libMesh::ExactErrorEstimator Class Reference

#include <exact_error_estimator.h>

Inheritance diagram for libMesh::ExactErrorEstimator:

Public Types
typedef Number(*	ValueFunctionPointer) (const Point &p, const Parameters &Parameters, const std::string &sys_name, const std::string &unknown_name)
typedef Gradient(*	GradientFunctionPointer) (const Point &p, const Parameters &parameters, const std::string &sys_name, const std::string &unknown_name)
typedef Tensor(*	HessianFunctionPointer) (const Point &p, const Parameters &parameters, const std::string &sys_name, const std::string &unknown_name)
typedef std::map< std::pair< const System *, unsigned int >, ErrorVector * >	ErrorMap

Public Member Functions
	ExactErrorEstimator ()
	ExactErrorEstimator (const ExactErrorEstimator &)=delete
ExactErrorEstimator &	operator= (const ExactErrorEstimator &)=delete
	ExactErrorEstimator (ExactErrorEstimator &&)=default
ExactErrorEstimator &	operator= (ExactErrorEstimator &&)=default
virtual	~ExactErrorEstimator ()=default
void	attach_exact_values (std::vector< FunctionBase< Number > *> f)
void	attach_exact_value (unsigned int sys_num, FunctionBase< Number > *f)
void	attach_exact_value (ValueFunctionPointer fptr)
void	attach_exact_derivs (std::vector< FunctionBase< Gradient > *> g)
void	attach_exact_deriv (unsigned int sys_num, FunctionBase< Gradient > *g)
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)
void	attach_exact_hessian (HessianFunctionPointer hptr)
void	attach_reference_solution (EquationSystems *es_fine)
void	extra_quadrature_order (const int extraorder)
virtual void	estimate_error (const System &system, ErrorVector &error_per_cell, const NumericVector< Number > *solution_vector=nullptr, bool estimate_parent_error=false) override
virtual ErrorEstimatorType	type () const override
virtual void	estimate_errors (const EquationSystems &equation_systems, ErrorVector &error_per_cell, const std::map< const System *, SystemNorm > &error_norms, const std::map< const System *, const NumericVector< Number > *> *solution_vectors=nullptr, bool estimate_parent_error=false)
virtual void	estimate_errors (const EquationSystems &equation_systems, ErrorMap &errors_per_cell, const std::map< const System *, const NumericVector< Number > *> *solution_vectors=nullptr, bool estimate_parent_error=false)

Public Attributes
SystemNorm	error_norm

Protected Member Functions
void	reduce_error (std::vector< ErrorVectorReal > &error_per_cell, const Parallel::Communicator &comm) const

Private Member Functions
Real	find_squared_element_error (const System &system, const std::string &var_name, const Elem *elem, const DenseVector< Number > &Uelem, FEBase *fe, MeshFunction *fine_values) const
void	clear_functors ()

Private Attributes
ValueFunctionPointer	_exact_value
GradientFunctionPointer	_exact_deriv
HessianFunctionPointer	_exact_hessian
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
EquationSystems *	_equation_systems_fine
int	_extra_order

Detailed Description

This class implements an "error estimator" based on the difference between the approximate and exact solution. In theory the quadrature error in this estimate should be much lower than the approximation error in other estimates, so this estimator can be used to calculate effectivity.

Author

Roy Stogner

Date

2006

Definition at line 57 of file exact_error_estimator.h.

Member Typedef Documentation

ErrorMap

typedef std::map<std::pair<const System *, unsigned int>, ErrorVector *> libMesh::ErrorEstimator::ErrorMap

inherited

When calculating many error vectors at once, we need a data structure to hold them all

Definition at line 124 of file error_estimator.h.

GradientFunctionPointer

typedef Gradient(* libMesh::ExactErrorEstimator::GradientFunctionPointer) (const 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 122 of file exact_error_estimator.h.

HessianFunctionPointer

typedef Tensor(* libMesh::ExactErrorEstimator::HessianFunctionPointer) (const 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 145 of file exact_error_estimator.h.

ValueFunctionPointer

typedef Number(* libMesh::ExactErrorEstimator::ValueFunctionPointer) (const 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.

Definition at line 99 of file exact_error_estimator.h.

Constructor & Destructor Documentation

ExactErrorEstimator() [1/3]

libMesh::ExactErrorEstimator::ExactErrorEstimator

(

)

Constructor. Responsible for initializing the _bc_function function pointer to nullptr, and defaulting the norm type to H1.

Definition at line 48 of file exact_error_estimator.C.

References libMesh::ErrorEstimator::error_norm, and libMesh::H1.

                                         :
    ErrorEstimator(),
    _exact_value(nullptr),
    _exact_deriv(nullptr),
    _exact_hessian(nullptr),
    _equation_systems_fine(nullptr),
    _extra_order(0)
{
  error_norm = H1;
}

ExactErrorEstimator() [2/3]

libMesh::ExactErrorEstimator::ExactErrorEstimator ( const ExactErrorEstimator &  )

delete

This class cannot be (default) copy constructed/assigned because it has containers of unique_ptrs. Explicitly deleting these functions is the best way to document this fact.

ExactErrorEstimator() [3/3]

libMesh::ExactErrorEstimator::ExactErrorEstimator ( ExactErrorEstimator &&  )

default

Defaulted move ctor, move assignment operator, and destructor.

~ExactErrorEstimator()

virtual libMesh::ExactErrorEstimator::~ExactErrorEstimator ( )

virtualdefault

Member Function Documentation

attach_exact_deriv() [1/2]

void libMesh::ExactErrorEstimator::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 125 of file exact_error_estimator.C.

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

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

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

attach_exact_deriv() [2/2]

void libMesh::ExactErrorEstimator::attach_exact_deriv

(

GradientFunctionPointer

gptr

)

Definition at line 101 of file exact_error_estimator.C.

References _equation_systems_fine, _exact_deriv, and clear_functors().

{
  libmesh_assert(gptr);
  _exact_deriv = gptr;

  // We're not using a fine grid solution
  _equation_systems_fine = nullptr;

  // We're not using user-provided functors
  this->clear_functors();
}

attach_exact_derivs()

void libMesh::ExactErrorEstimator::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 114 of file exact_error_estimator.C.

References _exact_derivs.

{
  // Automatically delete any previous _exact_derivs entries, then add a new
  // entry for each system.
  _exact_derivs.clear();

  for (auto ptr : g)
    _exact_derivs.emplace_back(ptr ? ptr->clone() : nullptr);
}

attach_exact_hessian() [1/2]

void libMesh::ExactErrorEstimator::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 162 of file exact_error_estimator.C.

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

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

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

attach_exact_hessian() [2/2]

void libMesh::ExactErrorEstimator::attach_exact_hessian

(

HessianFunctionPointer

hptr

)

Definition at line 138 of file exact_error_estimator.C.

References _equation_systems_fine, _exact_hessian, and clear_functors().

{
  libmesh_assert(hptr);
  _exact_hessian = hptr;

  // We're not using a fine grid solution
  _equation_systems_fine = nullptr;

  // We're not using user-provided functors
  this->clear_functors();
}

attach_exact_hessians()

void libMesh::ExactErrorEstimator::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 151 of file exact_error_estimator.C.

References _exact_hessians.

{
  // Automatically delete any previous _exact_hessians entries, then add a new
  // entry for each system.
  _exact_hessians.clear();

  for (auto ptr : h)
    _exact_hessians.emplace_back(ptr ? ptr->clone() : nullptr);
}

attach_exact_value() [1/2]

void libMesh::ExactErrorEstimator::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 90 of file exact_error_estimator.C.

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

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

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

attach_exact_value() [2/2]

void libMesh::ExactErrorEstimator::attach_exact_value

(

ValueFunctionPointer

fptr

)

Definition at line 66 of file exact_error_estimator.C.

References _equation_systems_fine, _exact_value, and clear_functors().

{
  libmesh_assert(fptr);
  _exact_value = fptr;

  // We're not using a fine grid solution
  _equation_systems_fine = nullptr;

  // We're not using user-provided functors
  this->clear_functors();
}

attach_exact_values()

void libMesh::ExactErrorEstimator::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 79 of file exact_error_estimator.C.

References _exact_values.

{
  // Automatically delete any previous _exact_values entries, then add a new
  // entry for each system.
  _exact_values.clear();

  for (auto ptr : f)
    _exact_values.emplace_back(ptr ? ptr->clone() : nullptr);
}

attach_reference_solution()

void libMesh::ExactErrorEstimator::attach_reference_solution

(

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 173 of file exact_error_estimator.C.

References _equation_systems_fine, _exact_deriv, _exact_hessian, _exact_value, and clear_functors().

{
  libmesh_assert(es_fine);
  _equation_systems_fine = es_fine;

  // If we're using a fine grid solution, we're not using exact value
  // function pointers or functors.
  _exact_value = nullptr;
  _exact_deriv = nullptr;
  _exact_hessian = nullptr;

  this->clear_functors();
}

clear_functors()

void libMesh::ExactErrorEstimator::clear_functors ( )

private

Helper method for cleanup

Definition at line 534 of file exact_error_estimator.C.

References _exact_derivs, _exact_hessians, and _exact_values.

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

{
  _exact_values.clear();
  _exact_derivs.clear();
  _exact_hessians.clear();
}

estimate_error()

void libMesh::ExactErrorEstimator::estimate_error ( const System &  system, ErrorVector &  error_per_cell, const NumericVector< Number > *  solution_vector = nullptr, bool  estimate_parent_error = false  )

overridevirtual

This function uses the exact solution function to estimate the error on each cell. The estimated error is output in the vector error_per_cell

Implements libMesh::ErrorEstimator.

Definition at line 187 of file exact_error_estimator.C.

References _equation_systems_fine, _exact_derivs, _exact_hessians, _exact_values, _extra_order, libMesh::FEGenericBase< OutputType >::build(), libMesh::NumericVector< T >::build(), libMesh::Elem::child_ref_range(), libMesh::FEGenericBase< OutputType >::coarsened_dof_values(), libMesh::ParallelObject::comm(), libMesh::System::current_local_solution, libMesh::System::current_solution(), libMesh::FEType::default_quadrature_rule(), libMesh::DofMap::dof_indices(), libMesh::ErrorEstimator::error_norm, libMesh::ErrorVectorReal, find_squared_element_error(), libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::EquationSystems::get_system(), libMesh::DofObject::id(), libMesh::libmesh_ignore(), mesh, n_vars, libMesh::System::n_vars(), libMesh::System::name(), libMesh::Elem::parent(), libMesh::ErrorEstimator::reduce_error(), libMesh::SERIAL, libMesh::System::solution, libMesh::NumericVector< T >::swap(), libMesh::System::update_global_solution(), libMesh::System::variable_name(), libMesh::System::variable_number(), libMesh::DofMap::variable_type(), and libMesh::SystemNorm::weight().

{
  // Ignore the fact that this variable is unused when !LIBMESH_ENABLE_AMR
  libmesh_ignore(estimate_parent_error);

  // The current mesh
  const MeshBase & mesh = system.get_mesh();

  // The dimensionality of the mesh
  const unsigned int dim = mesh.mesh_dimension();

  // The number of variables in the system
  const unsigned int n_vars = system.n_vars();

  // The DofMap for this system
  const DofMap & dof_map = system.get_dof_map();

  // Resize the error_per_cell vector to be
  // the number of elements, initialize it to 0.
  error_per_cell.resize (mesh.max_elem_id());
  std::fill (error_per_cell.begin(), error_per_cell.end(), 0.);

  // Prepare current_local_solution to localize a non-standard
  // solution vector if necessary
  if (solution_vector && solution_vector != system.solution.get())
    {
      NumericVector<Number> * newsol =
        const_cast<NumericVector<Number> *>(solution_vector);
      System & sys = const_cast<System &>(system);
      newsol->swap(*sys.solution);
      sys.update();
    }

  // Loop over all the variables in the system
  for (unsigned int var=0; var<n_vars; var++)
    {
      // Possibly skip this variable
      if (error_norm.weight(var) == 0.0) continue;

      // The (string) name of this variable
      const std::string & var_name = system.variable_name(var);

      // The type of finite element to use for this variable
      const FEType & fe_type = dof_map.variable_type (var);

      std::unique_ptr<FEBase> fe (FEBase::build (dim, fe_type));

      // Build an appropriate Gaussian quadrature rule
      std::unique_ptr<QBase> qrule =
        fe_type.default_quadrature_rule (dim,
                                         _extra_order);

      fe->attach_quadrature_rule (qrule.get());

      // Prepare a global solution and a MeshFunction of the fine system if we need one
      std::unique_ptr<MeshFunction> fine_values;
      std::unique_ptr<NumericVector<Number>> fine_soln = NumericVector<Number>::build(system.comm());
      if (_equation_systems_fine)
        {
          const System & fine_system = _equation_systems_fine->get_system(system.name());

          std::vector<Number> global_soln;
          // FIXME - we're assuming that the fine system solution gets
          // used even when a different vector is used for the coarse
          // system
          fine_system.update_global_solution(global_soln);
          fine_soln->init
            (cast_int<numeric_index_type>(global_soln.size()), true,
             SERIAL);
          (*fine_soln) = global_soln;

          fine_values = std::unique_ptr<MeshFunction>
            (new MeshFunction(*_equation_systems_fine,
                              *fine_soln,
                              fine_system.get_dof_map(),
                              fine_system.variable_number(var_name)));
          fine_values->init();
        } else {
        // Initialize functors if we're using them
        for (auto & ev : _exact_values)
          if (ev)
            ev->init();

        for (auto & ed : _exact_derivs)
          if (ed)
            ed->init();

        for (auto & eh : _exact_hessians)
          if (eh)
            eh->init();
      }

      // Request the data we'll need to compute with
      fe->get_JxW();
      fe->get_phi();
      fe->get_dphi();
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
      fe->get_d2phi();
#endif
      fe->get_xyz();

#ifdef LIBMESH_ENABLE_AMR
      // If we compute on parent elements, we'll want to do so only
      // once on each, so we need to keep track of which we've done.
      std::vector<bool> computed_var_on_parent;

      if (estimate_parent_error)
        computed_var_on_parent.resize(error_per_cell.size(), false);
#endif

      // TODO: this ought to be threaded (and using subordinate
      // MeshFunction objects in each thread rather than a single
      // master)

      // Iterate over all the active elements in the mesh
      // that live on this processor.
      for (const auto & elem : mesh.active_local_element_ptr_range())
        {
          const dof_id_type e_id = elem->id();

#ifdef LIBMESH_ENABLE_AMR
          // See if the parent of element e has been examined yet;
          // if not, we may want to compute the estimator on it
          const Elem * parent = elem->parent();

          // We only can compute and only need to compute on
          // parents with all active children
          bool compute_on_parent = true;
          if (!parent || !estimate_parent_error)
            compute_on_parent = false;
          else
            for (auto & child : parent->child_ref_range())
              if (!child.active())
                compute_on_parent = false;

          if (compute_on_parent &&
              !computed_var_on_parent[parent->id()])
            {
              computed_var_on_parent[parent->id()] = true;

              // Compute a projection onto the parent
              DenseVector<Number> Uparent;
              FEBase::coarsened_dof_values(*(system.current_local_solution),
                                           dof_map, parent, Uparent,
                                           var, false);

              error_per_cell[parent->id()] +=
                static_cast<ErrorVectorReal>
                (find_squared_element_error(system, var_name,
                                            parent, Uparent,
                                            fe.get(),
                                            fine_values.get()));
            }
#endif

          // Get the local to global degree of freedom maps
          std::vector<dof_id_type> dof_indices;
          dof_map.dof_indices (elem, dof_indices, var);
          const unsigned int n_dofs =
            cast_int<unsigned int>(dof_indices.size());
          DenseVector<Number> Uelem(n_dofs);
          for (unsigned int i=0; i != n_dofs; ++i)
            Uelem(i) = system.current_solution(dof_indices[i]);

          error_per_cell[e_id] +=
            static_cast<ErrorVectorReal>
            (find_squared_element_error(system, var_name, elem,
                                        Uelem, fe.get(),
                                        fine_values.get()));

        } // End loop over active local elements
    } // End loop over variables



  // Each processor has now computed the error contributions
  // for its local elements.  We need to sum the vector
  // and then take the square-root of each component.  Note
  // that we only need to sum if we are running on multiple
  // processors, and we only need to take the square-root
  // if the value is nonzero.  There will in general be many
  // zeros for the inactive elements.

  // First sum the vector of estimated error values
  this->reduce_error(error_per_cell, system.comm());

  // Compute the square-root of each component.
  {
    LOG_SCOPE("std::sqrt()", "ExactErrorEstimator");
    for (auto & val : error_per_cell)
      if (val != 0.)
        {
          libmesh_assert_greater (val, 0.);
          val = std::sqrt(val);
        }
  }

  // If we used a non-standard solution before, now is the time to fix
  // the current_local_solution
  if (solution_vector && solution_vector != system.solution.get())
    {
      NumericVector<Number> * newsol =
        const_cast<NumericVector<Number> *>(solution_vector);
      System & sys = const_cast<System &>(system);
      newsol->swap(*sys.solution);
      sys.update();
    }
}

estimate_errors() [1/2]

void libMesh::ErrorEstimator::estimate_errors ( const EquationSystems &  equation_systems, ErrorVector &  error_per_cell, const std::map< const System *, SystemNorm > &  error_norms, const std::map< const System *, const NumericVector< Number > *> *  solution_vectors = nullptr, bool  estimate_parent_error = false  )

virtualinherited

This virtual function can be redefined in derived classes, but by default computes the sum of the error_per_cell for each system in the equation_systems.

Currently this function ignores the error_norm member variable, and uses the function argument error_norms instead.

This function is named estimate_errors instead of estimate_error because otherwise C++ can get confused.

Reimplemented in libMesh::UniformRefinementEstimator.

Definition at line 47 of file error_estimator.C.

References libMesh::ErrorEstimator::error_norm, libMesh::ErrorEstimator::estimate_error(), libMesh::EquationSystems::get_system(), libMesh::index_range(), and libMesh::EquationSystems::n_systems().

{
  SystemNorm old_error_norm = this->error_norm;

  // Sum the error values from each system
  for (unsigned int s = 0; s != equation_systems.n_systems(); ++s)
    {
      ErrorVector system_error_per_cell;
      const System & sys = equation_systems.get_system(s);
      if (error_norms.find(&sys) == error_norms.end())
        this->error_norm = old_error_norm;
      else
        this->error_norm = error_norms.find(&sys)->second;

      const NumericVector<Number> * solution_vector = nullptr;
      if (solution_vectors &&
          solution_vectors->find(&sys) != solution_vectors->end())
        solution_vector = solution_vectors->find(&sys)->second;

      this->estimate_error(sys, system_error_per_cell,
                           solution_vector, estimate_parent_error);

      if (s)
        {
          libmesh_assert_equal_to (error_per_cell.size(), system_error_per_cell.size());
          for (auto i : index_range(error_per_cell))
            error_per_cell[i] += system_error_per_cell[i];
        }
      else
        error_per_cell = system_error_per_cell;
    }

  // Restore our old state before returning
  this->error_norm = old_error_norm;
}

estimate_errors() [2/2]

void libMesh::ErrorEstimator::estimate_errors ( const EquationSystems &  equation_systems, ErrorMap &  errors_per_cell, const std::map< const System *, const NumericVector< Number > *> *  solution_vectors = nullptr, bool  estimate_parent_error = false  )

virtualinherited

This virtual function can be redefined in derived classes, but by default it calls estimate_error repeatedly to calculate the requested error vectors.

Currently this function ignores the error_norm.weight() values because it calculates each variable's error individually, unscaled.

The user selects which errors get computed by filling a map with error vectors: If errors_per_cell[&system][v] exists, it will be filled with the error values in variable v of system

FIXME: This is a default implementation - derived classes should reimplement it for efficiency.

Reimplemented in libMesh::UniformRefinementEstimator.

Definition at line 93 of file error_estimator.C.

References libMesh::ErrorEstimator::error_norm, libMesh::ErrorEstimator::estimate_error(), libMesh::EquationSystems::get_system(), libMesh::EquationSystems::n_systems(), n_vars, libMesh::System::n_vars(), and libMesh::SystemNorm::type().

{
  SystemNorm old_error_norm = this->error_norm;

  // Find the requested error values from each system
  for (unsigned int s = 0; s != equation_systems.n_systems(); ++s)
    {
      const System & sys = equation_systems.get_system(s);

      unsigned int n_vars = sys.n_vars();

      for (unsigned int v = 0; v != n_vars; ++v)
        {
          // Only fill in ErrorVectors the user asks for
          if (errors_per_cell.find(std::make_pair(&sys, v)) ==
              errors_per_cell.end())
            continue;

          // Calculate error in only one variable
          std::vector<Real> weights(n_vars, 0.0);
          weights[v] = 1.0;
          this->error_norm =
            SystemNorm(std::vector<FEMNormType>(n_vars, old_error_norm.type(v)),
                       weights);

          const NumericVector<Number> * solution_vector = nullptr;
          if (solution_vectors &&
              solution_vectors->find(&sys) != solution_vectors->end())
            solution_vector = solution_vectors->find(&sys)->second;

          this->estimate_error
            (sys, *errors_per_cell[std::make_pair(&sys, v)],
             solution_vector, estimate_parent_error);
        }
    }

  // Restore our old state before returning
  this->error_norm = old_error_norm;
}

extra_quadrature_order()

void libMesh::ExactErrorEstimator::extra_quadrature_order ( const int  extraorder )

inline

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

Definition at line 163 of file exact_error_estimator.h.

References _extra_order.

  { _extra_order = extraorder; }

find_squared_element_error()

Real libMesh::ExactErrorEstimator::find_squared_element_error ( const System &  system, const std::string &  var_name, const Elem *  elem, const DenseVector< Number > &  Uelem, FEBase *  fe, MeshFunction *  fine_values  ) const

private

Helper method for calculating on each element

Definition at line 401 of file exact_error_estimator.C.

References _equation_systems_fine, _exact_deriv, _exact_derivs, _exact_hessian, _exact_hessians, _exact_value, _exact_values, libMesh::ErrorEstimator::error_norm, libMesh::FEGenericBase< OutputType >::get_d2phi(), libMesh::FEGenericBase< OutputType >::get_dphi(), libMesh::System::get_equation_systems(), libMesh::FEAbstract::get_JxW(), libMesh::FEGenericBase< OutputType >::get_phi(), libMesh::FEAbstract::get_xyz(), libMesh::MeshFunction::gradient(), libMesh::H1, libMesh::H1_SEMINORM, libMesh::H2, libMesh::H2_SEMINORM, libMesh::MeshFunction::hessian(), libMesh::L2, libMesh::System::name(), libMesh::TensorTools::norm_sq(), libMesh::TypeVector< T >::norm_sq(), libMesh::TypeTensor< T >::norm_sq(), libMesh::System::number(), libMesh::EquationSystems::parameters, libMesh::Real, libMesh::FEAbstract::reinit(), libMesh::DenseVector< T >::size(), libMesh::System::time, libMesh::SystemNorm::type(), libMesh::System::variable_number(), and libMesh::System::variable_scalar_number().

Referenced by estimate_error().

{
  // The (string) name of this system
  const std::string & sys_name = system.name();
  const unsigned int sys_num = system.number();

  const unsigned int var = system.variable_number(var_name);
  const unsigned int var_component =
    system.variable_scalar_number(var, 0);

  const Parameters & parameters = system.get_equation_systems().parameters;

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

  // Get the data we need to compute with
  const std::vector<Real> &                      JxW          = fe->get_JxW();
  const std::vector<std::vector<Real>> &         phi_values   = fe->get_phi();
  const std::vector<std::vector<RealGradient>> & dphi_values  = fe->get_dphi();
  const std::vector<Point> &                     q_point      = fe->get_xyz();
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
  const std::vector<std::vector<RealTensor>> &   d2phi_values = fe->get_d2phi();
#endif

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

  // The number of quadrature points
  const unsigned int n_qp =
    cast_int<unsigned int>(JxW.size());

  Real error_val = 0;

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

      Number u_h = 0.;

      Gradient grad_u_h;
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
      Tensor grad2_u_h;
#endif

      // Compute solution values at the current
      // quadrature point.  This requires 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]*Uelem(i);
          grad_u_h += dphi_values[i][qp]*Uelem(i);
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
          grad2_u_h += d2phi_values[i][qp]*Uelem(i);
#endif
        }

      // Compute the value of the error at this quadrature point
      if (error_norm.type(var) == L2 ||
          error_norm.type(var) == H1 ||
          error_norm.type(var) == H2)
        {
          Number val_error = u_h;
          if (_exact_value)
            val_error -= _exact_value(q_point[qp],parameters,sys_name,var_name);
          else if (_exact_values.size() > sys_num && _exact_values[sys_num])
            val_error -= _exact_values[sys_num]->
              component(var_component, q_point[qp], system.time);
          else if (_equation_systems_fine)
            val_error -= (*fine_values)(q_point[qp]);

          // Add the squares of the error to each contribution
          error_val += JxW[qp]*TensorTools::norm_sq(val_error);
        }

      // Compute the value of the error in the gradient at this
      // quadrature point
      if (error_norm.type(var) == H1 ||
          error_norm.type(var) == H1_SEMINORM ||
          error_norm.type(var) == H2)
        {
          Gradient grad_error = grad_u_h;
          if (_exact_deriv)
            grad_error -= _exact_deriv(q_point[qp],parameters,sys_name,var_name);
          else if (_exact_derivs.size() > sys_num && _exact_derivs[sys_num])
            grad_error -= _exact_derivs[sys_num]->
              component(var_component, q_point[qp], system.time);
          else if (_equation_systems_fine)
            grad_error -= fine_values->gradient(q_point[qp]);

          error_val += JxW[qp]*grad_error.norm_sq();
        }


#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
      // Compute the value of the error in the hessian at this
      // quadrature point
      if ((error_norm.type(var) == H2_SEMINORM ||
           error_norm.type(var) == H2))
        {
          Tensor grad2_error = grad2_u_h;
          if (_exact_hessian)
            grad2_error -= _exact_hessian(q_point[qp],parameters,sys_name,var_name);
          else if (_exact_hessians.size() > sys_num && _exact_hessians[sys_num])
            grad2_error -= _exact_hessians[sys_num]->
              component(var_component, q_point[qp], system.time);
          else if (_equation_systems_fine)
            grad2_error -= fine_values->hessian(q_point[qp]);

          error_val += JxW[qp]*grad2_error.norm_sq();
        }
#endif

    } // end qp loop

  libmesh_assert_greater_equal (error_val, 0.);

  return error_val;
}

operator=() [1/2]

ExactErrorEstimator& libMesh::ExactErrorEstimator::operator= ( const ExactErrorEstimator &  )

delete

operator=() [2/2]

ExactErrorEstimator& libMesh::ExactErrorEstimator::operator= ( ExactErrorEstimator &&  )

default

reduce_error()

void libMesh::ErrorEstimator::reduce_error ( std::vector< ErrorVectorReal > &  error_per_cell, const Parallel::Communicator &  comm  ) const

protectedinherited

This method takes the local error contributions in error_per_cell from each processor and combines them to get the global error vector.

Definition at line 32 of file error_estimator.C.

References libMesh::Parallel::Communicator::sum().

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::WeightedPatchRecoveryErrorEstimator::estimate_error(), libMesh::PatchRecoveryErrorEstimator::estimate_error(), libMesh::JumpErrorEstimator::estimate_error(), libMesh::AdjointRefinementEstimator::estimate_error(), and estimate_error().

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

  // Each processor has now computed the error contributions
  // for its local elements.  We may need to sum the vector to
  // recover the error for each element.

  comm.sum(error_per_cell);
}

type()

ErrorEstimatorType libMesh::ExactErrorEstimator::type ( ) const

overridevirtual

Returns

The type for the ErrorEstimator subclass.

Implements libMesh::ErrorEstimator.

Definition at line 60 of file exact_error_estimator.C.

References libMesh::EXACT.

{
  return EXACT;
}

Member Data Documentation

_equation_systems_fine

EquationSystems* libMesh::ExactErrorEstimator::_equation_systems_fine

private

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

Definition at line 229 of file exact_error_estimator.h.

Referenced by attach_exact_deriv(), attach_exact_hessian(), attach_exact_value(), attach_reference_solution(), estimate_error(), and find_squared_element_error().

_exact_deriv

GradientFunctionPointer libMesh::ExactErrorEstimator::_exact_deriv

private

Function pointer to user-provided function which computes the exact derivative of the solution.

Definition at line 199 of file exact_error_estimator.h.

Referenced by attach_exact_deriv(), attach_reference_solution(), and find_squared_element_error().

_exact_derivs

std::vector<std::unique_ptr<FunctionBase<Gradient> > > libMesh::ExactErrorEstimator::_exact_derivs

private

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

Definition at line 217 of file exact_error_estimator.h.

Referenced by attach_exact_deriv(), attach_exact_derivs(), clear_functors(), estimate_error(), and find_squared_element_error().

_exact_hessian

HessianFunctionPointer libMesh::ExactErrorEstimator::_exact_hessian

private

Function pointer to user-provided function which computes the exact hessian of the solution.

Definition at line 205 of file exact_error_estimator.h.

Referenced by attach_exact_hessian(), attach_reference_solution(), and find_squared_element_error().

_exact_hessians

std::vector<std::unique_ptr<FunctionBase<Tensor> > > libMesh::ExactErrorEstimator::_exact_hessians

private

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

Definition at line 223 of file exact_error_estimator.h.

Referenced by attach_exact_hessian(), attach_exact_hessians(), clear_functors(), estimate_error(), and find_squared_element_error().

_exact_value

ValueFunctionPointer libMesh::ExactErrorEstimator::_exact_value

private

Function pointer to user-provided function which computes the exact value of the solution.

Definition at line 193 of file exact_error_estimator.h.

Referenced by attach_exact_value(), attach_reference_solution(), and find_squared_element_error().

_exact_values

std::vector<std::unique_ptr<FunctionBase<Number> > > libMesh::ExactErrorEstimator::_exact_values

private

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

Definition at line 211 of file exact_error_estimator.h.

Referenced by attach_exact_value(), attach_exact_values(), clear_functors(), estimate_error(), and find_squared_element_error().

_extra_order

int libMesh::ExactErrorEstimator::_extra_order

private

Extra order to use for quadrature rule

Definition at line 249 of file exact_error_estimator.h.

Referenced by estimate_error(), and extra_quadrature_order().

error_norm

SystemNorm libMesh::ErrorEstimator::error_norm

inherited

When estimating the error in a single system, the error_norm is used to control the scaling and norm choice for each variable. Not all estimators will support all norm choices. The default scaling is for all variables to be weighted equally. The default norm choice depends on the error estimator.

Part of this functionality was supported via component_scale and sobolev_order in older libMesh versions, and a small part was supported via component_mask in even older versions. Hopefully the encapsulation here will allow us to avoid changing this API again.

Definition at line 161 of file error_estimator.h.

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::AdjointRefinementEstimator::AdjointRefinementEstimator(), libMesh::DiscontinuityMeasure::boundary_side_integration(), libMesh::KellyErrorEstimator::boundary_side_integration(), libMesh::DiscontinuityMeasure::DiscontinuityMeasure(), libMesh::JumpErrorEstimator::estimate_error(), libMesh::AdjointResidualErrorEstimator::estimate_error(), estimate_error(), libMesh::ErrorEstimator::estimate_errors(), ExactErrorEstimator(), find_squared_element_error(), libMesh::LaplacianErrorEstimator::init_context(), libMesh::DiscontinuityMeasure::init_context(), libMesh::KellyErrorEstimator::init_context(), libMesh::LaplacianErrorEstimator::internal_side_integration(), libMesh::DiscontinuityMeasure::internal_side_integration(), libMesh::KellyErrorEstimator::internal_side_integration(), libMesh::KellyErrorEstimator::KellyErrorEstimator(), libMesh::LaplacianErrorEstimator::LaplacianErrorEstimator(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::PatchRecoveryErrorEstimator::PatchRecoveryErrorEstimator(), libMesh::JumpErrorEstimator::reinit_sides(), and libMesh::UniformRefinementEstimator::UniformRefinementEstimator().

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

• exact_error_estimator.h
• exact_error_estimator.C