (const EquationSystems *es_fine)
void	attach_exact_values (std::vector< FunctionBase< Number > * > f)
void	attach_exact_value (unsigned int sys_num, FunctionBase< Number > *f)
void	attach_exact_value (Number fptr(const Point &p, const Parameters &Parameters, const std::string &sys_name, const std::string &unknown_name))
void	attach_exact_derivs (std::vector< FunctionBase< Gradient > * > g)
void	attach_exact_deriv (unsigned int sys_num, FunctionBase< Gradient > *g)
void	attach_exact_deriv (Gradient gptr(const Point &p, const Parameters &parameters, const std::string &sys_name, const std::string &unknown_name))
void	attach_exact_hessians (std::vector< FunctionBase< Tensor > * > h)
void	attach_exact_hessian (unsigned int sys_num, FunctionBase< Tensor > *h)
void	attach_exact_hessian (Tensor hptr(const Point &p, const Parameters &parameters, const std::string &sys_name, const std::string &unknown_name))
void	extra_quadrature_order (const int 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 Types
typedef std::map< std::string, std::vector< Real > >	SystemErrorMap
Private Member Functions
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)
Private Attributes
std::vector< FunctionBase < Number > * >	_exact_values
std::vector< FunctionBase < Gradient > * >	_exact_derivs
std::vector< FunctionBase < Tensor > * >	_exact_hessians
std::map< std::string, SystemErrorMap >	_errors
const EquationSystems &	_equation_systems
const EquationSystems *	_equation_systems_fine
int	_extra_order

---

Detailed Description

This class handles the computation of the L2 and/or H1 error for the Systems in the EquationSystems object which is passed to it. Note that for it to be useful, the user must attach at least one, and possibly two functions which can compute the exact solution and its derivative for any component of any system. These are the exact_value and exact_deriv functions below.

Author:

Benjamin S. Kirk w/ modifications for libmesh by John W. Peterson

Definition at line 64 of file exact_solution.h.

---

Member Typedef Documentation

typedef std::map<std::string, std::vector<Real> > libMesh::ExactSolution::SystemErrorMap [private]

Data structure which stores the errors: ||e|| = ||u - u_h|| ||grad(e)|| = ||grad(u) - grad(u_h)|| for each unknown in a single system. The name of the unknown is the key for the map.

Definition at line 293 of file exact_solution.h.

---

Constructor & Destructor Documentation

libMesh::ExactSolution::ExactSolution

(

const EquationSystems &

es

)

[explicit]

Constructor. The ExactSolution object must be initialized with an EquationSystems object.

Definition at line 41 of file exact_solution.C.

References _equation_systems, _errors, libMesh::EquationSystems::get_system(), libMesh::EquationSystems::n_systems(), libMesh::System::n_vars(), libMesh::System::name(), and libMesh::System::variable_name().

                                                      :
  _equation_systems(es),
  _equation_systems_fine(NULL),
  _extra_order(0)
{
  // Initialize the _errors data structure which holds all
  // the eventual values of the error.
  for (unsigned int sys=0; sys<_equation_systems.n_systems(); ++sys)
    {
      // Reference to the system
      const System& system = _equation_systems.get_system(sys);

      // The name of the system
      const std::string& sys_name = system.name();

      // The SystemErrorMap to be inserted
      ExactSolution::SystemErrorMap sem;

      for (unsigned int var=0; var<system.n_vars(); ++var)
        {
          // The name of this variable
          const std::string& var_name = system.variable_name(var);
          sem[var_name] = std::vector<Real>(5, 0.);
        }

      _errors[sys_name] = sem;
    }
}

libMesh::ExactSolution::~ExactSolution

(

)

Destructor.

Definition at line 71 of file exact_solution.C.

References _exact_derivs, _exact_hessians, and _exact_values.

{
  // delete will clean up any cloned functors and no-op on any NULL
  // pointers

  for (unsigned int i=0; i != _exact_values.size(); ++i)
    delete (_exact_values[i]);

  for (unsigned int i=0; i != _exact_derivs.size(); ++i)
    delete (_exact_derivs[i]);

  for (unsigned int i=0; i != _exact_hessians.size(); ++i)
    delete (_exact_hessians[i]);
}

---

Member Function Documentation

std::vector< Real > & libMesh::ExactSolution::_check_inputs	(	const std::string &	sys_name,
		const std::string &	unknown_name
	)			[private]

This function is responsible for checking the validity of the sys_name and unknown_name inputs, and returning a reference to the proper vector for storing the values.

Definition at line 261 of file exact_solution.C.

References _errors, and libMesh::err.

Referenced by compute_error(), error_norm(), h1_error(), h2_error(), l1_error(), l2_error(), and l_inf_error().

{
  // If no exact solution function or fine grid solution has been
  // attached, we now just compute the solution norm (i.e. the
  // difference from an "exact solution" of zero

  // Make sure the requested sys_name exists.
  std::map<std::string, SystemErrorMap>::iterator sys_iter =
    _errors.find(sys_name);

  if (sys_iter == _errors.end())
    {
      libMesh::err << "Sorry, couldn't find the requested system '"
                    << sys_name << "'."
                    << std::endl;
      libmesh_error();
    }

  // Make sure the requested unknown_name exists.
  SystemErrorMap::iterator var_iter = (*sys_iter).second.find(unknown_name);

  if (var_iter == (*sys_iter).second.end())
    {
      libMesh::err << "Sorry, couldn't find the requested variable '"
                    << unknown_name << "'."
                    << std::endl;
      libmesh_error();
    }

  // Return a reference to the proper error entry
  return (*var_iter).second;
}

template<typename OutputShape >

template void libMesh::ExactSolution::_compute_error< RealGradient >	(	const std::string &	sys_name,
		const std::string &	unknown_name,
		std::vector< Real > &	error_vals
	)			[inline, private]

This function computes the error (in the solution and its first derivative) for a single unknown in a single system. It is a private function since it is used by the implementation when solving for several unknowns in several systems.

Definition at line 533 of file exact_solution.C.

References _equation_systems, _equation_systems_fine, _exact_derivs, _exact_hessians, _exact_values, _extra_order, libMesh::MeshBase::active_local_elements_begin(), libMesh::MeshBase::active_local_elements_end(), libMesh::CommWorld, libMesh::TensorTools::curl_from_grad(), libMesh::System::current_solution(), libMesh::FEType::default_quadrature_rule(), libMesh::TensorTools::div_from_grad(), libMesh::DofMap::dof_indices(), libMesh::err, libMesh::FEInterface::field_type(), libMesh::AutoPtr< Tp >::get(), libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::EquationSystems::get_system(), libMesh::Parallel::Communicator::max(), libMesh::MeshBase::mesh_dimension(), libMesh::FEInterface::n_vec_dim(), libMesh::TensorTools::norm_sq(), libMesh::System::number(), libMesh::Real, libMeshEnums::SERIAL, libMesh::TypeVector< T >::size_sq(), libMesh::System::solution, libMesh::MeshBase::spatial_dimension(), libMesh::Parallel::Communicator::sum(), libMeshEnums::TYPE_VECTOR, libMesh::System::update_global_solution(), libMesh::System::variable_number(), libMesh::System::variable_scalar_number(), and libMesh::DofMap::variable_type().

{
  // This function must be run on all processors at once
  parallel_only();

  // Make sure we aren't "overconfigured"
  libmesh_assert (!(_exact_values.size() && _equation_systems_fine));

  // Get a reference to the system whose error is being computed.
  // If we have a fine grid, however, we'll integrate on that instead
  // for more accuracy.
  const System& computed_system = _equation_systems_fine ?
    _equation_systems_fine->get_system(sys_name) :
    _equation_systems.get_system (sys_name);

  const Real time = _equation_systems.get_system(sys_name).time;

  const unsigned int sys_num = computed_system.number();
  const unsigned int var = computed_system.variable_number(unknown_name);
  const unsigned int var_component =
    computed_system.variable_scalar_number(var, 0);

  // Prepare a global solution and a MeshFunction of the coarse system if we need one
  AutoPtr<MeshFunction> coarse_values;
  AutoPtr<NumericVector<Number> > comparison_soln = NumericVector<Number>::build();
  if (_equation_systems_fine)
    {
      const System& comparison_system
        = _equation_systems.get_system(sys_name);

      std::vector<Number> global_soln;
      comparison_system.update_global_solution(global_soln);
      comparison_soln->init(comparison_system.solution->size(), true, SERIAL);
      (*comparison_soln) = global_soln;

      coarse_values = AutoPtr<MeshFunction>
        (new MeshFunction(_equation_systems,
                          *comparison_soln,
                          comparison_system.get_dof_map(),
                          comparison_system.variable_number(unknown_name)));
      coarse_values->init();
    }

  // Initialize any functors we're going to use
  for (unsigned int i=0; i != _exact_values.size(); ++i)
    if (_exact_values[i])
      _exact_values[i]->init();

  for (unsigned int i=0; i != _exact_derivs.size(); ++i)
    if (_exact_derivs[i])
      _exact_derivs[i]->init();

  for (unsigned int i=0; i != _exact_hessians.size(); ++i)
    if (_exact_hessians[i])
      _exact_hessians[i]->init();

  // Get a reference to the dofmap and mesh for that system
  const DofMap& computed_dof_map = computed_system.get_dof_map();

  const MeshBase& _mesh = computed_system.get_mesh();

  const unsigned int dim = _mesh.mesh_dimension();

  // Zero the error before summation
  // 0 - sum of square of function error (L2)
  // 1 - sum of square of gradient error (H1 semi)
  // 2 - sum of square of Hessian error (H2 semi)
  // 3 - sum of sqrt(square of function error) (L1)
  // 4 - max of sqrt(square of function error) (Linfty)
  // 5 - sum of square of curl error (HCurl semi)
  // 6 - sum of square of div error (HDiv semi)
  error_vals = std::vector<Real>(7, 0.);

  // Construct Quadrature rule based on default quadrature order
  const FEType& fe_type  = computed_dof_map.variable_type(var);

  unsigned int n_vec_dim = FEInterface::n_vec_dim( _mesh, fe_type );

  // FIXME: MeshFunction needs to be updated to support vector-valued
  //        elements before we can use a reference solution.
  if( (n_vec_dim > 1) && _equation_systems_fine )
    {
      libMesh::err << "Error calculation using reference solution not yet\n"
                   << "supported for vector-valued elements."
                   << std::endl;
      libmesh_not_implemented();
    }

  AutoPtr<QBase> qrule =
    fe_type.default_quadrature_rule (dim,
                                     _extra_order);

  // Construct finite element object

  AutoPtr<FEGenericBase<OutputShape> > fe(FEGenericBase<OutputShape>::build(dim, fe_type));

  // Attach quadrature rule to FE object
  fe->attach_quadrature_rule (qrule.get());

  // The Jacobian*weight at the quadrature points.
  const std::vector<Real>& JxW                               = fe->get_JxW();

  // The value of the shape functions at the quadrature points
  // i.e. phi(i) = phi_values[i][qp]
  const std::vector<std::vector<OutputShape> >&  phi_values         = fe->get_phi();

  // The value of the shape function gradients at the quadrature points
  const std::vector<std::vector<typename FEGenericBase<OutputShape>::OutputGradient> >& 
                    dphi_values = fe->get_dphi();

  // The value of the shape function curls at the quadrature points
  // Only computed for vector-valued elements
  const std::vector<std::vector<typename FEGenericBase<OutputShape>::OutputShape> >* curl_values = NULL;

  // The value of the shape function divergences at the quadrature points
  // Only computed for vector-valued elements
  const std::vector<std::vector<typename FEGenericBase<OutputShape>::OutputDivergence> >* div_values = NULL;

  if( FEInterface::field_type(fe_type) == TYPE_VECTOR )
    {
      curl_values = &fe->get_curl_phi();
      div_values = &fe->get_div_phi();
    }

#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
  // The value of the shape function second derivatives at the quadrature points
  const std::vector<std::vector<typename FEGenericBase<OutputShape>::OutputTensor> >& 
                    d2phi_values = fe->get_d2phi(); 
#endif

  // The XYZ locations (in physical space) of the quadrature points
  const std::vector<Point>& q_point                          = fe->get_xyz();

  // The global degree of freedom indices associated
  // with the local degrees of freedom.
  std::vector<dof_id_type> dof_indices;


  //
  // Begin the loop over the elements
  //
  // TODO: this ought to be threaded (and using subordinate
  // MeshFunction objects in each thread rather than a single
  // master)
  MeshBase::const_element_iterator       el     = _mesh.active_local_elements_begin();
  const MeshBase::const_element_iterator end_el = _mesh.active_local_elements_end();

  for ( ; el != end_el; ++el)
    {
      // Store a pointer to the element we are currently
      // working on.  This allows for nicer syntax later.
      const Elem* elem = *el;

      // reinitialize the element-specific data
      // for the current element
      fe->reinit (elem);

      // Get the local to global degree of freedom maps
      computed_dof_map.dof_indices    (elem, dof_indices, var);

      // The number of quadrature points
      const unsigned int n_qp = qrule->n_points();

      // The number of shape functions
      const unsigned int n_sf = 
        libmesh_cast_int<unsigned int>(dof_indices.size());

      //
      // Begin the loop over the Quadrature points.
      //
      for (unsigned int qp=0; qp<n_qp; qp++)
        {
          // Real u_h = 0.;
          // RealGradient grad_u_h;

          typename FEGenericBase<OutputShape>::OutputNumber u_h = 0.;

          typename FEGenericBase<OutputShape>::OutputNumberGradient grad_u_h;
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
          typename FEGenericBase<OutputShape>::OutputNumberTensor grad2_u_h;
#endif
          typename FEGenericBase<OutputShape>::OutputNumber curl_u_h = 0.0;
          typename FEGenericBase<OutputShape>::OutputNumberDivergence div_u_h = 0.0;

          // Compute solution values at the current
          // quadrature point.  This reqiures a sum
          // over all the shape functions evaluated
          // at the quadrature point.
          for (unsigned int i=0; i<n_sf; i++)
            {
              // Values from current solution.
              u_h      += phi_values[i][qp]*computed_system.current_solution  (dof_indices[i]);
              grad_u_h += dphi_values[i][qp]*computed_system.current_solution (dof_indices[i]);
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
              grad2_u_h += d2phi_values[i][qp]*computed_system.current_solution (dof_indices[i]);
#endif
              if( FEInterface::field_type(fe_type) == TYPE_VECTOR )
                {
                  curl_u_h += (*curl_values)[i][qp]*computed_system.current_solution (dof_indices[i]);
                  div_u_h += (*div_values)[i][qp]*computed_system.current_solution (dof_indices[i]);
                }
            }

          // Compute the value of the error at this quadrature point
          typename FEGenericBase<OutputShape>::OutputNumber exact_val = 0;
          RawAccessor<typename FEGenericBase<OutputShape>::OutputNumber> exact_val_accessor( exact_val, dim );
          if (_exact_values.size() > sys_num && _exact_values[sys_num])
            {
              for( unsigned int c = 0; c < n_vec_dim; c++)
                exact_val_accessor(c) =
                  _exact_values[sys_num]->
                  component(var_component+c, q_point[qp], time);
            }
          else if (_equation_systems_fine)
            {
              // FIXME: Needs to be updated for vector-valued elements
              exact_val = (*coarse_values)(q_point[qp]);
            }
          const typename FEGenericBase<OutputShape>::OutputNumber val_error = u_h - exact_val;

          // Add the squares of the error to each contribution
          Real error_sq = TensorTools::norm_sq(val_error);
          error_vals[0] += JxW[qp]*error_sq;

          Real norm = sqrt(error_sq);
          error_vals[3] += JxW[qp]*norm;

          if(error_vals[4]<norm) { error_vals[4] = norm; }

          // Compute the value of the error in the gradient at this
          // quadrature point
          typename FEGenericBase<OutputShape>::OutputNumberGradient exact_grad;
          RawAccessor<typename FEGenericBase<OutputShape>::OutputNumberGradient> exact_grad_accessor( exact_grad, _mesh.spatial_dimension() );
          if (_exact_derivs.size() > sys_num && _exact_derivs[sys_num])
            {
              for( unsigned int c = 0; c < n_vec_dim; c++)
                for( unsigned int d = 0; d < _mesh.spatial_dimension(); d++ )
                  exact_grad_accessor(d + c*_mesh.spatial_dimension() ) =
                    _exact_derivs[sys_num]->
                    component(var_component+c, q_point[qp], time)(d);
            }
          else if (_equation_systems_fine)
            {
              // FIXME: Needs to be updated for vector-valued elements
              exact_grad = coarse_values->gradient(q_point[qp]);
            }

          const typename FEGenericBase<OutputShape>::OutputNumberGradient grad_error = grad_u_h - exact_grad;
          
          error_vals[1] += JxW[qp]*grad_error.size_sq();


          if( FEInterface::field_type(fe_type) == TYPE_VECTOR )
            {
              // Compute the value of the error in the curl at this
              // quadrature point
              typename FEGenericBase<OutputShape>::OutputNumber exact_curl = 0.0;
              if (_exact_derivs.size() > sys_num && _exact_derivs[sys_num])
                {
                  exact_curl = TensorTools::curl_from_grad( exact_grad );
                }
              else if (_equation_systems_fine)
                {
                  // FIXME: Need to implement curl for MeshFunction and support reference
                  //        solution for vector-valued elements
                }

              const typename FEGenericBase<OutputShape>::OutputNumber curl_error = curl_u_h - exact_curl;
              
              error_vals[5] += JxW[qp]*TensorTools::norm_sq(curl_error);

              // Compute the value of the error in the divergence at this
              // quadrature point
              typename FEGenericBase<OutputShape>::OutputNumberDivergence exact_div = 0.0;
              if (_exact_derivs.size() > sys_num && _exact_derivs[sys_num])
                {
                  exact_div = TensorTools::div_from_grad( exact_grad );
                }
              else if (_equation_systems_fine)
                {
                  // FIXME: Need to implement div for MeshFunction and support reference
                  //        solution for vector-valued elements
                }
              
              const typename FEGenericBase<OutputShape>::OutputNumberDivergence div_error = div_u_h - exact_div;
              
              error_vals[6] += JxW[qp]*TensorTools::norm_sq(div_error);
            }

#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
          // Compute the value of the error in the hessian at this
          // quadrature point
          typename FEGenericBase<OutputShape>::OutputNumberTensor exact_hess;
          RawAccessor<typename FEGenericBase<OutputShape>::OutputNumberTensor> exact_hess_accessor( exact_hess, dim );
          if (_exact_hessians.size() > sys_num && _exact_hessians[sys_num])
            {
              //FIXME: This needs to be implemented to support rank 3 tensors 
              //       which can't happen until type_n_tensor is fully implemented
              //       and a RawAccessor<TypeNTensor> is fully implemented
              if( FEInterface::field_type(fe_type) == TYPE_VECTOR )
                libmesh_not_implemented();

              for( unsigned int c = 0; c < n_vec_dim; c++)
                for( unsigned int d = 0; d < dim; d++ )
                  for( unsigned int e =0; e < dim; e++ )
                    exact_hess_accessor(d + e*dim + c*dim*dim) =
                      _exact_hessians[sys_num]->
                      component(var_component+c, q_point[qp], time)(d,e);
            }
          else if (_equation_systems_fine)
            {
              // FIXME: Needs to be updated for vector-valued elements
              exact_hess = coarse_values->hessian(q_point[qp]);
            }
          
          const typename FEGenericBase<OutputShape>::OutputNumberTensor grad2_error = grad2_u_h - exact_hess;
          
          // FIXME: PB: Is this what we want for rank 3 tensors?
          error_vals[2] += JxW[qp]*grad2_error.size_sq();
#endif

        } // end qp loop
    } // end element loop

  // Add up the error values on all processors, except for the L-infty
  // norm, for which the maximum is computed.
  Real l_infty_norm = error_vals[4];
  CommWorld.max(l_infty_norm);
  CommWorld.sum(error_vals);
  error_vals[4] = l_infty_norm;
}

void libMesh::ExactSolution::attach_exact_deriv

(

Gradient

gptrconst Point &p,const Parameters &parameters,const std::string &sys_name,const std::string &unknown_name

)

Attach an arbitrary function which computes the exact gradient of the solution at any point.

Definition at line 153 of file exact_solution.C.

References _equation_systems, _equation_systems_fine, _exact_derivs, libMesh::EquationSystems::get_system(), libMesh::EquationSystems::n_systems(), and libMesh::EquationSystems::parameters.

{
  libmesh_assert(gptr);

  // Clear out any previous _exact_derivs entries, then add a new
  // entry for each system.
  _exact_derivs.clear();

  for (unsigned int sys=0; sys<_equation_systems.n_systems(); ++sys)
    {
      const System& system = _equation_systems.get_system(sys);
      _exact_derivs.push_back
        (new WrappedFunction<Gradient>
          (system, gptr, &_equation_systems.parameters));
    }

  // If we're using exact values, we're not using a fine grid solution
  _equation_systems_fine = NULL;
}

void libMesh::ExactSolution::attach_exact_deriv	(	unsigned int	sys_num,
		FunctionBase< Gradient > *	g
	)

Clone and attach an arbitrary functor which computes the exact gradient of the system sys_num solution at any point.

Definition at line 196 of file exact_solution.C.

References _exact_derivs, libMesh::FunctionBase< Output >::clone(), and libMesh::AutoPtr< Tp >::release().

{
  if (_exact_derivs.size() <= sys_num)
  _exact_derivs.resize(sys_num+1, NULL);

  if (g)
    _exact_derivs[sys_num] = g->clone().release();
}

void libMesh::ExactSolution::attach_exact_derivs

(

std::vector< FunctionBase< Gradient > * >

g

)

Clone and attach arbitrary functors which compute the exact gradients of the EquationSystems' solutions at any point.

Definition at line 177 of file exact_solution.C.

References _exact_derivs.

{
  // Clear out any previous _exact_derivs entries, then add a new
  // entry for each system.
  for (unsigned int i=0; i != _exact_derivs.size(); ++i)
    delete (_exact_derivs[i]);

  _exact_derivs.clear();
  _exact_derivs.resize(g.size(), NULL);

  // We use clone() to get non-sliced copies of FunctionBase
  // subclasses, but we can't put the resulting AutoPtrs into an STL
  // container.
  for (unsigned int i=0; i != g.size(); ++i)
    if (g[i])
      _exact_derivs[i] = g[i]->clone().release();
}

void libMesh::ExactSolution::attach_exact_hessian

(

Tensor

hptrconst Point &p,const Parameters &parameters,const std::string &sys_name,const std::string &unknown_name

)

Attach an arbitrary function which computes the exact second derivatives of the solution at any point.

Definition at line 207 of file exact_solution.C.

References _equation_systems, _equation_systems_fine, _exact_hessians, libMesh::EquationSystems::get_system(), libMesh::EquationSystems::n_systems(), and libMesh::EquationSystems::parameters.

{
  libmesh_assert(hptr);

  // Clear out any previous _exact_hessians entries, then add a new
  // entry for each system.
  _exact_hessians.clear();

  for (unsigned int sys=0; sys<_equation_systems.n_systems(); ++sys)
    {
      const System& system = _equation_systems.get_system(sys);
      _exact_hessians.push_back
        (new WrappedFunction<Tensor>
          (system, hptr, &_equation_systems.parameters));
    }

  // If we're using exact values, we're not using a fine grid solution
  _equation_systems_fine = NULL;
}

void libMesh::ExactSolution::attach_exact_hessian	(	unsigned int	sys_num,
		FunctionBase< Tensor > *	h
	)

Clone and attach an arbitrary functor which computes the exact second derivatives of the system sys_num solution at any point.

Definition at line 250 of file exact_solution.C.

References _exact_hessians, and libMesh::FunctionBase< Output >::clone().

{
  if (_exact_hessians.size() <= sys_num)
  _exact_hessians.resize(sys_num+1, NULL);

  if (h)
    _exact_hessians[sys_num] = h->clone().release();
}

void libMesh::ExactSolution::attach_exact_hessians

(

std::vector< FunctionBase< Tensor > * >

h

)

Clone and attach arbitrary functors which compute the exact second derivatives of the EquationSystems' solutions at any point.

Definition at line 231 of file exact_solution.C.

References _exact_hessians.

{
  // Clear out any previous _exact_hessians entries, then add a new
  // entry for each system.
  for (unsigned int i=0; i != _exact_hessians.size(); ++i)
    delete (_exact_hessians[i]);

  _exact_hessians.clear();
  _exact_hessians.resize(h.size(), NULL);

  // We use clone() to get non-sliced copies of FunctionBase
  // subclasses, but we can't put the resulting AutoPtrs into an STL
  // container.
  for (unsigned int i=0; i != h.size(); ++i)
    if (h[i])
      _exact_hessians[i] = h[i]->clone().release();
}

void libMesh::ExactSolution::attach_exact_value

(

Number

fptrconst Point &p, const Parameters &Parameters, const std::string &sys_name, const std::string &unknown_name

)

Attach an arbitrary function which computes the exact value of the solution at any point.

void libMesh::ExactSolution::attach_exact_value	(	unsigned int	sys_num,
		FunctionBase< Number > *	f
	)

Clone and attach an arbitrary functor which computes the exact value of the system sys_num solution at any point.

Definition at line 142 of file exact_solution.C.

References _exact_values, libMesh::FunctionBase< Output >::clone(), and libMesh::AutoPtr< Tp >::release().

{
  if (_exact_values.size() <= sys_num)
  _exact_values.resize(sys_num+1, NULL);

  if (f)
    _exact_values[sys_num] = f->clone().release();
}

void libMesh::ExactSolution::attach_exact_values

(

std::vector< FunctionBase< Number > * >

f

)

Clone and attach arbitrary functors which compute the exact values of the EquationSystems' solutions at any point.

Definition at line 123 of file exact_solution.C.

References _exact_values.

{
  // Clear out any previous _exact_values entries, then add a new
  // entry for each system.
  for (unsigned int i=0; i != _exact_values.size(); ++i)
    delete (_exact_values[i]);

  _exact_values.clear();
  _exact_values.resize(f.size(), NULL);

  // We use clone() to get non-sliced copies of FunctionBase
  // subclasses, but we can't put the resulting AutoPtrs into an STL
  // container.
  for (unsigned int i=0; i != f.size(); ++i)
    if (f[i])
      _exact_values[i] = f[i]->clone().release();
}

void libMesh::ExactSolution::attach_reference_solution

(

const EquationSystems *

es_fine

)

Attach function similar to system.h which allows the user to attach a second EquationSystems object with a reference fine grid solution.

Definition at line 87 of file exact_solution.C.

References _equation_systems_fine, _exact_derivs, _exact_hessians, and _exact_values.

{
  libmesh_assert(es_fine);
  _equation_systems_fine = es_fine;

  // If we're using a fine grid solution, we're not using exact values
  _exact_values.clear();
  _exact_derivs.clear();
  _exact_hessians.clear();
}

void libMesh::ExactSolution::compute_error	(	const std::string &	sys_name,
		const std::string &	unknown_name
	)

Computes and stores the error in the solution value e = u-u_h, the gradient grad(e) = grad(u) - grad(u_h), and possibly the hessian grad(grad(e)) = grad(grad(u)) - grad(grad(u_h)). Does not return any value. For that you need to call the l2_error(), h1_error() or h2_error() functions respectively.

Definition at line 297 of file exact_solution.C.

References _check_inputs(), _equation_systems, libMesh::FEInterface::field_type(), libMesh::EquationSystems::get_system(), libMesh::EquationSystems::has_system(), libMeshEnums::TYPE_SCALAR, and libMeshEnums::TYPE_VECTOR.

{
  // Check the inputs for validity, and get a reference
  // to the proper location to store the error
  std::vector<Real>& error_vals = this->_check_inputs(sys_name,
                                                      unknown_name);

  libmesh_assert( _equation_systems.has_system(sys_name) );
  const System& sys = _equation_systems.get_system<System>( sys_name );
  
  libmesh_assert( sys.has_variable( unknown_name ) );
  switch( FEInterface::field_type(sys.variable_type( unknown_name )) )
    {
    case TYPE_SCALAR:
      {
        this->_compute_error<Real>(sys_name,
                                   unknown_name,
                                   error_vals);
        break;
      }
    case TYPE_VECTOR:
      {
        this->_compute_error<RealGradient>(sys_name,
                                           unknown_name,
                                           error_vals);
        break;
      }
    default:
      libmesh_error();
    }

  return;
}

Real libMesh::ExactSolution::error_norm	(	const std::string &	sys_name,
		const std::string &	unknown_name,
		const FEMNormType &	norm
	)

This function returns the error in the requested norm for the system sys_name for the unknown unknown_name. Note that no error computations are actually performed, you must call compute_error() for that. Note also that the result is not exact, but an approximation based on the chosen quadrature rule.

Definition at line 336 of file exact_solution.C.

References _check_inputs(), _equation_systems, libMesh::err, libMesh::FEInterface::field_type(), libMesh::EquationSystems::get_system(), libMeshEnums::H1, libMeshEnums::H1_SEMINORM, libMeshEnums::H2, libMeshEnums::H2_SEMINORM, libMesh::EquationSystems::has_system(), libMeshEnums::HCURL, libMeshEnums::HCURL_SEMINORM, libMeshEnums::HDIV, libMeshEnums::HDIV_SEMINORM, libMeshEnums::L1, libMeshEnums::L2, libMeshEnums::L_INF, and libMeshEnums::TYPE_SCALAR.

Referenced by hcurl_error(), and hdiv_error().

{
  // Check the inputs for validity, and get a reference
  // to the proper location to store the error
  std::vector<Real>& error_vals = this->_check_inputs(sys_name,
                                                      unknown_name);

  libmesh_assert(_equation_systems.has_system(sys_name));
  libmesh_assert(_equation_systems.get_system(sys_name).has_variable( unknown_name ));
  const FEType& fe_type = _equation_systems.get_system(sys_name).variable_type(unknown_name);

  switch (norm)
    {
    case L2:
      return std::sqrt(error_vals[0]);
    case H1:
      return std::sqrt(error_vals[0] + error_vals[1]);
    case H2:
      return std::sqrt(error_vals[0] + error_vals[1] + error_vals[2]);
    case HCURL:
      {
        if(FEInterface::field_type(fe_type) == TYPE_SCALAR)
          {
            libMesh::err << "Cannot compute HCurl error norm of scalar-valued variables!" << std::endl;
            libmesh_error();
          }
        else
          return std::sqrt(error_vals[0] + error_vals[5]);
      }
    case HDIV:
      {
        if(FEInterface::field_type(fe_type) == TYPE_SCALAR)
          {
            libMesh::err << "Cannot compute HDiv error norm of scalar-valued variables!" << std::endl;
            libmesh_error();
          }
        else
          return std::sqrt(error_vals[0] + error_vals[6]);
      }
    case H1_SEMINORM:
      return std::sqrt(error_vals[1]);
    case H2_SEMINORM:
      return std::sqrt(error_vals[2]);
    case HCURL_SEMINORM:
      {
        if(FEInterface::field_type(fe_type) == TYPE_SCALAR)
          {
            libMesh::err << "Cannot compute HCurl error seminorm of scalar-valued variables!" << std::endl;
            libmesh_error();
          }
        else
          return std::sqrt(error_vals[5]);
      }
    case HDIV_SEMINORM:
      {
        if(FEInterface::field_type(fe_type) == TYPE_SCALAR)
          {
            libMesh::err << "Cannot compute HDiv error seminorm of scalar-valued variables!" << std::endl;
            libmesh_error();
          }
        else
          return std::sqrt(error_vals[6]);
      }
    case L1:
      return error_vals[3];
    case L_INF:
      return error_vals[4];
    
    // Currently only Sobolev norms/seminorms are supported
    default:
      libmesh_error();
    }
}

void libMesh::ExactSolution::extra_quadrature_order

(

const int

extraorder

)

[inline]

Increases or decreases the order of the quadrature rule used for numerical integration.

Definition at line 159 of file exact_solution.h.

References _extra_order.

    { _extra_order = extraorder; }

Real libMesh::ExactSolution::h1_error	(	const std::string &	sys_name,
		const std::string &	unknown_name
	)

This function computes and returns the H1 error for the system sys_name for the unknown unknown_name. Note that no error computations are actually performed, you must call compute_error() for that.

Definition at line 478 of file exact_solution.C.

References _check_inputs().

{
  // If the user has supplied no exact derivative function, we
  // just integrate the H1 norm of the solution; i.e. its
  // difference from an "exact solution" of zero.

  // Check the inputs for validity, and get a reference
  // to the proper location to store the error
  std::vector<Real>& error_vals = this->_check_inputs(sys_name,
                                                      unknown_name);

  // Return the square root of the sum of the computed errors.
  return std::sqrt(error_vals[0] + error_vals[1]);
}

Real libMesh::ExactSolution::h2_error	(	const std::string &	sys_name,
		const std::string &	unknown_name
	)

This function computes and returns the H2 error for the system sys_name for the unknown unknown_name. Note that no error computations are actually performed, you must call compute_error() for that.

Definition at line 510 of file exact_solution.C.

References _check_inputs().

{
  // If the user has supplied no exact derivative functions, we
  // just integrate the H2 norm of the solution; i.e. its
  // difference from an "exact solution" of zero.

  // Check the inputs for validity, and get a reference
  // to the proper location to store the error
  std::vector<Real>& error_vals = this->_check_inputs(sys_name,
                                                      unknown_name);

  // Return the square root of the sum of the computed errors.
  return std::sqrt(error_vals[0] + error_vals[1] + error_vals[2]);
}

Real libMesh::ExactSolution::hcurl_error	(	const std::string &	sys_name,
		const std::string &	unknown_name
	)

This function computes and returns the HCurl error for the system sys_name for the unknown unknown_name. Note that no error computations are actually performed, you must call compute_error() for that. This is only valid for vector-valued element. An error is thrown if requested for scalar-valued elements.

Definition at line 495 of file exact_solution.C.

References error_norm(), and libMeshEnums::HCURL.

{
  return this->error_norm(sys_name,unknown_name,HCURL);
}

Real libMesh::ExactSolution::hdiv_error	(	const std::string &	sys_name,
		const std::string &	unknown_name
	)

This function computes and returns the HDiv error for the system sys_name for the unknown unknown_name. Note that no error computations are actually performed, you must call compute_error() for that. This is only valid for vector-valued element. An error is thrown if requested for scalar-valued elements.

Definition at line 502 of file exact_solution.C.

References error_norm(), and libMeshEnums::HDIV.

{
  return this->error_norm(sys_name,unknown_name,HDIV);
}

Real libMesh::ExactSolution::l1_error	(	const std::string &	sys_name,
		const std::string &	unknown_name
	)

This function returns the integrated L1 error for the system sys_name for the unknown unknown_name. Note that no error computations are actually performed, you must call compute_error() for that.

Definition at line 438 of file exact_solution.C.

References _check_inputs().

{

  // Check the inputs for validity, and get a reference
  // to the proper location to store the error
  std::vector<Real>& error_vals = this->_check_inputs(sys_name,
                                                      unknown_name);

  // Return the square root of the first component of the
  // computed error.
  return error_vals[3];
}

Real libMesh::ExactSolution::l2_error	(	const std::string &	sys_name,
		const std::string &	unknown_name
	)

This function returns the integrated L2 error for the system sys_name for the unknown unknown_name. Note that no error computations are actually performed, you must call compute_error() for that.

Definition at line 418 of file exact_solution.C.

References _check_inputs().

{

  // Check the inputs for validity, and get a reference
  // to the proper location to store the error
  std::vector<Real>& error_vals = this->_check_inputs(sys_name,
                                                      unknown_name);

  // Return the square root of the first component of the
  // computed error.
  return std::sqrt(error_vals[0]);
}

Real libMesh::ExactSolution::l_inf_error	(	const std::string &	sys_name,
		const std::string &	unknown_name
	)

This function returns the L_INF error for the system sys_name for the unknown unknown_name. Note that no error computations are actually performed, you must call compute_error() for that. Note also that the result (as for the other norms as well) is not exact, but an approximation based on the chosen quadrature rule: to compute it, we take the max of the absolute value of the error over all the quadrature points.

Definition at line 458 of file exact_solution.C.

References _check_inputs().

{

  // Check the inputs for validity, and get a reference
  // to the proper location to store the error
  std::vector<Real>& error_vals = this->_check_inputs(sys_name,
                                                      unknown_name);

  // Return the square root of the first component of the
  // computed error.
  return error_vals[4];
}

---

Member Data Documentation

const EquationSystems& libMesh::ExactSolution::_equation_systems [private]

Constant reference to the EquationSystems object used for the simulation.

Definition at line 307 of file exact_solution.h.

Referenced by _compute_error(), attach_exact_deriv(), attach_exact_hessian(), compute_error(), error_norm(), and ExactSolution().

const EquationSystems* libMesh::ExactSolution::_equation_systems_fine [private]

Constant pointer to the EquationSystems object containing the fine grid solution.

Definition at line 313 of file exact_solution.h.

Referenced by _compute_error(), attach_exact_deriv(), attach_exact_hessian(), and attach_reference_solution().

std::map<std::string, SystemErrorMap> libMesh::ExactSolution::_errors [private]

A map of SystemErrorMaps, which contains entries for each system in the EquationSystems object. This is required, since it is possible for two systems to have unknowns with the *same name*.

Definition at line 301 of file exact_solution.h.

Referenced by _check_inputs(), and ExactSolution().

std::vector<FunctionBase<Gradient> *> libMesh::ExactSolution::_exact_derivs [private]

User-provided functors which compute the exact derivative of the solution for each system.

Definition at line 277 of file exact_solution.h.

Referenced by _compute_error(), attach_exact_deriv(), attach_exact_derivs(), attach_reference_solution(), and ~ExactSolution().

std::vector<FunctionBase<Tensor> *> libMesh::ExactSolution::_exact_hessians [private]

User-provided functors which compute the exact hessians of the solution for each system.

Definition at line 283 of file exact_solution.h.

Referenced by _compute_error(), attach_exact_hessian(), attach_exact_hessians(), attach_reference_solution(), and ~ExactSolution().

std::vector<FunctionBase<Number> *> libMesh::ExactSolution::_exact_values [private]

User-provided functors which compute the exact value of the solution for each system.

Definition at line 271 of file exact_solution.h.

Referenced by _compute_error(), attach_exact_value(), attach_exact_values(), attach_reference_solution(), and ~ExactSolution().

int libMesh::ExactSolution::_extra_order [private]

Extra order to use for quadrature rule

Definition at line 318 of file exact_solution.h.

Referenced by _compute_error(), and extra_quadrature_order().

---

The documentation for this class was generated from the following files:

• exact_solution.h
• exact_solution.C