void JumpErrorEstimator::estimate_error (const System& system,
ErrorVector& error_per_cell,
const NumericVector<Number>* solution_vector,
bool estimate_parent_error)
{
START_LOG("estimate_error()", "JumpErrorEstimator");
/*
Conventions for assigning the direction of the normal:
- e & f are global element ids
Case (1.) Elements are at the same level, e<f
Compute the flux jump on the face and
add it as a contribution to error_per_cell[e]
and error_per_cell[f]
----------------------
| | |
| | f |
| | |
| e |---> n |
| | |
| | |
----------------------
Case (2.) The neighbor is at a higher level.
Compute the flux jump on e's face and
add it as a contribution to error_per_cell[e]
and error_per_cell[f]
----------------------
| | | |
| | e |---> n |
| | | |
|-----------| f |
| | | |
| | | |
| | | |
----------------------
*/
// The current mesh
const MeshBase& mesh = system.get_mesh();
// 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.);
// Declare a vector of floats which is as long as
// error_per_cell above, and fill with zeros. This vector will be
// used to keep track of the number of edges (faces) on each active
// element which are either:
// 1) an internal edge
// 2) an edge on a Neumann boundary for which a boundary condition
// function has been specified.
// The error estimator can be scaled by the number of flux edges (faces)
// which the element actually has to obtain a more uniform measure
// of the error. Use floats instead of ints since in case 2 (above)
// f gets 1/2 of a flux face contribution from each of his
// neighbors
std::vector<float> n_flux_faces;
if (scale_by_n_flux_faces)
n_flux_faces.resize(error_per_cell.size(), 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();
}
fine_context.reset(new FEMContext(system));
coarse_context.reset(new FEMContext(system));
// Loop over all the variables we've been requested to find jumps in, to
// pre-request
for (var=0; var<n_vars; var++)
{
// Possibly skip this variable
if (error_norm.weight(var) == 0.0) continue;
// FIXME: Need to generalize this to vector-valued elements. [PB]
FEBase* side_fe = NULL;
const std::set<unsigned char>& elem_dims =
fine_context->elem_dimensions();
for (std::set<unsigned char>::const_iterator dim_it =
elem_dims.begin(); dim_it != elem_dims.end(); ++dim_it)
{
const unsigned char dim = *dim_it;
fine_context->get_side_fe( var, side_fe, dim );
libmesh_assert_not_equal_to(side_fe->get_fe_type().family, SCALAR);
side_fe->get_xyz();
}
}
this->init_context(*fine_context);
this->init_context(*coarse_context);
// Iterate over all the active elements in the mesh
// that live on this processor.
MeshBase::const_element_iterator elem_it = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator elem_end = mesh.active_local_elements_end();
for (; elem_it != elem_end; ++elem_it)
{
// e is necessarily an active element on the local processor
const Elem* e = *elem_it;
const dof_id_type e_id = e->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 = e->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 (unsigned int c=0; c != parent->n_children(); ++c)
if (!parent->child(c)->active())
compute_on_parent = false;
if (compute_on_parent &&
!error_per_cell[parent->id()])
{
// Compute a projection onto the parent
DenseVector<Number> Uparent;
FEBase::coarsened_dof_values
(*(system.solution), dof_map, parent, Uparent, false);
// Loop over the neighbors of the parent
for (unsigned int n_p=0; n_p<parent->n_neighbors(); n_p++)
{
if (parent->neighbor(n_p) != NULL) // parent has a neighbor here
{
// Find the active neighbors in this direction
std::vector<const Elem*> active_neighbors;
parent->neighbor(n_p)->
active_family_tree_by_neighbor(active_neighbors,
parent);
// Compute the flux to each active neighbor
for (unsigned int a=0;
a != active_neighbors.size(); ++a)
{
const Elem *f = active_neighbors[a];
// FIXME - what about when f->level <
// parent->level()??
if (f->level() >= parent->level())
{
fine_context->pre_fe_reinit(system, f);
coarse_context->pre_fe_reinit(system, parent);
libmesh_assert_equal_to
(coarse_context->get_elem_solution().size(),
Uparent.size());
coarse_context->get_elem_solution() = Uparent;
this->reinit_sides();
// Loop over all significant variables in the system
for (var=0; var<n_vars; var++)
if (error_norm.weight(var) != 0.0)
{
this->internal_side_integration();
error_per_cell[fine_context->get_elem().id()] +=
static_cast<ErrorVectorReal>(fine_error);
error_per_cell[coarse_context->get_elem().id()] +=
static_cast<ErrorVectorReal>(coarse_error);
}
// Keep track of the number of internal flux
// sides found on each element
if (scale_by_n_flux_faces)
{
n_flux_faces[fine_context->get_elem().id()]++;
n_flux_faces[coarse_context->get_elem().id()] +=
this->coarse_n_flux_faces_increment();
}
}
}
}
else if (integrate_boundary_sides)
{
fine_context->pre_fe_reinit(system, parent);
libmesh_assert_equal_to
(fine_context->get_elem_solution().size(),
Uparent.size());
fine_context->get_elem_solution() = Uparent;
fine_context->side = n_p;
fine_context->side_fe_reinit();
// If we find a boundary flux for any variable,
// let's just count it as a flux face for all
// variables. Otherwise we'd need to keep track of
// a separate n_flux_faces and error_per_cell for
// every single var.
bool found_boundary_flux = false;
for (var=0; var<n_vars; var++)
if (error_norm.weight(var) != 0.0)
{
if (this->boundary_side_integration())
{
error_per_cell[fine_context->get_elem().id()] +=
static_cast<ErrorVectorReal>(fine_error);
found_boundary_flux = true;
}
}
if (scale_by_n_flux_faces && found_boundary_flux)
n_flux_faces[fine_context->get_elem().id()]++;
}
}
}
#endif // #ifdef LIBMESH_ENABLE_AMR
// If we do any more flux integration, e will be the fine element
fine_context->pre_fe_reinit(system, e);
// Loop over the neighbors of element e
for (unsigned int n_e=0; n_e<e->n_neighbors(); n_e++)
{
if ((e->neighbor(n_e) != NULL) ||
integrate_boundary_sides)
{
fine_context->side = n_e;
fine_context->side_fe_reinit();
}
if (e->neighbor(n_e) != NULL) // e is not on the boundary
{
const Elem* f = e->neighbor(n_e);
const dof_id_type f_id = f->id();
// Compute flux jumps if we are in case 1 or case 2.
if ((f->active() && (f->level() == e->level()) && (e_id < f_id))
|| (f->level() < e->level()))
{
// f is now the coarse element
coarse_context->pre_fe_reinit(system, f);
this->reinit_sides();
// Loop over all significant variables in the system
for (var=0; var<n_vars; var++)
if (error_norm.weight(var) != 0.0)
{
this->internal_side_integration();
error_per_cell[fine_context->get_elem().id()] +=
static_cast<ErrorVectorReal>(fine_error);
error_per_cell[coarse_context->get_elem().id()] +=
static_cast<ErrorVectorReal>(coarse_error);
}
// Keep track of the number of internal flux
// sides found on each element
if (scale_by_n_flux_faces)
{
n_flux_faces[fine_context->get_elem().id()]++;
n_flux_faces[coarse_context->get_elem().id()] +=
this->coarse_n_flux_faces_increment();
}
} // end if (case1 || case2)
} // if (e->neigbor(n_e) != NULL)
// Otherwise, e is on the boundary. If it happens to
// be on a Dirichlet boundary, we need not do anything.
// On the other hand, if e is on a Neumann (flux) boundary
// with grad(u).n = g, we need to compute the additional residual
// (h * \int |g - grad(u_h).n|^2 dS)^(1/2).
// We can only do this with some knowledge of the boundary
// conditions, i.e. the user must have attached an appropriate
// BC function.
else if (integrate_boundary_sides)
{
bool found_boundary_flux = false;
for (var=0; var<n_vars; var++)
if (error_norm.weight(var) != 0.0)
if (this->boundary_side_integration())
{
error_per_cell[fine_context->get_elem().id()] +=
static_cast<ErrorVectorReal>(fine_error);
found_boundary_flux = true;
}
if (scale_by_n_flux_faces && found_boundary_flux)
n_flux_faces[fine_context->get_elem().id()]++;
} // end if (e->neighbor(n_e) == NULL)
} // end loop over neighbors
} // End loop over active local elements
// Each processor has now computed the error contribuions
// 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.
for (std::size_t i=0; i<error_per_cell.size(); i++)
if (error_per_cell[i] != 0.)
error_per_cell[i] = std::sqrt(error_per_cell[i]);
if (this->scale_by_n_flux_faces)
{
// Sum the vector of flux face counts
this->reduce_error(n_flux_faces, system.comm());
// Sanity check: Make sure the number of flux faces is
// always an integer value
#ifdef DEBUG
for (unsigned int i=0; i<n_flux_faces.size(); ++i)
libmesh_assert_equal_to (n_flux_faces[i], static_cast<float>(static_cast<unsigned int>(n_flux_faces[i])) );
#endif
// Scale the error by the number of flux faces for each element
for (unsigned int i=0; i<n_flux_faces.size(); ++i)
{
if (n_flux_faces[i] == 0.0) // inactive or non-local element
continue;
//libMesh::out << "Element " << i << " has " << n_flux_faces[i] << " flux faces." << std::endl;
error_per_cell[i] /= static_cast<ErrorVectorReal>(n_flux_faces[i]);
}
}
// 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();
}
STOP_LOG("estimate_error()", "JumpErrorEstimator");
}
void AdjointRefinementEstimator::estimate_error (const System& _system,
ErrorVector& error_per_cell,
const NumericVector<Number>* solution_vector,
bool /*estimate_parent_error*/)
{
// We have to break the rules here, because we can't refine a const System
System& system = const_cast<System&>(_system);
// An EquationSystems reference will be convenient.
EquationSystems& es = system.get_equation_systems();
// The current mesh
MeshBase& mesh = es.get_mesh();
// Resize the error_per_cell vector to be
// the number of elements, initialized to 0.
error_per_cell.clear();
error_per_cell.resize (mesh.max_elem_id(), 0.);
// We'll want to back up all coarse grid vectors
std::map<std::string, NumericVector<Number> *> coarse_vectors;
for (System::vectors_iterator vec = system.vectors_begin(); vec !=
system.vectors_end(); ++vec)
{
// The (string) name of this vector
const std::string& var_name = vec->first;
coarse_vectors[var_name] = vec->second->clone().release();
}
// Back up the coarse solution and coarse local solution
NumericVector<Number> * coarse_solution =
system.solution->clone().release();
NumericVector<Number> * coarse_local_solution =
system.current_local_solution->clone().release();
// And make copies of the projected solution
NumericVector<Number> * projected_solution;
// And we'll need to temporarily change solution projection settings
bool old_projection_setting;
old_projection_setting = system.project_solution_on_reinit();
// Make sure the solution is projected when we refine the mesh
system.project_solution_on_reinit() = true;
// And it'll be best to avoid any repartitioning
AutoPtr<Partitioner> old_partitioner = mesh.partitioner();
mesh.partitioner().reset(NULL);
// And we can't allow any renumbering
const bool old_renumbering_setting = mesh.allow_renumbering();
mesh.allow_renumbering(false);
// Use a non-standard solution vector if necessary
if (solution_vector && solution_vector != system.solution.get())
{
NumericVector<Number> *newsol =
const_cast<NumericVector<Number>*> (solution_vector);
newsol->swap(*system.solution);
system.update();
}
#ifndef NDEBUG
// n_coarse_elem is only used in an assertion later so
// avoid declaring it unless asserts are active.
const dof_id_type n_coarse_elem = mesh.n_elem();
#endif
// Uniformly refine the mesh
MeshRefinement mesh_refinement(mesh);
libmesh_assert (number_h_refinements > 0 || number_p_refinements > 0);
// FIXME: this may break if there is more than one System
// on this mesh but estimate_error was still called instead of
// estimate_errors
for (unsigned int i = 0; i != number_h_refinements; ++i)
{
mesh_refinement.uniformly_refine(1);
es.reinit();
}
for (unsigned int i = 0; i != number_p_refinements; ++i)
{
mesh_refinement.uniformly_p_refine(1);
es.reinit();
}
// Copy the projected coarse grid solutions, which will be
// overwritten by solve()
projected_solution = NumericVector<Number>::build(mesh.comm()).release();
projected_solution->init(system.solution->size(), true, SERIAL);
system.solution->localize(*projected_solution,
system.get_dof_map().get_send_list());
// Rebuild the rhs with the projected primal solution
(dynamic_cast<ImplicitSystem&>(system)).assembly(true, false);
NumericVector<Number> & projected_residual = (dynamic_cast<ExplicitSystem&>(system)).get_vector("RHS Vector");
projected_residual.close();
// Solve the adjoint problem on the refined FE space
system.adjoint_solve();
// Now that we have the refined adjoint solution and the projected primal solution,
// we first compute the global QoI error estimate
// Resize the computed_global_QoI_errors vector to hold the error estimates for each QoI
computed_global_QoI_errors.resize(system.qoi.size());
// Loop over all the adjoint solutions and get the QoI error
// contributions from all of them
for (unsigned int j=0; j != system.qoi.size(); j++)
{
computed_global_QoI_errors[j] = projected_residual.dot(system.get_adjoint_solution(j));
}
// Done with the global error estimates, now construct the element wise error indicators
// We ought to account for 'spill-over' effects while computing the
// element error indicators This happens because the same dof is
// shared by multiple elements, one way of mitigating this is to
// scale the contribution from each dof by the number of elements it
// belongs to We first obtain the number of elements each node
// belongs to
// A map that relates a node id to an int that will tell us how many elements it is a node of
LIBMESH_BEST_UNORDERED_MAP<dof_id_type, unsigned int>shared_element_count;
// To fill this map, we will loop over elements, and then in each element, we will loop
// over the nodes each element contains, and then query it for the number of coarse
// grid elements it was a node of
// We will be iterating over all the active elements in the fine mesh that live on
// this processor
MeshBase::const_element_iterator elem_it = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator elem_end = mesh.active_local_elements_end();
// Keep track of which nodes we have already dealt with
LIBMESH_BEST_UNORDERED_SET<dof_id_type> processed_node_ids;
// Start loop over elems
for(; elem_it != elem_end; ++elem_it)
{
// Pointer to this element
const Elem* elem = *elem_it;
// Loop over the nodes in the element
for(unsigned int n=0; n != elem->n_nodes(); ++n)
{
// Get a pointer to the current node
Node* node = elem->get_node(n);
// Get the id of this node
dof_id_type node_id = node->id();
// If we havent already processed this node, do so now
if(processed_node_ids.find(node_id) == processed_node_ids.end())
{
// Declare a neighbor_set to be filled by the find_point_neighbors
std::set<const Elem *> fine_grid_neighbor_set;
// Call find_point_neighbors to fill the neighbor_set
elem->find_point_neighbors(*node, fine_grid_neighbor_set);
// A vector to hold the coarse grid parents neighbors
std::vector<dof_id_type> coarse_grid_neighbors;
// Iterators over the fine grid neighbors set
std::set<const Elem*>::iterator fine_neighbor_it = fine_grid_neighbor_set.begin();
const std::set<const Elem*>::iterator fine_neighbor_end = fine_grid_neighbor_set.end();
// Loop over all the fine neighbors of this node
for(; fine_neighbor_it != fine_neighbor_end ; ++fine_neighbor_it)
{
// Pointer to the current fine neighbor element
const Elem* fine_elem = *fine_neighbor_it;
// Find the element id for the corresponding coarse grid element
const Elem* coarse_elem = fine_elem;
for (unsigned int j = 0; j != number_h_refinements; ++j)
{
libmesh_assert (coarse_elem->parent());
coarse_elem = coarse_elem->parent();
}
// Loop over the existing coarse neighbors and check if this one is
// already in there
const dof_id_type coarse_id = coarse_elem->id();
std::size_t j = 0;
for (; j != coarse_grid_neighbors.size(); j++)
{
// If the set already contains this element break out of the loop
if(coarse_grid_neighbors[j] == coarse_id)
{
break;
}
}
// If we didn't leave the loop even at the last element,
// this is a new neighbour, put in the coarse_grid_neighbor_set
if(j == coarse_grid_neighbors.size())
{
coarse_grid_neighbors.push_back(coarse_id);
}
} // End loop over fine neighbors
// Set the shared_neighbour index for this node to the
// size of the coarse grid neighbor set
shared_element_count[node_id] =
libmesh_cast_int<unsigned int>(coarse_grid_neighbors.size());
// Add this node to processed_node_ids vector
processed_node_ids.insert(node_id);
} // End if not processed node
} // End loop over nodes
} // End loop over elems
// Get a DoF map, will be used to get the nodal dof_indices for each element
DofMap &dof_map = system.get_dof_map();
// The global DOF indices, we will use these later on when we compute the element wise indicators
std::vector<dof_id_type> dof_indices;
// Localize the global rhs and adjoint solution vectors (which might be shared on multiple processsors) onto a
// local ghosted vector, this ensures each processor has all the dof_indices to compute an error indicator for
// an element it owns
AutoPtr<NumericVector<Number> > localized_projected_residual = NumericVector<Number>::build(system.comm());
localized_projected_residual->init(system.n_dofs(), system.n_local_dofs(), system.get_dof_map().get_send_list(), false, GHOSTED);
projected_residual.localize(*localized_projected_residual, system.get_dof_map().get_send_list());
// Each adjoint solution will also require ghosting; for efficiency we'll reuse the same memory
AutoPtr<NumericVector<Number> > localized_adjoint_solution = NumericVector<Number>::build(system.comm());
localized_adjoint_solution->init(system.n_dofs(), system.n_local_dofs(), system.get_dof_map().get_send_list(), false, GHOSTED);
// We will loop over each adjoint solution, localize that adjoint
// solution and then loop over local elements
for (unsigned int i=0; i != system.qoi.size(); i++)
{
// Skip this QoI if not in the QoI Set
if (_qoi_set.has_index(i))
{
// Get the weight for the current QoI
Real error_weight = _qoi_set.weight(i);
(system.get_adjoint_solution(i)).localize(*localized_adjoint_solution, system.get_dof_map().get_send_list());
// Loop over elements
MeshBase::const_element_iterator elem_it = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator elem_end = mesh.active_local_elements_end();
for(; elem_it != elem_end; ++elem_it)
{
// Pointer to the element
const Elem* elem = *elem_it;
// Go up number_h_refinements levels up to find the coarse parent
const Elem* coarse = elem;
for (unsigned int j = 0; j != number_h_refinements; ++j)
{
libmesh_assert (coarse->parent());
coarse = coarse->parent();
}
const dof_id_type e_id = coarse->id();
// Get the local to global degree of freedom maps for this element
dof_map.dof_indices (elem, dof_indices);
// We will have to manually do the dot products.
Number local_contribution = 0.;
for (unsigned int j=0; j != dof_indices.size(); j++)
{
// The contribution to the error indicator for this element from the current QoI
local_contribution += (*localized_projected_residual)(dof_indices[j]) * (*localized_adjoint_solution)(dof_indices[j]);
}
// Multiply by the error weight for this QoI
local_contribution *= error_weight;
// FIXME: we're throwing away information in the
// --enable-complex case
error_per_cell[e_id] += static_cast<ErrorVectorReal>
(libmesh_real(local_contribution));
} // End loop over elements
} // End if belong to QoI set
} // End loop over QoIs
// Don't bother projecting the solution; we'll restore from backup
// after coarsening
system.project_solution_on_reinit() = false;
// Uniformly coarsen the mesh, without projecting the solution
libmesh_assert (number_h_refinements > 0 || number_p_refinements > 0);
for (unsigned int i = 0; i != number_h_refinements; ++i)
{
mesh_refinement.uniformly_coarsen(1);
// FIXME - should the reinits here be necessary? - RHS
es.reinit();
}
for (unsigned int i = 0; i != number_p_refinements; ++i)
{
mesh_refinement.uniformly_p_coarsen(1);
es.reinit();
}
// We should be back where we started
libmesh_assert_equal_to (n_coarse_elem, mesh.n_elem());
// Restore old solutions and clean up the heap
system.project_solution_on_reinit() = old_projection_setting;
// Restore the coarse solution vectors and delete their copies
*system.solution = *coarse_solution;
delete coarse_solution;
*system.current_local_solution = *coarse_local_solution;
delete coarse_local_solution;
delete projected_solution;
for (System::vectors_iterator vec = system.vectors_begin(); vec !=
system.vectors_end(); ++vec)
{
// The (string) name of this vector
const std::string& var_name = vec->first;
// If it's a vector we already had (and not a newly created
// vector like an adjoint rhs), we need to restore it.
std::map<std::string, NumericVector<Number> *>::iterator it =
coarse_vectors.find(var_name);
if (it != coarse_vectors.end())
{
NumericVector<Number> *coarsevec = it->second;
system.get_vector(var_name) = *coarsevec;
coarsevec->clear();
delete coarsevec;
}
}
// Restore old partitioner and renumbering settings
mesh.partitioner() = old_partitioner;
mesh.allow_renumbering(old_renumbering_setting);
// Fiinally sum the vector of estimated error values.
this->reduce_error(error_per_cell, system.comm());
// We don't take a square root here; this is a goal-oriented
// estimate not a Hilbert norm estimate.
} // end estimate_error function
void JumpErrorEstimator::estimate_error (const System& system,
ErrorVector& error_per_cell,
const NumericVector<Number>* solution_vector,
bool estimate_parent_error)
{
START_LOG("estimate_error()", "JumpErrorEstimator");
/*
Conventions for assigning the direction of the normal:
- e & f are global element ids
Case (1.) Elements are at the same level, e<f
Compute the flux jump on the face and
add it as a contribution to error_per_cell[e]
and error_per_cell[f]
----------------------
| | |
| | f |
| | |
| e |---> n |
| | |
| | |
----------------------
Case (2.) The neighbor is at a higher level.
Compute the flux jump on e's face and
add it as a contribution to error_per_cell[e]
and error_per_cell[f]
----------------------
| | | |
| | e |---> n |
| | | |
|-----------| f |
| | | |
| | | |
| | | |
----------------------
*/
// 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.);
// Declare a vector of floats which is as long as
// error_per_cell above, and fill with zeros. This vector will be
// used to keep track of the number of edges (faces) on each active
// element which are either:
// 1) an internal edge
// 2) an edge on a Neumann boundary for which a boundary condition
// function has been specified.
// The error estimator can be scaled by the number of flux edges (faces)
// which the element actually has to obtain a more uniform measure
// of the error. Use floats instead of ints since in case 2 (above)
// f gets 1/2 of a flux face contribution from each of his
// neighbors
std::vector<float> n_flux_faces (error_per_cell.size());
// 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 (var=0; var<n_vars; var++)
{
// Possibly skip this variable
if (error_norm.weight(var) == 0.0) continue;
// The type of finite element to use for this variable
const FEType& fe_type = dof_map.variable_type (var);
// Finite element objects for the same face from
// different sides
fe_fine = FEBase::build (dim, fe_type);
fe_coarse = FEBase::build (dim, fe_type);
// Build an appropriate Gaussian quadrature rule
QGauss qrule (dim-1, fe_type.default_quadrature_order());
// Tell the finite element for the fine element about the quadrature
// rule. The finite element for the coarse element need not know about it
fe_fine->attach_quadrature_rule (&qrule);
// By convention we will always do the integration
// on the face of element e. We'll need its Jacobian values and
// physical point locations, at least
fe_fine->get_JxW();
fe_fine->get_xyz();
// Our derived classes may want to do some initialization here
this->initialize(system, error_per_cell, estimate_parent_error);
// The global DOF indices for elements e & f
std::vector<dof_id_type> dof_indices_fine;
std::vector<dof_id_type> dof_indices_coarse;
// Iterate over all the active elements in the mesh
// that live on this processor.
MeshBase::const_element_iterator elem_it = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator elem_end = mesh.active_local_elements_end();
for (; elem_it != elem_end; ++elem_it)
{
// e is necessarily an active element on the local processor
const Elem* e = *elem_it;
const dof_id_type e_id = e->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 = e->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 (unsigned int c=0; c != parent->n_children(); ++c)
if (!parent->child(c)->active())
compute_on_parent = false;
if (compute_on_parent &&
!error_per_cell[parent->id()])
{
// Compute a projection onto the parent
DenseVector<Number> Uparent;
FEBase::coarsened_dof_values(*(system.solution),
dof_map, parent, Uparent,
var, false);
// Loop over the neighbors of the parent
for (unsigned int n_p=0; n_p<parent->n_neighbors(); n_p++)
{
if (parent->neighbor(n_p) != NULL) // parent has a neighbor here
{
// Find the active neighbors in this direction
std::vector<const Elem*> active_neighbors;
parent->neighbor(n_p)->
active_family_tree_by_neighbor(active_neighbors,
parent);
// Compute the flux to each active neighbor
for (unsigned int a=0;
a != active_neighbors.size(); ++a)
{
const Elem *f = active_neighbors[a];
// FIXME - what about when f->level <
// parent->level()??
if (f->level() >= parent->level())
{
fine_elem = f;
coarse_elem = parent;
Ucoarse = Uparent;
dof_map.dof_indices (fine_elem, dof_indices_fine, var);
const unsigned int n_dofs_fine =
libmesh_cast_int<unsigned int>(dof_indices_fine.size());
Ufine.resize(n_dofs_fine);
for (unsigned int i=0; i<n_dofs_fine; i++)
Ufine(i) = system.current_solution(dof_indices_fine[i]);
this->reinit_sides();
this->internal_side_integration();
error_per_cell[fine_elem->id()] +=
static_cast<ErrorVectorReal>(fine_error);
error_per_cell[coarse_elem->id()] +=
static_cast<ErrorVectorReal>(coarse_error);
// Keep track of the number of internal flux
// sides found on each element
n_flux_faces[fine_elem->id()]++;
n_flux_faces[coarse_elem->id()] += this->coarse_n_flux_faces_increment();
}
}
}
else if (integrate_boundary_sides)
{
fine_elem = parent;
Ufine = Uparent;
// Reinitialize shape functions on the fine element side
fe_fine->reinit (fine_elem, fine_side);
if (this->boundary_side_integration())
{
error_per_cell[fine_elem->id()] +=
static_cast<ErrorVectorReal>(fine_error);
n_flux_faces[fine_elem->id()]++;
}
}
}
}
#endif // #ifdef LIBMESH_ENABLE_AMR
// If we do any more flux integration, e will be the fine element
fine_elem = e;
// Loop over the neighbors of element e
for (unsigned int n_e=0; n_e<e->n_neighbors(); n_e++)
{
fine_side = n_e;
if (e->neighbor(n_e) != NULL) // e is not on the boundary
{
const Elem* f = e->neighbor(n_e);
const dof_id_type f_id = f->id();
// Compute flux jumps if we are in case 1 or case 2.
if ((f->active() && (f->level() == e->level()) && (e_id < f_id))
|| (f->level() < e->level()))
{
// f is now the coarse element
coarse_elem = f;
// Get the DOF indices for the two elements
dof_map.dof_indices (fine_elem, dof_indices_fine, var);
dof_map.dof_indices (coarse_elem, dof_indices_coarse, var);
// The number of DOFS on each element
const unsigned int n_dofs_fine =
libmesh_cast_int<unsigned int>(dof_indices_fine.size());
const unsigned int n_dofs_coarse =
libmesh_cast_int<unsigned int>(dof_indices_coarse.size());
Ufine.resize(n_dofs_fine);
Ucoarse.resize(n_dofs_coarse);
// The local solutions on each element
for (unsigned int i=0; i<n_dofs_fine; i++)
Ufine(i) = system.current_solution(dof_indices_fine[i]);
for (unsigned int i=0; i<n_dofs_coarse; i++)
Ucoarse(i) = system.current_solution(dof_indices_coarse[i]);
this->reinit_sides();
this->internal_side_integration();
error_per_cell[fine_elem->id()] +=
static_cast<ErrorVectorReal>(fine_error);
error_per_cell[coarse_elem->id()] +=
static_cast<ErrorVectorReal>(coarse_error);
// Keep track of the number of internal flux
// sides found on each element
n_flux_faces[fine_elem->id()]++;
n_flux_faces[coarse_elem->id()] += this->coarse_n_flux_faces_increment();
} // end if (case1 || case2)
} // if (e->neigbor(n_e) != NULL)
// Otherwise, e is on the boundary. If it happens to
// be on a Dirichlet boundary, we need not do anything.
// On the other hand, if e is on a Neumann (flux) boundary
// with grad(u).n = g, we need to compute the additional residual
// (h * \int |g - grad(u_h).n|^2 dS)^(1/2).
// We can only do this with some knowledge of the boundary
// conditions, i.e. the user must have attached an appropriate
// BC function.
else
{
if (integrate_boundary_sides)
{
// Reinitialize shape functions on the fine element side
fe_fine->reinit (fine_elem, fine_side);
// Get the DOF indices
dof_map.dof_indices (fine_elem, dof_indices_fine, var);
// The number of DOFS on each element
const unsigned int n_dofs_fine =
libmesh_cast_int<unsigned int>(dof_indices_fine.size());
Ufine.resize(n_dofs_fine);
for (unsigned int i=0; i<n_dofs_fine; i++)
Ufine(i) = system.current_solution(dof_indices_fine[i]);
if (this->boundary_side_integration())
{
error_per_cell[fine_elem->id()] +=
static_cast<ErrorVectorReal>(fine_error);
n_flux_faces[fine_elem->id()]++;
}
} // end if _bc_function != NULL
} // end if (e->neighbor(n_e) == NULL)
} // end loop over neighbors
} // End loop over active local elements
} // End loop over variables
// Each processor has now computed the error contribuions
// 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);
// Compute the square-root of each component.
for (std::size_t i=0; i<error_per_cell.size(); i++)
if (error_per_cell[i] != 0.)
error_per_cell[i] = std::sqrt(error_per_cell[i]);
if (this->scale_by_n_flux_faces)
{
// Sum the vector of flux face counts
this->reduce_error(n_flux_faces);
// Sanity check: Make sure the number of flux faces is
// always an integer value
#ifdef DEBUG
for (unsigned int i=0; i<n_flux_faces.size(); ++i)
libmesh_assert_equal_to (n_flux_faces[i], static_cast<float>(static_cast<unsigned int>(n_flux_faces[i])) );
#endif
// Scale the error by the number of flux faces for each element
for (unsigned int i=0; i<n_flux_faces.size(); ++i)
{
if (n_flux_faces[i] == 0.0) // inactive or non-local element
continue;
//libMesh::out << "Element " << i << " has " << n_flux_faces[i] << " flux faces." << std::endl;
error_per_cell[i] /= static_cast<ErrorVectorReal>(n_flux_faces[i]);
}
}
// 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();
}
STOP_LOG("estimate_error()", "JumpErrorEstimator");
}
void ExactErrorEstimator::estimate_error (const System& system,
ErrorVector& error_per_cell,
const NumericVector<Number>* solution_vector,
bool /* estimate_parent_error */ )
#endif
{
// 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);
AutoPtr<FEBase> fe (FEBase::build (dim, fe_type));
// Build an appropriate Gaussian quadrature rule
AutoPtr<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
AutoPtr<MeshFunction> fine_values;
AutoPtr<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 (global_soln.size(), true, SERIAL);
(*fine_soln) = global_soln;
fine_values = AutoPtr<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 (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();
}
// 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.
MeshBase::const_element_iterator
elem_it = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator
elem_end = mesh.active_local_elements_end();
for (;elem_it != elem_end; ++elem_it)
{
// e is necessarily an active element on the local processor
const Elem* elem = *elem_it;
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 (unsigned int c=0; c != parent->n_children(); ++c)
if (!parent->child(c)->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 =
libmesh_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 contribuions
// 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.
START_LOG("std::sqrt()", "ExactErrorEstimator");
for (dof_id_type i=0; i<error_per_cell.size(); i++)
{
if (error_per_cell[i] != 0.)
{
libmesh_assert_greater (error_per_cell[i], 0.);
error_per_cell[i] = std::sqrt(error_per_cell[i]);
}
}
STOP_LOG("std::sqrt()", "ExactErrorEstimator");
// 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();
}
}
