libMesh::AdjointResidualErrorEstimator Class Reference

#include <adjoint_residual_error_estimator.h>

Inheritance diagram for libMesh::AdjointResidualErrorEstimator:

Public Types
typedef std::map< std::pair< const System *, unsigned int >, ErrorVector * >	ErrorMap

Public Member Functions
	AdjointResidualErrorEstimator ()
	AdjointResidualErrorEstimator (const AdjointResidualErrorEstimator &)=delete
AdjointResidualErrorEstimator &	operator= (const AdjointResidualErrorEstimator &)=delete
	AdjointResidualErrorEstimator (AdjointResidualErrorEstimator &&)=default
AdjointResidualErrorEstimator &	operator= (AdjointResidualErrorEstimator &&)=default
virtual	~AdjointResidualErrorEstimator ()=default
std::unique_ptr< ErrorEstimator > &	primal_error_estimator ()
std::unique_ptr< ErrorEstimator > &	dual_error_estimator ()
QoISet &	qoi_set ()
const QoISet &	qoi_set () const
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
std::string	error_plot_suffix
SystemNorm	error_norm

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

Protected Attributes
std::unique_ptr< ErrorEstimator >	_primal_error_estimator
std::unique_ptr< ErrorEstimator >	_dual_error_estimator
QoISet	_qoi_set

Detailed Description

This class implements a goal oriented error indicator, by weighting residual-based estimates from the primal problem against estimates from the adjoint problem.

This is based on a trick suggested by Brian Carnes, (first proposed by Babuska and Miller in 1984) but if it doesn't actually work then the misunderstanding or misimplementation will be the fault of Roy Stogner. It's also Roy's fault there's no literature reference here yet.

Author

Roy H. Stogner

Date

2009

Definition at line 50 of file adjoint_residual_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.

Constructor & Destructor Documentation

AdjointResidualErrorEstimator() [1/3]

libMesh::AdjointResidualErrorEstimator::AdjointResidualErrorEstimator

(

)

Constructor. Responsible for picking default subestimators.

Definition at line 41 of file adjoint_residual_error_estimator.C.

                                                              :
  ErrorEstimator(),
  error_plot_suffix(),
  _primal_error_estimator(new PatchRecoveryErrorEstimator()),
  _dual_error_estimator(new PatchRecoveryErrorEstimator()),
  _qoi_set(QoISet())
{
}

AdjointResidualErrorEstimator() [2/3]

libMesh::AdjointResidualErrorEstimator::AdjointResidualErrorEstimator ( const AdjointResidualErrorEstimator &  )

delete

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

AdjointResidualErrorEstimator() [3/3]

libMesh::AdjointResidualErrorEstimator::AdjointResidualErrorEstimator ( AdjointResidualErrorEstimator &&  )

default

Defaulted move ctor, move assignment operator, and destructor.

~AdjointResidualErrorEstimator()

virtual libMesh::AdjointResidualErrorEstimator::~AdjointResidualErrorEstimator ( )

virtualdefault

Member Function Documentation

dual_error_estimator()

std::unique_ptr<ErrorEstimator>& libMesh::AdjointResidualErrorEstimator::dual_error_estimator ( )

inline

Access to the "subestimator" (default: PatchRecovery) to use on the dual/adjoint solution

Definition at line 84 of file adjoint_residual_error_estimator.h.

References _dual_error_estimator.

{ return _dual_error_estimator; }

estimate_error()

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

overridevirtual

Compute the adjoint-weighted error on each element and place it in the error_per_cell vector.

Note

this->error_norm is ignored; the error estimate is in the seminorm given by the absolute value of the error in the quantity of interest functional. The primal and dual subestimator error_norm values are used, and should be chosen appropriately for your model.

Implements libMesh::ErrorEstimator.

Definition at line 60 of file adjoint_residual_error_estimator.C.

References _dual_error_estimator, _primal_error_estimator, _qoi_set, libMesh::System::adjoint_solve(), libMesh::SystemNorm::calculate_norm(), libMesh::ErrorEstimator::error_norm, error_plot_suffix, libMesh::ErrorVectorReal, libMesh::System::get_adjoint_solution(), libMesh::System::get_equation_systems(), libMesh::System::get_mesh(), libMesh::QoISet::has_index(), libMesh::index_range(), libMesh::System::is_adjoint_already_solved(), libMesh::SystemNorm::is_identity(), mesh, libMesh::System::n_qois(), n_vars, libMesh::System::n_vars(), libMesh::ErrorVector::plot_error(), libMesh::Real, libMesh::System::solution, and libMesh::QoISet::weight().

{
  LOG_SCOPE("estimate_error()", "AdjointResidualErrorEstimator");

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

  // 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.);

  // Get the number of variables in the system
  unsigned int n_vars = _system.n_vars();

  // We need to make a map of the pointer to the solution vector
  std::map<const System *, const NumericVector<Number> *>solutionvecs;
  solutionvecs[&_system] = _system.solution.get();

  // Solve the dual problem if we have to
  if (!_system.is_adjoint_already_solved())
    {
      // FIXME - we'll need to change a lot of APIs to make this trick
      // work with a const System...
      System &  system = const_cast<System &>(_system);
      system.adjoint_solve(_qoi_set);
    }

  // Flag to check whether we have not been asked to weight the variable error contributions in any specific manner
  bool error_norm_is_identity = error_norm.is_identity();

  // Create an ErrorMap/ErrorVector to store the primal, dual and total_dual variable errors
  ErrorMap primal_errors_per_cell;
  ErrorMap dual_errors_per_cell;
  ErrorMap total_dual_errors_per_cell;
  // Allocate ErrorVectors to this map if we're going to use it
  if (!error_norm_is_identity)
    for (unsigned int v = 0; v < n_vars; v++)
      {
        primal_errors_per_cell[std::make_pair(&_system, v)] = new ErrorVector;
        dual_errors_per_cell[std::make_pair(&_system, v)] = new ErrorVector;
        total_dual_errors_per_cell[std::make_pair(&_system, v)] = new ErrorVector;
      }
  ErrorVector primal_error_per_cell;
  ErrorVector dual_error_per_cell;
  ErrorVector total_dual_error_per_cell;

  // Have we been asked to weight the variable error contributions in any specific manner
  if (!error_norm_is_identity) // If we do
    {
      // Estimate the primal problem error for each variable
      _primal_error_estimator->estimate_errors
        (_system.get_equation_systems(), primal_errors_per_cell, &solutionvecs, estimate_parent_error);
    }
  else // If not
    {
      // Just get the combined error estimate
      _primal_error_estimator->estimate_error
        (_system, primal_error_per_cell, solution_vector, estimate_parent_error);
    }

  // Sum and weight the dual error estimate based on our QoISet
  for (unsigned int i = 0, n_qois = _system.n_qois(); i != n_qois; ++i)
    {
      if (_qoi_set.has_index(i))
        {
          // Get the weight for the current QoI
          Real error_weight = _qoi_set.weight(i);

          // We need to make a map of the pointer to the adjoint solution vector
          std::map<const System *, const NumericVector<Number> *>adjointsolutionvecs;
          adjointsolutionvecs[&_system] = &_system.get_adjoint_solution(i);

          // Have we been asked to weight the variable error contributions in any specific manner
          if (!error_norm_is_identity) // If we have
            {
              _dual_error_estimator->estimate_errors
                (_system.get_equation_systems(), dual_errors_per_cell, &adjointsolutionvecs,
                 estimate_parent_error);
            }
          else // If not
            {
              // Just get the combined error estimate
              _dual_error_estimator->estimate_error
                (_system, dual_error_per_cell, &(_system.get_adjoint_solution(i)), estimate_parent_error);
            }

          std::size_t error_size;

          // Get the size of the first ErrorMap vector; this will give us the number of elements
          if (!error_norm_is_identity) // If in non default weights case
            {
              error_size = dual_errors_per_cell[std::make_pair(&_system, 0)]->size();
            }
          else // If in the standard default weights case
            {
              error_size = dual_error_per_cell.size();
            }

          // Resize the ErrorVector(s)
          if (!error_norm_is_identity)
            {
              // Loop over variables
              for (unsigned int v = 0; v < n_vars; v++)
                {
                  libmesh_assert(!total_dual_errors_per_cell[std::make_pair(&_system, v)]->size() ||
                                 total_dual_errors_per_cell[std::make_pair(&_system, v)]->size() == error_size) ;
                  total_dual_errors_per_cell[std::make_pair(&_system, v)]->resize(error_size);
                }
            }
          else
            {
              libmesh_assert(!total_dual_error_per_cell.size() ||
                             total_dual_error_per_cell.size() == error_size);
              total_dual_error_per_cell.resize(error_size);
            }

          for (std::size_t e = 0; e != error_size; ++e)
            {
              // Have we been asked to weight the variable error contributions in any specific manner
              if (!error_norm_is_identity) // If we have
                {
                  // Loop over variables
                  for (unsigned int v = 0; v < n_vars; v++)
                    {
                      // Now fill in total_dual_error ErrorMap with the weight
                      (*total_dual_errors_per_cell[std::make_pair(&_system, v)])[e] +=
                        static_cast<ErrorVectorReal>
                        (error_weight *
                         (*dual_errors_per_cell[std::make_pair(&_system, v)])[e]);
                    }
                }
              else // If not
                {
                  total_dual_error_per_cell[e] +=
                    static_cast<ErrorVectorReal>(error_weight * dual_error_per_cell[e]);
                }
            }
        }
    }

  // Do some debugging plots if requested
  if (!error_plot_suffix.empty())
    {
      if (!error_norm_is_identity) // If we have
        {
          // Loop over variables
          for (unsigned int v = 0; v < n_vars; v++)
            {
              std::ostringstream primal_out;
              std::ostringstream dual_out;
              primal_out << "primal_" << error_plot_suffix << ".";
              dual_out << "dual_" << error_plot_suffix << ".";

              primal_out << std::setw(1)
                         << std::setprecision(0)
                         << std::setfill('0')
                         << std::right
                         << v;

              dual_out << std::setw(1)
                       << std::setprecision(0)
                       << std::setfill('0')
                       << std::right
                       << v;

              (*primal_errors_per_cell[std::make_pair(&_system, v)]).plot_error(primal_out.str(), _system.get_mesh());
              (*total_dual_errors_per_cell[std::make_pair(&_system, v)]).plot_error(dual_out.str(), _system.get_mesh());

              primal_out.clear();
              dual_out.clear();
            }
        }
      else // If not
        {
          std::ostringstream primal_out;
          std::ostringstream dual_out;
          primal_out << "primal_" << error_plot_suffix ;
          dual_out << "dual_" << error_plot_suffix ;

          primal_error_per_cell.plot_error(primal_out.str(), _system.get_mesh());
          total_dual_error_per_cell.plot_error(dual_out.str(), _system.get_mesh());

          primal_out.clear();
          dual_out.clear();
        }
    }

  // Weight the primal error by the dual error using the system norm object
  // FIXME: we ought to thread this
  for (auto i : index_range(error_per_cell))
    {
      // Have we been asked to weight the variable error contributions in any specific manner
      if (!error_norm_is_identity) // If we do
        {
          // Create Error Vectors to pass to calculate_norm
          std::vector<Real> cell_primal_error;
          std::vector<Real> cell_dual_error;

          for (unsigned int v = 0; v < n_vars; v++)
            {
              cell_primal_error.push_back((*primal_errors_per_cell[std::make_pair(&_system, v)])[i]);
              cell_dual_error.push_back((*total_dual_errors_per_cell[std::make_pair(&_system, v)])[i]);
            }

          error_per_cell[i] =
            static_cast<ErrorVectorReal>
            (error_norm.calculate_norm(cell_primal_error, cell_dual_error));
        }
      else // If not
        {
          error_per_cell[i] = primal_error_per_cell[i]*total_dual_error_per_cell[i];
        }
    }

  // Deallocate the ErrorMap contents if we allocated them earlier
  if (!error_norm_is_identity)
    for (unsigned int v = 0; v < n_vars; v++)
      {
        delete primal_errors_per_cell[std::make_pair(&_system, v)];
        delete dual_errors_per_cell[std::make_pair(&_system, v)];
        delete total_dual_errors_per_cell[std::make_pair(&_system, v)];
      }
}

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;
}

operator=() [1/2]

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

delete

operator=() [2/2]

AdjointResidualErrorEstimator& libMesh::AdjointResidualErrorEstimator::operator= ( AdjointResidualErrorEstimator &&  )

default

primal_error_estimator()

std::unique_ptr<ErrorEstimator>& libMesh::AdjointResidualErrorEstimator::primal_error_estimator ( )

inline

Access to the "subestimator" (default: PatchRecovery) to use on the primal/forward solution

Definition at line 78 of file adjoint_residual_error_estimator.h.

References _primal_error_estimator.

{ return _primal_error_estimator; }

qoi_set() [1/2]

QoISet& libMesh::AdjointResidualErrorEstimator::qoi_set ( )

inline

Access to the QoISet (default: weight all QoIs equally) to use when computing errors

Definition at line 90 of file adjoint_residual_error_estimator.h.

References _qoi_set.

{ return _qoi_set; }

qoi_set() [2/2]

const QoISet& libMesh::AdjointResidualErrorEstimator::qoi_set ( ) const

inline

Access to the QoISet (default: weight all QoIs equally) to use when computing errors

Definition at line 96 of file adjoint_residual_error_estimator.h.

References _qoi_set.

{ return _qoi_set; }

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 libMesh::ExactErrorEstimator::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::AdjointResidualErrorEstimator::type ( ) const

overridevirtual

Returns

The type for the ErrorEstimator subclass.

Implements libMesh::ErrorEstimator.

Definition at line 53 of file adjoint_residual_error_estimator.C.

References libMesh::ADJOINT_RESIDUAL.

{
  return ADJOINT_RESIDUAL;
}

Member Data Documentation

_dual_error_estimator

std::unique_ptr<ErrorEstimator> libMesh::AdjointResidualErrorEstimator::_dual_error_estimator

protected

An error estimator for the adjoint problem

Definition at line 134 of file adjoint_residual_error_estimator.h.

Referenced by dual_error_estimator(), and estimate_error().

_primal_error_estimator

std::unique_ptr<ErrorEstimator> libMesh::AdjointResidualErrorEstimator::_primal_error_estimator

protected

An error estimator for the forward problem

Definition at line 129 of file adjoint_residual_error_estimator.h.

Referenced by estimate_error(), and primal_error_estimator().

_qoi_set

QoISet libMesh::AdjointResidualErrorEstimator::_qoi_set

protected

A QoISet to handle cases with multiple QoIs available

Definition at line 139 of file adjoint_residual_error_estimator.h.

Referenced by estimate_error(), and qoi_set().

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(), estimate_error(), libMesh::ExactErrorEstimator::estimate_error(), libMesh::ErrorEstimator::estimate_errors(), libMesh::ExactErrorEstimator::ExactErrorEstimator(), libMesh::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().

error_plot_suffix

std::string libMesh::AdjointResidualErrorEstimator::error_plot_suffix

To aid in investigating error estimator behavior, set this string to a suffix with which to plot (prefixed by "primal_" or "dual_") the subestimator results. The suffix should end with a file extension (e.g. ".gmv") that the ErrorVector::plot_error recognizes.

Definition at line 105 of file adjoint_residual_error_estimator.h.

Referenced by estimate_error().

---

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

• adjoint_residual_error_estimator.h
• adjoint_residual_error_estimator.C