void MeshRefinement::flag_elements_by_mean_stddev (const ErrorVector & error_per_cell,
const Real refine_frac,
const Real coarsen_frac,
const unsigned int max_l)
{
// The function arguments are currently just there for
// backwards_compatibility
if (!_use_member_parameters)
{
// If the user used non-default parameters, lets warn
// that they're deprecated
if (refine_frac != 0.3 ||
coarsen_frac != 0.0 ||
max_l != libMesh::invalid_uint)
libmesh_deprecated();
_refine_fraction = refine_frac;
_coarsen_fraction = coarsen_frac;
_max_h_level = max_l;
}
// Get the mean value from the error vector
const Real mean = error_per_cell.mean();
// Get the standard deviation. This equals the
// square-root of the variance
const Real stddev = std::sqrt (error_per_cell.variance());
// Check for valid fractions
libmesh_assert_greater_equal (_refine_fraction, 0);
libmesh_assert_less_equal (_refine_fraction, 1);
libmesh_assert_greater_equal (_coarsen_fraction, 0);
libmesh_assert_less_equal (_coarsen_fraction, 1);
// The refine and coarsen cutoff
const Real refine_cutoff = mean + _refine_fraction * stddev;
const Real coarsen_cutoff = std::max(mean - _coarsen_fraction * stddev, 0.);
// Loop over the elements and flag them for coarsening or
// refinement based on the element error
for (auto & elem : _mesh.active_element_ptr_range())
{
const dof_id_type id = elem->id();
libmesh_assert_less (id, error_per_cell.size());
const ErrorVectorReal elem_error = error_per_cell[id];
// Possibly flag the element for coarsening ...
if (elem_error <= coarsen_cutoff)
elem->set_refinement_flag(Elem::COARSEN);
// ... or refinement
if ((elem_error >= refine_cutoff) && (elem->level() < _max_h_level))
elem->set_refinement_flag(Elem::REFINE);
}
}
realv Layer::errorWeighting(ErrorVector _deltas, Mat _weights) {
if (_deltas.getLength() != ((uint) _weights.rows)) {
throw length_error("Layer : Uncorrect length between deltas and weights");
}
realv sum = 0;
for (uint i = 0; i < _deltas.getLength(); i++) {
sum += _deltas[i] * _weights.at<realv>(i, 0);
}
return sum;
}
void 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,
bool estimate_parent_error)
{
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 (std::size_t i=0; i != error_per_cell.size(); ++i)
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;
}
int main(int argc, char** argv)
{
// Initialize libMesh.
LibMeshInit init (argc, argv);
// Adaptive constraint calculations for fine Hermite elements seems
// to require half-decent precision
#ifdef LIBMESH_DEFAULT_SINGLE_PRECISION
libmesh_example_assert(false, "double precision");
#endif
// This example requires Adaptive Mesh Refinement support
#ifndef LIBMESH_ENABLE_AMR
libmesh_example_assert(false, "--enable-amr");
#else
// This example requires second derivative calculation support
#ifndef LIBMESH_ENABLE_SECOND_DERIVATIVES
libmesh_example_assert(false, "--enable-second");
#else
// Parse the input file
GetPot input_file("adaptivity_ex4.in");
// Read in parameters from the input file
const unsigned int max_r_level = input_file("max_r_level", 10);
const unsigned int max_r_steps = input_file("max_r_steps", 4);
const std::string approx_type = input_file("approx_type",
"HERMITE");
const unsigned int uniform_refine =
input_file("uniform_refine", 0);
const Real refine_percentage =
input_file("refine_percentage", 0.5);
const Real coarsen_percentage =
input_file("coarsen_percentage", 0.5);
const unsigned int dim =
input_file("dimension", 2);
const unsigned int max_linear_iterations =
input_file("max_linear_iterations", 10000);
// Skip higher-dimensional examples on a lower-dimensional libMesh build
libmesh_example_assert(dim <= LIBMESH_DIM, "2D/3D support");
// We have only defined 2 and 3 dimensional problems
libmesh_assert (dim == 2 || dim == 3);
// Currently only the Hermite cubics give a 3D C^1 basis
libmesh_assert (dim == 2 || approx_type == "HERMITE");
// Create a mesh.
Mesh mesh;
// Output file for plotting the error
std::string output_file = "";
if (dim == 2)
output_file += "2D_";
else if (dim == 3)
output_file += "3D_";
if (approx_type == "HERMITE")
output_file += "hermite_";
else if (approx_type == "SECOND")
output_file += "reducedclough_";
else
output_file += "clough_";
if (uniform_refine == 0)
output_file += "adaptive";
else
output_file += "uniform";
std::string exd_file = output_file;
exd_file += ".e";
output_file += ".m";
std::ofstream out (output_file.c_str());
out << "% dofs L2-error H1-error H2-error\n"
<< "e = [\n";
// Set up the dimension-dependent coarse mesh and solution
// We build more than one cell so as to avoid bugs on fewer than
// 4 processors in 2D or 8 in 3D.
if (dim == 2)
{
MeshTools::Generation::build_square(mesh, 2, 2);
exact_solution = &exact_2D_solution;
exact_derivative = &exact_2D_derivative;
exact_hessian = &exact_2D_hessian;
forcing_function = &forcing_function_2D;
}
else if (dim == 3)
{
MeshTools::Generation::build_cube(mesh, 2, 2, 2);
exact_solution = &exact_3D_solution;
exact_derivative = &exact_3D_derivative;
exact_hessian = &exact_3D_hessian;
forcing_function = &forcing_function_3D;
}
// Convert the mesh to second order: necessary for computing with
// Clough-Tocher elements, useful for getting slightly less
// broken visualization output with Hermite elements
mesh.all_second_order();
// Convert it to triangles if necessary
if (approx_type != "HERMITE")
MeshTools::Modification::all_tri(mesh);
// Mesh Refinement object
MeshRefinement mesh_refinement(mesh);
mesh_refinement.refine_fraction() = refine_percentage;
mesh_refinement.coarsen_fraction() = coarsen_percentage;
mesh_refinement.max_h_level() = max_r_level;
// Create an equation systems object.
EquationSystems equation_systems (mesh);
// Declare the system and its variables.
// Create a system named "Biharmonic"
LinearImplicitSystem& system =
equation_systems.add_system<LinearImplicitSystem> ("Biharmonic");
// Adds the variable "u" to "Biharmonic". "u"
// will be approximated using Hermite tensor product squares
// or (possibly reduced) cubic Clough-Tocher triangles
if (approx_type == "HERMITE")
system.add_variable("u", THIRD, HERMITE);
else if (approx_type == "SECOND")
system.add_variable("u", SECOND, CLOUGH);
else if (approx_type == "CLOUGH")
system.add_variable("u", THIRD, CLOUGH);
else
libmesh_error();
// Give the system a pointer to the matrix assembly
// function.
system.attach_assemble_function (assemble_biharmonic);
// Initialize the data structures for the equation system.
equation_systems.init();
// Set linear solver max iterations
equation_systems.parameters.set<unsigned int>
("linear solver maximum iterations") = max_linear_iterations;
// Linear solver tolerance.
equation_systems.parameters.set<Real>
("linear solver tolerance") = TOLERANCE * TOLERANCE;
// Prints information about the system to the screen.
equation_systems.print_info();
// Construct ExactSolution object and attach function to compute exact solution
ExactSolution exact_sol(equation_systems);
exact_sol.attach_exact_value(exact_solution);
exact_sol.attach_exact_deriv(exact_derivative);
exact_sol.attach_exact_hessian(exact_hessian);
// Construct zero solution object, useful for computing solution norms
// Attaching "zero_solution" functions is unnecessary
ExactSolution zero_sol(equation_systems);
// A refinement loop.
for (unsigned int r_step=0; r_step<max_r_steps; r_step++)
{
mesh.print_info();
equation_systems.print_info();
std::cout << "Beginning Solve " << r_step << std::endl;
// Solve the system "Biharmonic", just like example 2.
system.solve();
std::cout << "Linear solver converged at step: "
<< system.n_linear_iterations()
<< ", final residual: "
<< system.final_linear_residual()
<< std::endl;
// Compute the error.
exact_sol.compute_error("Biharmonic", "u");
// Compute the norm.
zero_sol.compute_error("Biharmonic", "u");
// Print out the error values
std::cout << "L2-Norm is: "
<< zero_sol.l2_error("Biharmonic", "u")
<< std::endl;
std::cout << "H1-Norm is: "
<< zero_sol.h1_error("Biharmonic", "u")
<< std::endl;
std::cout << "H2-Norm is: "
<< zero_sol.h2_error("Biharmonic", "u")
<< std::endl
<< std::endl;
std::cout << "L2-Error is: "
<< exact_sol.l2_error("Biharmonic", "u")
<< std::endl;
std::cout << "H1-Error is: "
<< exact_sol.h1_error("Biharmonic", "u")
<< std::endl;
std::cout << "H2-Error is: "
<< exact_sol.h2_error("Biharmonic", "u")
<< std::endl
<< std::endl;
// Print to output file
out << equation_systems.n_active_dofs() << " "
<< exact_sol.l2_error("Biharmonic", "u") << " "
<< exact_sol.h1_error("Biharmonic", "u") << " "
<< exact_sol.h2_error("Biharmonic", "u") << std::endl;
// Possibly refine the mesh
if (r_step+1 != max_r_steps)
{
std::cout << " Refining the mesh..." << std::endl;
if (uniform_refine == 0)
{
ErrorVector error;
LaplacianErrorEstimator error_estimator;
error_estimator.estimate_error(system, error);
mesh_refinement.flag_elements_by_elem_fraction (error);
std::cout << "Mean Error: " << error.mean() <<
std::endl;
std::cout << "Error Variance: " << error.variance() <<
std::endl;
mesh_refinement.refine_and_coarsen_elements();
}
else
{
mesh_refinement.uniformly_refine(1);
}
// This call reinitializes the \p EquationSystems object for
// the newly refined mesh. One of the steps in the
// reinitialization is projecting the \p solution,
// \p old_solution, etc... vectors from the old mesh to
// the current one.
equation_systems.reinit ();
}
}
#ifdef LIBMESH_HAVE_EXODUS_API
// Write out the solution
// After solving the system write the solution
// to a ExodusII-formatted plot file.
ExodusII_IO (mesh).write_equation_systems (exd_file,
equation_systems);
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
// Close up the output file.
out << "];\n"
<< "hold on\n"
<< "loglog(e(:,1), e(:,2), 'bo-');\n"
<< "loglog(e(:,1), e(:,3), 'ro-');\n"
<< "loglog(e(:,1), e(:,4), 'go-');\n"
<< "xlabel('log(dofs)');\n"
<< "ylabel('log(error)');\n"
<< "title('C1 " << approx_type << " elements');\n"
<< "legend('L2-error', 'H1-error', 'H2-error');\n";
// All done.
return 0;
#endif // #ifndef LIBMESH_ENABLE_SECOND_DERIVATIVES
#endif // #ifndef LIBMESH_ENABLE_AMR
}
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();
// Get coarse grid adjoint solutions. This should be a relatively
// quick (especially with preconditioner reuse) way to get a good
// initial guess for the fine grid adjoint solutions. More
// importantly, subtracting off a coarse adjoint approximation gives
// us better local error indication, and subtracting off *some* lift
// function is necessary for correctness if we have heterogeneous
// adjoint Dirichlet conditions.
// Solve the adjoint problem(s) on the coarse FE space
// Only if the user didn't already solve it for us
if (!system.is_adjoint_already_solved())
system.adjoint_solve(_qoi_set);
// Loop over all the adjoint problems and, if any have heterogenous
// Dirichlet conditions, get the corresponding coarse lift
// function(s)
for (unsigned int j=0; j != system.qoi.size(); j++)
{
// Skip this QoI if it is not in the QoI Set or if there are no
// heterogeneous Dirichlet boundaries for it
if (_qoi_set.has_index(j) &&
system.get_dof_map().has_adjoint_dirichlet_boundaries(j))
{
std::ostringstream liftfunc_name;
liftfunc_name << "adjoint_lift_function" << j;
NumericVector<Number> & liftvec =
system.add_vector(liftfunc_name.str());
system.get_dof_map().enforce_constraints_exactly
(system, &liftvec, true);
}
}
// 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 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
UniquePtr<Partitioner> old_partitioner(mesh.partitioner().release());
// 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();
}
// 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.);
#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()
std::vector<NumericVector<Number> *> coarse_adjoints;
for (unsigned int j=0; j != system.qoi.size(); j++)
{
if (_qoi_set.has_index(j))
{
NumericVector<Number> * coarse_adjoint =
NumericVector<Number>::build(mesh.comm()).release();
// Can do "fast" init since we're overwriting this in a sec
coarse_adjoint->init(system.get_adjoint_solution(j),
/* fast = */ true);
*coarse_adjoint = system.get_adjoint_solution(j);
coarse_adjoints.push_back(coarse_adjoint);
}
else
coarse_adjoints.push_back(static_cast<NumericVector<Number> *>(libmesh_nullptr));
}
// 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(s) on the refined FE space
system.adjoint_solve(_qoi_set);
// 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. While we're looping anyway we'll
// pull off the coarse adjoints
for (unsigned int j=0; j != system.qoi.size(); j++)
{
// Skip this QoI if not in the QoI Set
if (_qoi_set.has_index(j))
{
// If the adjoint solution has heterogeneous dirichlet
// values, then to get a proper error estimate here we need
// to subtract off a coarse grid lift function. In any case
// we can get a better error estimate by separating off a
// coarse representation of the adjoint solution, so we'll
// use that for our lift function.
system.get_adjoint_solution(j) -= *coarse_adjoints[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
// Keep track of which nodes we have already dealt with
LIBMESH_BEST_UNORDERED_SET<dof_id_type> processed_node_ids;
// 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();
// 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 reference to the current node
const Node & node = elem->node_ref(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] =
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
UniquePtr<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
UniquePtr<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>
(std::abs(local_contribution));
} // End loop over elements
} // End if belong to QoI set
} // End loop over QoIs
for (unsigned int j=0; j != system.qoi.size(); j++)
{
if (_qoi_set.has_index(j))
{
delete coarse_adjoints[j];
}
}
// 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;
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().reset(old_partitioner.release());
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 ExactErrorEstimator::estimate_error (const System & system,
ErrorVector & error_per_cell,
const NumericVector<Number> * solution_vector,
bool estimate_parent_error)
{
// 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);
UniquePtr<FEBase> fe (FEBase::build (dim, fe_type));
// Build an appropriate Gaussian quadrature rule
UniquePtr<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
UniquePtr<MeshFunction> fine_values;
UniquePtr<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 = UniquePtr<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_ptr(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 =
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.
{
LOG_SCOPE("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]);
}
}
// 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();
}
}
int main(int argc, char** argv){
//initialize libMesh
LibMeshInit init(argc, argv);
//parameters
GetPot infile("fem_system_params.in");
const bool transient = infile("transient", true);
const Real deltat = infile("deltat", 0.005);
unsigned int n_timesteps = infile("n_timesteps", 20);
const int nx = infile("nx",100);
const int ny = infile("ny",100);
const int nz = infile("nz",100);
//const unsigned int dim = 3;
const unsigned int max_r_steps = infile("max_r_steps", 3);
const unsigned int max_r_level = infile("max_r_level", 3);
const Real refine_percentage = infile("refine_percentage", 0.1);
const Real coarsen_percentage = infile("coarsen_percentage", 0.0);
const std::string indicator_type = infile("indicator_type", "kelly");
const bool write_error = infile("write_error",false);
const bool flag_by_elem_frac = infile("flag_by_elem_frac",true);
#ifdef LIBMESH_HAVE_EXODUS_API
const unsigned int write_interval = infile("write_interval", 5);
#endif
// Create a mesh, with dimension to be overridden later, distributed
// across the default MPI communicator.
Mesh mesh(init.comm());
//create mesh
unsigned int dim;
if(nz == 0){ //to check if oscillations happen in 2D as well...
dim = 2;
MeshTools::Generation::build_square(mesh, nx, ny, 497150.0, 501750.0, 537350.0, 540650.0, QUAD9);
}else{
dim = 3;
MeshTools::Generation::build_cube(mesh,
nx, ny, nz,
497150.0, 501750.0,
537350.0, 540650.0,
0.0, 100.0,
HEX27);
}
// Print information about the mesh to the screen.
mesh.print_info();
// Create an equation systems object.
EquationSystems equation_systems (mesh);
//name system
ContamTransSysInv & system =
equation_systems.add_system<ContamTransSysInv>("ContamTransInv");
//solve as steady or transient
if(transient){
//system.time_solver = AutoPtr<TimeSolver>(new EulerSolver(system)); //backward Euler
system.time_solver = AutoPtr<TimeSolver>(new SteadySolver(system));
std::cout << "\n\nAaahhh transience not yet available!\n" << std::endl;
n_timesteps = 1;
}
else{
system.time_solver = AutoPtr<TimeSolver>(new SteadySolver(system));
libmesh_assert_equal_to (n_timesteps, 1); //this doesn't seem to work?
}
// Initialize the system
equation_systems.init ();
//initial conditions
read_initial_parameters();
system.project_solution(initial_value, initial_grad,
equation_systems.parameters);
finish_initialization();
// Set the time stepping options...
system.deltat = deltat;
//...and the nonlinear solver options...
NewtonSolver *solver = new NewtonSolver(system);
system.time_solver->diff_solver() = AutoPtr<DiffSolver>(solver);
solver->quiet = infile("solver_quiet", true);
solver->verbose = !solver->quiet;
solver->max_nonlinear_iterations =
infile("max_nonlinear_iterations", 15);
solver->relative_step_tolerance =
infile("relative_step_tolerance", 1.e-3);
solver->relative_residual_tolerance =
infile("relative_residual_tolerance", 0.0);
solver->absolute_residual_tolerance =
infile("absolute_residual_tolerance", 0.0);
// And the linear solver options
solver->max_linear_iterations = infile("max_linear_iterations", 10000);
solver->initial_linear_tolerance = infile("initial_linear_tolerance",1.e-13);
solver->minimum_linear_tolerance = infile("minimum_linear_tolerance",1.e-13);
solver->linear_tolerance_multiplier = infile("linear_tolerance_multiplier",1.e-3);
// Mesh Refinement object - to test effect of constant refined mesh (not refined at every timestep)
MeshRefinement mesh_refinement(mesh);
mesh_refinement.refine_fraction() = refine_percentage;
mesh_refinement.coarsen_fraction() = coarsen_percentage;
mesh_refinement.max_h_level() = max_r_level;
// Print information about the system to the screen.
equation_systems.print_info();
ExodusII_IO exodusIO = ExodusII_IO(mesh); //for writing multiple timesteps to one file
for (unsigned int r_step=0; r_step<max_r_steps; r_step++)
{
std::cout << "\nBeginning Solve " << r_step+1 << std::endl;
for (unsigned int t_step=0; t_step != n_timesteps; ++t_step)
{
std::cout << "\n\nSolving time step " << t_step << ", time = "
<< system.time << std::endl;
system.solve();
system.postprocess();
// Advance to the next timestep in a transient problem
system.time_solver->advance_timestep();
} //end stepping through time loop
std::cout << "\n Refining the mesh..." << std::endl;
// The \p ErrorVector is a particular \p StatisticsVector
// for computing error information on a finite element mesh.
ErrorVector error;
if (indicator_type == "patch")
{
// The patch recovery estimator should give a
// good estimate of the solution interpolation
// error.
PatchRecoveryErrorEstimator error_estimator;
error_estimator.set_patch_reuse(false); //anisotropy trips up reuse
error_estimator.estimate_error (system, error);
}
else if (indicator_type == "kelly")
{
// The Kelly error estimator is based on
// an error bound for the Poisson problem
// on linear elements, but is useful for
// driving adaptive refinement in many problems
KellyErrorEstimator error_estimator;
error_estimator.estimate_error (system, error);
}
// Write out the error distribution
if(write_error){
std::ostringstream ss;
ss << r_step;
#ifdef LIBMESH_HAVE_EXODUS_API
std::string error_output = "error_"+ss.str()+".e";
#else
std::string error_output = "error_"+ss.str()+".gmv";
#endif
error.plot_error( error_output, mesh );
}
// This takes the error in \p error and decides which elements
// will be coarsened or refined.
if(flag_by_elem_frac)
mesh_refinement.flag_elements_by_elem_fraction(error);
else
mesh_refinement.flag_elements_by_error_fraction (error);
// This call actually refines and coarsens the flagged
// elements.
mesh_refinement.refine_and_coarsen_elements();
// This call reinitializes the \p EquationSystems object for
// the newly refined mesh. One of the steps in the
// reinitialization is projecting the \p solution,
// \p old_solution, etc... vectors from the old mesh to
// the current one.
equation_systems.reinit ();
std::cout << "System has: " << equation_systems.n_active_dofs()
<< " degrees of freedom."
<< std::endl;
} //end refinement loop
//use that final refinement
for (unsigned int t_step=0; t_step != n_timesteps; ++t_step)
{
std::cout << "\n\nSolving time step " << t_step << ", time = "
<< system.time << std::endl;
system.solve();
system.postprocess();
Number QoI_computed = system.get_QoI_value("computed", 0);
std::cout<< "Computed QoI is " << std::setprecision(17) << QoI_computed << std::endl;
// Advance to the next timestep in a transient problem
system.time_solver->advance_timestep();
} //end stepping through time loop
#ifdef LIBMESH_HAVE_EXODUS_API
for (unsigned int t_step=0; t_step != n_timesteps; ++t_step)
{
// Write out this timestep if we're requested to
if ((t_step+1)%write_interval == 0)
{
std::ostringstream ex_file_name;
std::ostringstream tplot_file_name;
// We write the file in the ExodusII format.
//ex_file_name << "out_"
// << std::setw(3)
// << std::setfill('0')
// << std::right
// << t_step+1
// << ".e";
tplot_file_name << "out_"
<< std::setw(3)
<< std::setfill('0')
<< std::right
<< t_step+1
<< ".plt";
//ExodusII_IO(mesh).write_timestep(ex_file_name.str(),
// equation_systems,
// 1, /* This number indicates how many time steps
// are being written to the file */
// system.time);
exodusIO.write_timestep("output.exo", equation_systems, t_step+1, system.time); //outputs all timesteps in one file
TecplotIO(mesh).write_equation_systems(tplot_file_name.str(), equation_systems);
}
}
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
// All done.
return 0;
} //end main
// The main program
int main(int argc, char** argv)
{
// Initialize libMesh
LibMeshInit init(argc, argv);
// Parameters
GetPot infile("fem_system_params.in");
const Real global_tolerance = infile("global_tolerance", 0.);
const unsigned int nelem_target = infile("n_elements", 400);
const bool transient = infile("transient", true);
const Real deltat = infile("deltat", 0.005);
unsigned int n_timesteps = infile("n_timesteps", 1);
//const unsigned int coarsegridsize = infile("coarsegridsize", 1);
const unsigned int coarserefinements = infile("coarserefinements", 0);
const unsigned int max_adaptivesteps = infile("max_adaptivesteps", 10);
//const unsigned int dim = 2;
#ifdef LIBMESH_HAVE_EXODUS_API
const unsigned int write_interval = infile("write_interval", 5);
#endif
// Create a mesh, with dimension to be overridden later, distributed
// across the default MPI communicator.
Mesh mesh(init.comm());
GetPot infileForMesh("convdiff_mprime.in");
std::string find_mesh_here = infileForMesh("mesh","psiLF_mesh.xda");
mesh.read(find_mesh_here);
std::cout << "Read in mesh from: " << find_mesh_here << "\n\n";
// And an object to refine it
MeshRefinement mesh_refinement(mesh);
mesh_refinement.coarsen_by_parents() = true;
mesh_refinement.absolute_global_tolerance() = global_tolerance;
mesh_refinement.nelem_target() = nelem_target;
mesh_refinement.refine_fraction() = 0.3;
mesh_refinement.coarsen_fraction() = 0.3;
mesh_refinement.coarsen_threshold() = 0.1;
//mesh_refinement.uniformly_refine(coarserefinements);
// Print information about the mesh to the screen.
mesh.print_info();
// Create an equation systems object.
EquationSystems equation_systems (mesh);
// Name system
ConvDiff_MprimeSys & system =
equation_systems.add_system<ConvDiff_MprimeSys>("Diff_ConvDiff_MprimeSys");
// Steady-state problem
system.time_solver =
AutoPtr<TimeSolver>(new SteadySolver(system));
// Sanity check that we are indeed solving a steady problem
libmesh_assert_equal_to (n_timesteps, 1);
// Read in all the equation systems data from the LF solve (system, solutions, rhs, etc)
std::string find_psiLF_here = infileForMesh("psiLF_file","psiLF.xda");
std::cout << "Looking for psiLF at: " << find_psiLF_here << "\n\n";
equation_systems.read(find_psiLF_here, READ,
EquationSystems::READ_HEADER |
EquationSystems::READ_DATA |
EquationSystems::READ_ADDITIONAL_DATA);
// Check that the norm of the solution read in is what we expect it to be
Real readin_L2 = system.calculate_norm(*system.solution, 0, L2);
std::cout << "Read in solution norm: "<< readin_L2 << std::endl << std::endl;
//DEBUG
//equation_systems.write("right_back_out.xda", WRITE, EquationSystems::WRITE_DATA |
// EquationSystems::WRITE_ADDITIONAL_DATA);
#ifdef LIBMESH_HAVE_GMV
//GMVIO(equation_systems.get_mesh()).write_equation_systems(std::string("right_back_out.gmv"), equation_systems);
#endif
// Initialize the system
//equation_systems.init (); //already initialized by read-in
// And the nonlinear solver options
NewtonSolver *solver = new NewtonSolver(system);
system.time_solver->diff_solver() = AutoPtr<DiffSolver>(solver);
solver->quiet = infile("solver_quiet", true);
solver->verbose = !solver->quiet;
solver->max_nonlinear_iterations =
infile("max_nonlinear_iterations", 15);
solver->relative_step_tolerance =
infile("relative_step_tolerance", 1.e-3);
solver->relative_residual_tolerance =
infile("relative_residual_tolerance", 0.0);
solver->absolute_residual_tolerance =
infile("absolute_residual_tolerance", 0.0);
// And the linear solver options
solver->max_linear_iterations =
infile("max_linear_iterations", 50000);
solver->initial_linear_tolerance =
infile("initial_linear_tolerance", 1.e-3);
// Print information about the system to the screen.
equation_systems.print_info();
// Now we begin the timestep loop to compute the time-accurate
// solution of the equations...not that this is transient, but eh, why not...
for (unsigned int t_step=0; t_step != n_timesteps; ++t_step)
{
// A pretty update message
std::cout << "\n\nSolving time step " << t_step << ", time = "
<< system.time << std::endl;
// Adaptively solve the timestep
unsigned int a_step = 0;
for (; a_step != max_adaptivesteps; ++a_step)
{ // VESTIGIAL for now ('vestigial' eh ? ;) )
std::cout << "\n\n I should be skipped what are you doing here lalalalalalala *!**!*!*!*!*!* \n\n";
system.solve();
system.postprocess();
ErrorVector error;
AutoPtr<ErrorEstimator> error_estimator;
// To solve to a tolerance in this problem we
// need a better estimator than Kelly
if (global_tolerance != 0.)
{
// We can't adapt to both a tolerance and a mesh
// size at once
libmesh_assert_equal_to (nelem_target, 0);
UniformRefinementEstimator *u =
new UniformRefinementEstimator;
// The lid-driven cavity problem isn't in H1, so
// lets estimate L2 error
u->error_norm = L2;
error_estimator.reset(u);
}
else
{
// If we aren't adapting to a tolerance we need a
// target mesh size
libmesh_assert_greater (nelem_target, 0);
// Kelly is a lousy estimator to use for a problem
// not in H1 - if we were doing more than a few
// timesteps we'd need to turn off or limit the
// maximum level of our adaptivity eventually
error_estimator.reset(new KellyErrorEstimator);
}
// Calculate error
std::vector<Real> weights(9,1.0); // based on u, v, p, c, their adjoints, and source parameter
// Keep the same default norm type.
std::vector<FEMNormType>
norms(1, error_estimator->error_norm.type(0));
error_estimator->error_norm = SystemNorm(norms, weights);
error_estimator->estimate_error(system, error);
// Print out status at each adaptive step.
Real global_error = error.l2_norm();
std::cout << "Adaptive step " << a_step << ": " << std::endl;
if (global_tolerance != 0.)
std::cout << "Global_error = " << global_error
<< std::endl;
if (global_tolerance != 0.)
std::cout << "Worst element error = " << error.maximum()
<< ", mean = " << error.mean() << std::endl;
if (global_tolerance != 0.)
{
// If we've reached our desired tolerance, we
// don't need any more adaptive steps
if (global_error < global_tolerance)
break;
mesh_refinement.flag_elements_by_error_tolerance(error);
}
else
{
// If flag_elements_by_nelem_target returns true, this
// should be our last adaptive step.
if (mesh_refinement.flag_elements_by_nelem_target(error))
{
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
a_step = max_adaptivesteps;
break;
}
}
// Carry out the adaptive mesh refinement/coarsening
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
std::cout << "Refined mesh to "
<< mesh.n_active_elem()
<< " active elements and "
<< equation_systems.n_active_dofs()
<< " active dofs." << std::endl;
} // End loop over adaptive steps
// Do one last solve if necessary
if (a_step == max_adaptivesteps)
{
QoISet qois;
std::vector<unsigned int> qoi_indices;
qoi_indices.push_back(0);
qois.add_indices(qoi_indices);
qois.set_weight(0, 1.0);
system.assemble_qoi_sides = true; //QoI doesn't involve sides
std::cout << "\n~*~*~*~*~*~*~*~*~ adjoint solve start ~*~*~*~*~*~*~*~*~\n" << std::endl;
std::pair<unsigned int, Real> adjsolve = system.adjoint_solve();
std::cout << "number of iterations to solve adjoint: " << adjsolve.first << std::endl;
std::cout << "final residual of adjoint solve: " << adjsolve.second << std::endl;
std::cout << "\n~*~*~*~*~*~*~*~*~ adjoint solve end ~*~*~*~*~*~*~*~*~" << std::endl;
NumericVector<Number> &dual_solution = system.get_adjoint_solution(0);
NumericVector<Number> &primal_solution = *system.solution;
primal_solution.swap(dual_solution);
ExodusII_IO(mesh).write_timestep("super_adjoint.exo",
equation_systems,
1, /* This number indicates how many time steps
are being written to the file */
system.time);
primal_solution.swap(dual_solution);
system.assemble(); //overwrite residual read in from psiLF solve
// The total error estimate
system.postprocess(); //to compute M_HF(psiLF) and M_LF(psiLF) terms
Real QoI_error_estimate = (-0.5*(system.rhs)->dot(dual_solution)) + system.get_MHF_psiLF() - system.get_MLF_psiLF();
std::cout << "\n\n 0.5*M'_HF(psiLF)(superadj): " << std::setprecision(17) << 0.5*(system.rhs)->dot(dual_solution) << "\n";
std::cout << " M_HF(psiLF): " << std::setprecision(17) << system.get_MHF_psiLF() << "\n";
std::cout << " M_LF(psiLF): " << std::setprecision(17) << system.get_MLF_psiLF() << "\n";
std::cout << "\n\n Residual L2 norm: " << system.calculate_norm(*system.rhs, L2) << "\n";
std::cout << " Residual discrete L2 norm: " << system.calculate_norm(*system.rhs, DISCRETE_L2) << "\n";
std::cout << " Super-adjoint L2 norm: " << system.calculate_norm(dual_solution, L2) << "\n";
std::cout << " Super-adjoint discrete L2 norm: " << system.calculate_norm(dual_solution, DISCRETE_L2) << "\n";
std::cout << "\n\n QoI error estimate: " << std::setprecision(17) << QoI_error_estimate << "\n\n";
//DEBUG
std::cout << "\n------------ herp derp ------------" << std::endl;
//libMesh::out.precision(16);
//dual_solution.print();
//system.get_adjoint_rhs().print();
AutoPtr<NumericVector<Number> > adjresid = system.solution->clone();
(system.matrix)->vector_mult(*adjresid,system.get_adjoint_solution(0));
SparseMatrix<Number>& adjmat = *system.matrix;
(system.matrix)->get_transpose(adjmat);
adjmat.vector_mult(*adjresid,system.get_adjoint_solution(0));
//std::cout << "******************** matrix-superadj product (libmesh) ************************" << std::endl;
//adjresid->print();
adjresid->add(-1.0, system.get_adjoint_rhs(0));
//std::cout << "******************** superadjoint system residual (libmesh) ***********************" << std::endl;
//adjresid->print();
std::cout << "\n\nadjoint system residual (discrete L2): " << system.calculate_norm(*adjresid,DISCRETE_L2) << std::endl;
std::cout << "adjoint system residual (L2, all): " << system.calculate_norm(*adjresid,L2) << std::endl;
std::cout << "adjoint system residual (L2, 0): " << system.calculate_norm(*adjresid,0,L2) << std::endl;
std::cout << "adjoint system residual (L2, 1): " << system.calculate_norm(*adjresid,1,L2) << std::endl;
std::cout << "adjoint system residual (L2, 2): " << system.calculate_norm(*adjresid,2,L2) << std::endl;
std::cout << "adjoint system residual (L2, 3): " << system.calculate_norm(*adjresid,3,L2) << std::endl;
std::cout << "adjoint system residual (L2, 4): " << system.calculate_norm(*adjresid,4,L2) << std::endl;
std::cout << "adjoint system residual (L2, 5): " << system.calculate_norm(*adjresid,5,L2) << std::endl;
/*
AutoPtr<NumericVector<Number> > sadj_matlab = system.solution->clone();
AutoPtr<NumericVector<Number> > adjresid_matlab = system.solution->clone();
if(FILE *fp=fopen("superadj_matlab.txt","r")){
Real value;
int counter = 0;
int flag = 1;
while(flag != -1){
flag = fscanf(fp,"%lf",&value);
if(flag != -1){
sadj_matlab->set(counter, value);
counter += 1;
}
}
fclose(fp);
}
(system.matrix)->vector_mult(*adjresid_matlab,*sadj_matlab);
//std::cout << "******************** matrix-superadj product (matlab) ***********************" << std::endl;
//adjresid_matlab->print();
adjresid_matlab->add(-1.0, system.get_adjoint_rhs(0));
//std::cout << "******************** superadjoint system residual (matlab) ***********************" << std::endl;
//adjresid_matlab->print();
std::cout << "\n\nmatlab import adjoint system residual (discrete L2): " << system.calculate_norm(*adjresid_matlab,DISCRETE_L2) << "\n" << std::endl;
*/
/*
AutoPtr<NumericVector<Number> > sadj_fwd_hack = system.solution->clone();
AutoPtr<NumericVector<Number> > adjresid_fwd_hack = system.solution->clone();
if(FILE *fp=fopen("superadj_forward_hack.txt","r")){
Real value;
int counter = 0;
int flag = 1;
while(flag != -1){
flag = fscanf(fp,"%lf",&value);
if(flag != -1){
sadj_fwd_hack->set(counter, value);
counter += 1;
}
}
fclose(fp);
}
(system.matrix)->vector_mult(*adjresid_fwd_hack,*sadj_fwd_hack);
//std::cout << "******************** matrix-superadj product (fwd_hack) ***********************" << std::endl;
//adjresid_fwd_hack->print();
adjresid_fwd_hack->add(-1.0, system.get_adjoint_rhs(0));
//std::cout << "******************** superadjoint system residual (fwd_hack) ***********************" << std::endl;
//adjresid_fwd_hack->print();
std::cout << "\n\nfwd_hack import adjoint system residual (discrete L2): " << system.calculate_norm(*adjresid_fwd_hack,DISCRETE_L2) << "\n" << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 0): " << system.calculate_norm(*adjresid_fwd_hack,0,L2) << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 1): " << system.calculate_norm(*adjresid_fwd_hack,1,L2) << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 2): " << system.calculate_norm(*adjresid_fwd_hack,2,L2) << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 3): " << system.calculate_norm(*adjresid_fwd_hack,3,L2) << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 4): " << system.calculate_norm(*adjresid_fwd_hack,4,L2) << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 5): " << system.calculate_norm(*adjresid_fwd_hack,5,L2) << std::endl;
*/
//std::cout << "************************ system.matrix ***********************" << std::endl;
//system.matrix->print();
std::cout << "\n------------ herp derp ------------" << std::endl;
// The cell wise breakdown
ErrorVector cell_wise_error;
cell_wise_error.resize((system.rhs)->size());
for(unsigned int i = 0; i < (system.rhs)->size() ; i++)
{
if(i < system.get_mesh().n_elem())
cell_wise_error[i] = fabs(-0.5*((system.rhs)->el(i) * dual_solution(i))
+ system.get_MHF_psiLF(i) - system.get_MLF_psiLF(i));
else
cell_wise_error[i] = fabs(-0.5*((system.rhs)->el(i) * dual_solution(i)));
/*csv from 'save data' from gmv output gives a few values at each node point (value
for every element that shares that node), yet paraview display only seems to show one
of them -> the value in an element is given at each of the nodes that it has, hence the
repetition; what is displayed in paraview is each element's value; even though MHF_psiLF
and MLF_psiLF are stored by element this seems to give elemental contributions that
agree with if we had taken the superadj-residual dot product by integrating over elements*/
/*at higher mesh resolutions and lower k, weird-looking artifacts start to appear and
it no longer agrees with output from manual integration of superadj-residual...*/
}
// Plot it
std::ostringstream error_gmv;
error_gmv << "error.gmv";
cell_wise_error.plot_error(error_gmv.str(), equation_systems.get_mesh());
//alternate element-wise breakdown, outputed as values matched to element centroids; for matlab plotz
primal_solution.swap(dual_solution);
system.postprocess(1);
primal_solution.swap(dual_solution);
system.postprocess(2);
std::cout << "\n\n -0.5*M'_HF(psiLF)(superadj): " << std::setprecision(17) << system.get_half_adj_weighted_resid() << "\n";
primal_solution.swap(dual_solution);
std::string write_error_here = infileForMesh("error_est_output_file", "error_est_breakdown.dat");
std::ofstream output(write_error_here);
for(unsigned int i = 0 ; i < system.get_mesh().n_elem(); i++) {
Point elem_cent = system.get_mesh().elem(i)->centroid();
if(output.is_open()) {
output << elem_cent(0) << " " << elem_cent(1) << " "
<< fabs(system.get_half_adj_weighted_resid(i) + system.get_MHF_psiLF(i) - system.get_MLF_psiLF(i)) << "\n";
}
}
output.close();
} // End if at max adaptive steps
#ifdef LIBMESH_HAVE_EXODUS_API
// Write out this timestep if we're requested to
if ((t_step+1)%write_interval == 0)
{
std::ostringstream file_name;
/*
// We write the file in the ExodusII format.
file_name << "out_"
<< std::setw(3)
<< std::setfill('0')
<< std::right
<< t_step+1
<< ".e";
//this should write out the primal which should be the same as what's read in...
ExodusII_IO(mesh).write_timestep(file_name.str(),
equation_systems,
1, //number of time steps written to file
system.time);
*/
}
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
}
// All done.
return 0;
} //end main
void AdjointResidualErrorEstimator::estimate_error (const System & _system,
ErrorVector & error_per_cell,
const NumericVector<Number> * solution_vector,
bool estimate_parent_error)
{
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; i != _system.qoi.size(); ++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 (unsigned int i=0; i != error_per_cell.size(); ++i)
{
// 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)];
}
}
//-----------------------------------------------------------------
// Mesh refinement methods
void MeshRefinement::flag_elements_by_error_fraction (const ErrorVector& error_per_cell,
const Real refine_frac,
const Real coarsen_frac,
const unsigned int max_l)
{
parallel_only();
// The function arguments are currently just there for
// backwards_compatibility
if (!_use_member_parameters)
{
// If the user used non-default parameters, lets warn
// that they're deprecated
if (refine_frac != 0.3 ||
coarsen_frac != 0.0 ||
max_l != libMesh::invalid_uint)
libmesh_deprecated();
_refine_fraction = refine_frac;
_coarsen_fraction = coarsen_frac;
_max_h_level = max_l;
}
// Check for valid fractions..
// The fraction values must be in [0,1]
libmesh_assert_greater_equal (_refine_fraction, 0);
libmesh_assert_less_equal (_refine_fraction, 1);
libmesh_assert_greater_equal (_coarsen_fraction, 0);
libmesh_assert_less_equal (_coarsen_fraction, 1);
// Clean up the refinement flags. These could be left
// over from previous refinement steps.
this->clean_refinement_flags();
// We're getting the minimum and maximum error values
// for the ACTIVE elements
Real error_min = 1.e30;
Real error_max = 0.;
// And, if necessary, for their parents
Real parent_error_min = 1.e30;
Real parent_error_max = 0.;
// Prepare another error vector if we need to sum parent errors
ErrorVector error_per_parent;
if (_coarsen_by_parents)
{
create_parent_error_vector(error_per_cell,
error_per_parent,
parent_error_min,
parent_error_max);
}
// We need to loop over all active elements to find the minimum
MeshBase::element_iterator el_it =
_mesh.active_local_elements_begin();
const MeshBase::element_iterator el_end =
_mesh.active_local_elements_end();
for (; el_it != el_end; ++el_it)
{
const unsigned int id = (*el_it)->id();
libmesh_assert_less (id, error_per_cell.size());
error_max = std::max (error_max, error_per_cell[id]);
error_min = std::min (error_min, error_per_cell[id]);
}
CommWorld.max(error_max);
CommWorld.min(error_min);
// Compute the cutoff values for coarsening and refinement
const Real error_delta = (error_max - error_min);
const Real parent_error_delta = parent_error_max - parent_error_min;
const Real refine_cutoff = (1.- _refine_fraction)*error_max;
const Real coarsen_cutoff = _coarsen_fraction*error_delta + error_min;
const Real parent_cutoff = _coarsen_fraction*parent_error_delta + error_min;
// // Print information about the error
// libMesh::out << " Error Information:" << std::endl
// << " ------------------" << std::endl
// << " min: " << error_min << std::endl
// << " max: " << error_max << std::endl
// << " delta: " << error_delta << std::endl
// << " refine_cutoff: " << refine_cutoff << std::endl
// << " coarsen_cutoff: " << coarsen_cutoff << std::endl;
// Loop over the elements and flag them for coarsening or
// refinement based on the element error
MeshBase::element_iterator e_it =
_mesh.active_elements_begin();
const MeshBase::element_iterator e_end =
_mesh.active_elements_end();
for (; e_it != e_end; ++e_it)
{
Elem* elem = *e_it;
const unsigned int id = elem->id();
libmesh_assert_less (id, error_per_cell.size());
const float elem_error = error_per_cell[id];
if (_coarsen_by_parents)
{
Elem* parent = elem->parent();
if (parent)
{
const unsigned int parentid = parent->id();
if (error_per_parent[parentid] >= 0. &&
error_per_parent[parentid] <= parent_cutoff)
elem->set_refinement_flag(Elem::COARSEN);
}
}
// Flag the element for coarsening if its error
// is <= coarsen_fraction*delta + error_min
else if (elem_error <= coarsen_cutoff)
{
elem->set_refinement_flag(Elem::COARSEN);
}
// Flag the element for refinement if its error
// is >= refinement_cutoff.
if (elem_error >= refine_cutoff)
if (elem->level() < _max_h_level)
elem->set_refinement_flag(Elem::REFINE);
}
}
bool MeshRefinement::flag_elements_by_nelem_target (const ErrorVector& error_per_cell)
{
parallel_only();
// Check for valid fractions..
// The fraction values must be in [0,1]
libmesh_assert_greater_equal (_refine_fraction, 0);
libmesh_assert_less_equal (_refine_fraction, 1);
libmesh_assert_greater_equal (_coarsen_fraction, 0);
libmesh_assert_less_equal (_coarsen_fraction, 1);
// This function is currently only coded to work when coarsening by
// parents - it's too hard to guess how many coarsenings will be
// performed otherwise.
libmesh_assert (_coarsen_by_parents);
// The number of active elements in the mesh - hopefully less than
// 2 billion on 32 bit machines
const unsigned int n_active_elem = _mesh.n_active_elem();
// The maximum number of active elements to flag for coarsening
const unsigned int max_elem_coarsen =
static_cast<unsigned int>(_coarsen_fraction * n_active_elem) + 1;
// The maximum number of elements to flag for refinement
const unsigned int max_elem_refine =
static_cast<unsigned int>(_refine_fraction * n_active_elem) + 1;
// Clean up the refinement flags. These could be left
// over from previous refinement steps.
this->clean_refinement_flags();
// The target number of elements to add or remove
const int n_elem_new = _nelem_target - n_active_elem;
// Create an vector with active element errors and ids,
// sorted by highest errors first
const unsigned int max_elem_id = _mesh.max_elem_id();
std::vector<std::pair<float, unsigned int> > sorted_error;
sorted_error.reserve (n_active_elem);
// On a ParallelMesh, we need to communicate to know which remote ids
// correspond to active elements.
{
std::vector<bool> is_active(max_elem_id, false);
MeshBase::element_iterator elem_it = _mesh.active_local_elements_begin();
const MeshBase::element_iterator elem_end = _mesh.active_local_elements_end();
for (; elem_it != elem_end; ++elem_it)
{
const unsigned int eid = (*elem_it)->id();
is_active[eid] = true;
libmesh_assert_less (eid, error_per_cell.size());
sorted_error.push_back
(std::make_pair(error_per_cell[eid], eid));
}
CommWorld.max(is_active);
CommWorld.allgather(sorted_error);
}
// Default sort works since pairs are sorted lexicographically
std::sort (sorted_error.begin(), sorted_error.end());
std::reverse (sorted_error.begin(), sorted_error.end());
// Create a sorted error vector with coarsenable parent elements
// only, sorted by lowest errors first
ErrorVector error_per_parent;
std::vector<std::pair<float, unsigned int> > sorted_parent_error;
Real parent_error_min, parent_error_max;
create_parent_error_vector(error_per_cell,
error_per_parent,
parent_error_min,
parent_error_max);
// create_parent_error_vector sets values for non-parents and
// non-coarsenable parents to -1. Get rid of them.
for (unsigned int i=0; i != error_per_parent.size(); ++i)
if (error_per_parent[i] != -1)
sorted_parent_error.push_back(std::make_pair(error_per_parent[i], i));
std::sort (sorted_parent_error.begin(), sorted_parent_error.end());
// Keep track of how many elements we plan to coarsen & refine
unsigned int coarsen_count = 0;
unsigned int refine_count = 0;
const unsigned int dim = _mesh.mesh_dimension();
unsigned int twotodim = 1;
for (unsigned int i=0; i!=dim; ++i)
twotodim *= 2;
// First, let's try to get our element count to target_nelem
if (n_elem_new >= 0)
{
// Every element refinement creates at least
// 2^dim-1 new elements
refine_count =
std::min(static_cast<unsigned int>(n_elem_new / (twotodim-1)),
max_elem_refine);
}
else
{
// Every successful element coarsening is likely to destroy
// 2^dim-1 net elements.
coarsen_count =
std::min(static_cast<unsigned int>(-n_elem_new / (twotodim-1)),
max_elem_coarsen);
}
// Next, let's see if we can trade any refinement for coarsening
while (coarsen_count < max_elem_coarsen &&
refine_count < max_elem_refine &&
coarsen_count < sorted_parent_error.size() &&
refine_count < sorted_error.size() &&
sorted_error[refine_count].first >
sorted_parent_error[coarsen_count].first * _coarsen_threshold)
{
coarsen_count++;
refine_count++;
}
// On a ParallelMesh, we need to communicate to know which remote ids
// correspond to refinable elements
unsigned int successful_refine_count = 0;
{
std::vector<bool> is_refinable(max_elem_id, false);
for (unsigned int i=0; i != sorted_error.size(); ++i)
{
unsigned int eid = sorted_error[i].second;
Elem *elem = _mesh.query_elem(eid);
if (elem && elem->level() < _max_h_level)
is_refinable[eid] = true;
}
CommWorld.max(is_refinable);
if (refine_count > max_elem_refine)
refine_count = max_elem_refine;
for (unsigned int i=0; i != sorted_error.size(); ++i)
{
if (successful_refine_count >= refine_count)
break;
unsigned int eid = sorted_error[i].second;
Elem *elem = _mesh.query_elem(eid);
if (is_refinable[eid])
{
if (elem)
elem->set_refinement_flag(Elem::REFINE);
successful_refine_count++;
}
}
}
// If we couldn't refine enough elements, don't coarsen too many
// either
if (coarsen_count < (refine_count - successful_refine_count))
coarsen_count = 0;
else
coarsen_count -= (refine_count - successful_refine_count);
if (coarsen_count > max_elem_coarsen)
coarsen_count = max_elem_coarsen;
unsigned int successful_coarsen_count = 0;
if (coarsen_count)
{
for (unsigned int i=0; i != sorted_parent_error.size(); ++i)
{
if (successful_coarsen_count >= coarsen_count * twotodim)
break;
unsigned int parent_id = sorted_parent_error[i].second;
Elem *parent = _mesh.query_elem(parent_id);
// On a ParallelMesh we skip remote elements
if (!parent)
continue;
libmesh_assert(parent->has_children());
for (unsigned int c=0; c != parent->n_children(); ++c)
{
Elem *elem = parent->child(c);
if (elem && elem != remote_elem)
{
libmesh_assert(elem->active());
elem->set_refinement_flag(Elem::COARSEN);
successful_coarsen_count++;
}
}
}
}
// Return true if we've done all the AMR/C we can
if (!successful_coarsen_count &&
!successful_refine_count)
return true;
// And false if there may still be more to do.
return false;
}
Real ErrorVector::median() const
{
ErrorVector ev = (*this);
return ev.median();
}
// The main program.
int main (int argc, char** argv)
{
// Initialize libMesh.
LibMeshInit init (argc, argv);
// This example fails without at least double precision FP
#ifdef LIBMESH_DEFAULT_SINGLE_PRECISION
libmesh_example_assert(false, "--disable-singleprecision");
#endif
#ifndef LIBMESH_ENABLE_AMR
libmesh_example_assert(false, "--enable-amr");
#else
// Trilinos solver NaNs by default on the zero pressure block.
// We'll skip this example for now.
if (libMesh::default_solver_package() == TRILINOS_SOLVERS)
{
std::cout << "We skip fem_system_ex1 when using the Trilinos solvers.\n"
<< std::endl;
return 0;
}
// Parse the input file
GetPot infile("fem_system_ex1.in");
// Read in parameters from the input file
const Real global_tolerance = infile("global_tolerance", 0.);
const unsigned int nelem_target = infile("n_elements", 400);
const bool transient = infile("transient", true);
const Real deltat = infile("deltat", 0.005);
unsigned int n_timesteps = infile("n_timesteps", 20);
const unsigned int write_interval = infile("write_interval", 5);
const unsigned int coarsegridsize = infile("coarsegridsize", 1);
const unsigned int coarserefinements = infile("coarserefinements", 0);
const unsigned int max_adaptivesteps = infile("max_adaptivesteps", 10);
const unsigned int dim = infile("dimension", 2);
// Skip higher-dimensional examples on a lower-dimensional libMesh build
libmesh_example_assert(dim <= LIBMESH_DIM, "2D/3D support");
// We have only defined 2 and 3 dimensional problems
libmesh_assert (dim == 2 || dim == 3);
// Create a mesh.
Mesh mesh;
// And an object to refine it
MeshRefinement mesh_refinement(mesh);
mesh_refinement.coarsen_by_parents() = true;
mesh_refinement.absolute_global_tolerance() = global_tolerance;
mesh_refinement.nelem_target() = nelem_target;
mesh_refinement.refine_fraction() = 0.3;
mesh_refinement.coarsen_fraction() = 0.3;
mesh_refinement.coarsen_threshold() = 0.1;
// Use the MeshTools::Generation mesh generator to create a uniform
// grid on the square [-1,1]^D. We instruct the mesh generator
// to build a mesh of 8x8 \p Quad9 elements in 2D, or \p Hex27
// elements in 3D. Building these higher-order elements allows
// us to use higher-order approximation, as in example 3.
if (dim == 2)
MeshTools::Generation::build_square (mesh,
coarsegridsize,
coarsegridsize,
0., 1.,
0., 1.,
QUAD9);
else if (dim == 3)
MeshTools::Generation::build_cube (mesh,
coarsegridsize,
coarsegridsize,
coarsegridsize,
0., 1.,
0., 1.,
0., 1.,
HEX27);
mesh_refinement.uniformly_refine(coarserefinements);
// Print information about the mesh to the screen.
mesh.print_info();
// Create an equation systems object.
EquationSystems equation_systems (mesh);
// Declare the system "Navier-Stokes" and its variables.
NavierSystem & system =
equation_systems.add_system<NavierSystem> ("Navier-Stokes");
// Solve this as a time-dependent or steady system
if (transient)
system.time_solver =
AutoPtr<TimeSolver>(new EulerSolver(system));
else
{
system.time_solver =
AutoPtr<TimeSolver>(new SteadySolver(system));
libmesh_assert_equal_to (n_timesteps, 1);
}
// Initialize the system
equation_systems.init ();
// Set the time stepping options
system.deltat = deltat;
// And the nonlinear solver options
DiffSolver &solver = *(system.time_solver->diff_solver().get());
solver.quiet = infile("solver_quiet", true);
solver.verbose = !solver.quiet;
solver.max_nonlinear_iterations =
infile("max_nonlinear_iterations", 15);
solver.relative_step_tolerance =
infile("relative_step_tolerance", 1.e-3);
solver.relative_residual_tolerance =
infile("relative_residual_tolerance", 0.0);
solver.absolute_residual_tolerance =
infile("absolute_residual_tolerance", 0.0);
// And the linear solver options
solver.max_linear_iterations =
infile("max_linear_iterations", 50000);
solver.initial_linear_tolerance =
infile("initial_linear_tolerance", 1.e-3);
// Print information about the system to the screen.
equation_systems.print_info();
// Now we begin the timestep loop to compute the time-accurate
// solution of the equations.
for (unsigned int t_step=0; t_step != n_timesteps; ++t_step)
{
// A pretty update message
std::cout << "\n\nSolving time step " << t_step << ", time = "
<< system.time << std::endl;
// Adaptively solve the timestep
unsigned int a_step = 0;
for (; a_step != max_adaptivesteps; ++a_step)
{
system.solve();
system.postprocess();
ErrorVector error;
AutoPtr<ErrorEstimator> error_estimator;
// To solve to a tolerance in this problem we
// need a better estimator than Kelly
if (global_tolerance != 0.)
{
// We can't adapt to both a tolerance and a mesh
// size at once
libmesh_assert_equal_to (nelem_target, 0);
UniformRefinementEstimator *u =
new UniformRefinementEstimator;
// The lid-driven cavity problem isn't in H1, so
// lets estimate L2 error
u->error_norm = L2;
error_estimator.reset(u);
}
else
{
// If we aren't adapting to a tolerance we need a
// target mesh size
libmesh_assert_greater (nelem_target, 0);
// Kelly is a lousy estimator to use for a problem
// not in H1 - if we were doing more than a few
// timesteps we'd need to turn off or limit the
// maximum level of our adaptivity eventually
error_estimator.reset(new KellyErrorEstimator);
}
// Calculate error based on u and v (and w?) but not p
std::vector<Real> weights(2,1.0); // u, v
if (dim == 3)
weights.push_back(1.0); // w
weights.push_back(0.0); // p
// Keep the same default norm type.
std::vector<FEMNormType>
norms(1, error_estimator->error_norm.type(0));
error_estimator->error_norm = SystemNorm(norms, weights);
error_estimator->estimate_error(system, error);
// Print out status at each adaptive step.
Real global_error = error.l2_norm();
std::cout << "Adaptive step " << a_step << ": " << std::endl;
if (global_tolerance != 0.)
std::cout << "Global_error = " << global_error
<< std::endl;
if (global_tolerance != 0.)
std::cout << "Worst element error = " << error.maximum()
<< ", mean = " << error.mean() << std::endl;
if (global_tolerance != 0.)
{
// If we've reached our desired tolerance, we
// don't need any more adaptive steps
if (global_error < global_tolerance)
break;
mesh_refinement.flag_elements_by_error_tolerance(error);
}
else
{
// If flag_elements_by_nelem_target returns true, this
// should be our last adaptive step.
if (mesh_refinement.flag_elements_by_nelem_target(error))
{
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
a_step = max_adaptivesteps;
break;
}
}
// Carry out the adaptive mesh refinement/coarsening
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
std::cout << "Refined mesh to "
<< mesh.n_active_elem()
<< " active elements and "
<< equation_systems.n_active_dofs()
<< " active dofs." << std::endl;
}
// Do one last solve if necessary
if (a_step == max_adaptivesteps)
{
system.solve();
system.postprocess();
}
// Advance to the next timestep in a transient problem
system.time_solver->advance_timestep();
#ifdef LIBMESH_HAVE_EXODUS_API
// Write out this timestep if we're requested to
if ((t_step+1)%write_interval == 0)
{
std::ostringstream file_name;
// We write the file in the ExodusII format.
file_name << "out_"
<< std::setw(3)
<< std::setfill('0')
<< std::right
<< t_step+1
<< ".e";
ExodusII_IO(mesh).write_timestep(file_name.str(),
equation_systems,
1, /* This number indicates how many time steps
are being written to the file */
system.time);
}
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
}
#endif // #ifndef LIBMESH_ENABLE_AMR
// All done.
return 0;
}
// The main program.
int main (int argc, char ** argv)
{
// Initialize libMesh.
LibMeshInit init (argc, argv);
// This example requires a linear solver package.
libmesh_example_requires(libMesh::default_solver_package() != INVALID_SOLVER_PACKAGE,
"--enable-petsc, --enable-trilinos, or --enable-eigen");
#ifndef LIBMESH_ENABLE_AMR
libmesh_example_requires(false, "--enable-amr");
#else
// This doesn't converge with Eigen BICGSTAB for some reason...
libmesh_example_requires(libMesh::default_solver_package() != EIGEN_SOLVERS, "--enable-petsc");
// This doesn't converge without at least double precision
libmesh_example_requires(sizeof(Real) > 4, "--disable-singleprecision");
// Parse the input file
GetPot infile("fem_system_ex4.in");
// Read in parameters from the input file
const Real global_tolerance = infile("global_tolerance", 0.);
const unsigned int nelem_target = infile("n_elements", 400);
const Real deltat = infile("deltat", 0.005);
const unsigned int coarsegridsize = infile("coarsegridsize", 20);
const unsigned int coarserefinements = infile("coarserefinements", 0);
const unsigned int max_adaptivesteps = infile("max_adaptivesteps", 10);
const unsigned int dim = infile("dimension", 2);
// Skip higher-dimensional examples on a lower-dimensional libMesh build
libmesh_example_requires(dim <= LIBMESH_DIM, "2D/3D support");
// We have only defined 2 and 3 dimensional problems
libmesh_assert (dim == 2 || dim == 3);
// Create a mesh, with dimension to be overridden later, distributed
// across the default MPI communicator.
Mesh mesh(init.comm());
// And an object to refine it
MeshRefinement mesh_refinement(mesh);
mesh_refinement.coarsen_by_parents() = true;
mesh_refinement.absolute_global_tolerance() = global_tolerance;
mesh_refinement.nelem_target() = nelem_target;
mesh_refinement.refine_fraction() = 0.3;
mesh_refinement.coarsen_fraction() = 0.3;
mesh_refinement.coarsen_threshold() = 0.1;
// Use the MeshTools::Generation mesh generator to create a uniform
// grid on the square or cube. We crop the domain at y=2/3 to allow
// for a homogeneous Neumann BC in our benchmark there.
boundary_id_type bcid = 3; // +y in 3D
if (dim == 2)
{
MeshTools::Generation::build_square
(mesh,
coarsegridsize,
coarsegridsize*2/3, // int arithmetic best we can do here
0., 1.,
0., 2./3.,
QUAD9);
bcid = 2; // +y in 2D
}
else if (dim == 3)
{
MeshTools::Generation::build_cube
(mesh,
coarsegridsize,
coarsegridsize*2/3,
coarsegridsize,
0., 1.,
0., 2./3.,
0., 1.,
HEX27);
}
{
// Add boundary elements corresponding to the +y boundary of our
// volume mesh
std::set<boundary_id_type> bcids;
bcids.insert(bcid);
mesh.get_boundary_info().add_elements(bcids, mesh);
mesh.prepare_for_use();
}
// To work around ExodusII file format limitations, we need elements
// of different dimensionality to belong to different subdomains.
// Our interior elements defaulted to subdomain id 0, so we'll set
// boundary elements to subdomain 1.
for (auto & elem : mesh.element_ptr_range())
if (elem->dim() < dim)
elem->subdomain_id() = 1;
mesh_refinement.uniformly_refine(coarserefinements);
// Print information about the mesh to the screen.
mesh.print_info();
// Create an equation systems object.
EquationSystems equation_systems (mesh);
// Declare the system "Heat" and its variables.
HeatSystem & system =
equation_systems.add_system<HeatSystem> ("Heat");
// Solve this as a steady system
system.time_solver = libmesh_make_unique<SteadySolver>(system);
// Initialize the system
equation_systems.init ();
// Set the time stepping options
system.deltat = deltat;
// And the nonlinear solver options
DiffSolver & solver = *(system.time_solver->diff_solver().get());
solver.quiet = infile("solver_quiet", true);
solver.verbose = !solver.quiet;
solver.max_nonlinear_iterations = infile("max_nonlinear_iterations", 15);
solver.relative_step_tolerance = infile("relative_step_tolerance", 1.e-3);
solver.relative_residual_tolerance = infile("relative_residual_tolerance", 0.0);
solver.absolute_residual_tolerance = infile("absolute_residual_tolerance", 0.0);
// And the linear solver options
solver.max_linear_iterations = infile("max_linear_iterations", 50000);
solver.initial_linear_tolerance = infile("initial_linear_tolerance", 1.e-3);
// Print information about the system to the screen.
equation_systems.print_info();
// Adaptively solve the steady solution
unsigned int a_step = 0;
for (; a_step != max_adaptivesteps; ++a_step)
{
system.solve();
system.postprocess();
ErrorVector error;
std::unique_ptr<ErrorEstimator> error_estimator;
// To solve to a tolerance in this problem we
// need a better estimator than Kelly
if (global_tolerance != 0.)
{
// We can't adapt to both a tolerance and a mesh
// size at once
libmesh_assert_equal_to (nelem_target, 0);
UniformRefinementEstimator * u =
new UniformRefinementEstimator;
// The lid-driven cavity problem isn't in H1, so
// lets estimate L2 error
u->error_norm = L2;
error_estimator.reset(u);
}
else
{
// If we aren't adapting to a tolerance we need a
// target mesh size
libmesh_assert_greater (nelem_target, 0);
// Kelly is a lousy estimator to use for a problem
// not in H1 - if we were doing more than a few
// timesteps we'd need to turn off or limit the
// maximum level of our adaptivity eventually
error_estimator.reset(new KellyErrorEstimator);
}
error_estimator->estimate_error(system, error);
// Print out status at each adaptive step.
Real global_error = error.l2_norm();
libMesh::out << "Adaptive step "
<< a_step
<< ": "
<< std::endl;
if (global_tolerance != 0.)
libMesh::out << "Global_error = "
<< global_error
<< std::endl;
if (global_tolerance != 0.)
libMesh::out << "Worst element error = "
<< error.maximum()
<< ", mean = "
<< error.mean()
<< std::endl;
if (global_tolerance != 0.)
{
// If we've reached our desired tolerance, we
// don't need any more adaptive steps
if (global_error < global_tolerance)
break;
mesh_refinement.flag_elements_by_error_tolerance(error);
}
else
{
// If flag_elements_by_nelem_target returns true, this
// should be our last adaptive step.
if (mesh_refinement.flag_elements_by_nelem_target(error))
{
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
a_step = max_adaptivesteps;
break;
}
}
// Carry out the adaptive mesh refinement/coarsening
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
libMesh::out << "Refined mesh to "
<< mesh.n_active_elem()
<< " active elements and "
<< equation_systems.n_active_dofs()
<< " active dofs."
<< std::endl;
}
// Do one last solve if necessary
if (a_step == max_adaptivesteps)
{
system.solve();
system.postprocess();
}
#ifdef LIBMESH_HAVE_EXODUS_API
ExodusII_IO(mesh).write_equation_systems
("out.e", equation_systems);
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
#ifdef LIBMESH_HAVE_GMV
GMVIO(mesh).write_equation_systems
("out.gmv", equation_systems);
#endif // #ifdef LIBMESH_HAVE_GMV
#ifdef LIBMESH_HAVE_FPARSER
// Check that we got close to the analytic solution
ExactSolution exact_sol(equation_systems);
const std::string exact_str = (dim == 2) ?
"sin(pi*x)*sin(pi*y)" : "sin(pi*x)*sin(pi*y)*sin(pi*z)";
ParsedFunction<Number> exact_func(exact_str);
exact_sol.attach_exact_value(0, &exact_func);
exact_sol.compute_error("Heat", "T");
Number err = exact_sol.l2_error("Heat", "T");
// Print out the error value
libMesh::out << "L2-Error is: " << err << std::endl;
libmesh_assert_less(libmesh_real(err), 2e-3);
#endif // #ifdef LIBMESH_HAVE_FPARSER
#endif // #ifndef LIBMESH_ENABLE_AMR
// All done.
return 0;
}
int main(int argc, char** argv){
//initialize libMesh
LibMeshInit init(argc, argv);
//parameters
GetPot infile("fem_system_params.in");
const Real global_tolerance = infile("global_tolerance", 0.);
const unsigned int nelem_target = infile("n_elements", 400);
const bool transient = infile("transient", true);
const Real deltat = infile("deltat", 0.005);
unsigned int n_timesteps = infile("n_timesteps", 1);
//const unsigned int coarsegridsize = infile("coarsegridsize", 1);
const unsigned int coarserefinements = infile("coarserefinements", 0);
const unsigned int max_adaptivesteps = infile("max_adaptivesteps", 10);
const unsigned int dim = 2;
#ifdef LIBMESH_HAVE_EXODUS_API
const unsigned int write_interval = infile("write_interval", 5);
#endif
// Create a mesh, with dimension to be overridden later, distributed
// across the default MPI communicator.
Mesh mesh(init.comm());
GetPot infileForMesh("diff_convdiff_inv.in");
std::string find_mesh_here = infileForMesh("divided_mesh","meep.exo");
mesh.read(find_mesh_here);
// And an object to refine it
MeshRefinement mesh_refinement(mesh);
mesh_refinement.coarsen_by_parents() = true;
mesh_refinement.absolute_global_tolerance() = global_tolerance;
mesh_refinement.nelem_target() = nelem_target;
mesh_refinement.refine_fraction() = 0.3;
mesh_refinement.coarsen_fraction() = 0.3;
mesh_refinement.coarsen_threshold() = 0.1;
mesh_refinement.uniformly_refine(coarserefinements);
// Print information about the mesh to the screen.
mesh.print_info();
// Create an equation systems object.
EquationSystems equation_systems (mesh);
//name system
Diff_ConvDiff_InvSys & system =
equation_systems.add_system<Diff_ConvDiff_InvSys>("Diff_ConvDiff_InvSys");
//steady-state problem
system.time_solver =
AutoPtr<TimeSolver>(new SteadySolver(system));
libmesh_assert_equal_to (n_timesteps, 1);
std::string linearizeHere = "invHF.xda";
equation_systems.read(linearizeHere, READ,
EquationSystems::READ_HEADER |
EquationSystems::READ_DATA |
EquationSystems::READ_ADDITIONAL_DATA);
std::cout << "\n READING IN INITIAL GUESS" << std::endl;
// Initialize the system
//equation_systems.init ();
// Set the time stepping options
system.deltat = deltat; //this is ignored for SteadySolver...right?
// And the nonlinear solver options
NewtonSolver *solver = new NewtonSolver(system);
system.time_solver->diff_solver() = AutoPtr<DiffSolver>(solver);
solver->quiet = infile("solver_quiet", true);
solver->verbose = !solver->quiet;
solver->max_nonlinear_iterations =
infile("max_nonlinear_iterations", 15);
solver->relative_step_tolerance =
infile("relative_step_tolerance", 1.e-3);
solver->relative_residual_tolerance =
infile("relative_residual_tolerance", 0.0);
solver->absolute_residual_tolerance =
infile("absolute_residual_tolerance", 0.0);
// And the linear solver options
solver->max_linear_iterations =
infile("max_linear_iterations", 50000);
solver->initial_linear_tolerance =
infile("initial_linear_tolerance", 1.e-3);
// Print information about the system to the screen.
equation_systems.print_info();
// Now we begin the timestep loop to compute the time-accurate
// solution of the equations...not that this is transient, but eh, why not...
for (unsigned int t_step=0; t_step != n_timesteps; ++t_step){
// A pretty update message
std::cout << "\n\nSolving time step " << t_step << ", time = "
<< system.time << std::endl;
// Adaptively solve the timestep
unsigned int a_step = 0;
for (; a_step != max_adaptivesteps; ++a_step)
{
system.solve();
system.postprocess();
ErrorVector error;
AutoPtr<ErrorEstimator> error_estimator;
// To solve to a tolerance in this problem we
// need a better estimator than Kelly
if (global_tolerance != 0.)
{
// We can't adapt to both a tolerance and a mesh
// size at once
libmesh_assert_equal_to (nelem_target, 0);
UniformRefinementEstimator *u =
new UniformRefinementEstimator;
// The lid-driven cavity problem isn't in H1, so
// lets estimate L2 error
u->error_norm = L2;
error_estimator.reset(u);
}
else
{
// If we aren't adapting to a tolerance we need a
// target mesh size
libmesh_assert_greater (nelem_target, 0);
// Kelly is a lousy estimator to use for a problem
// not in H1 - if we were doing more than a few
// timesteps we'd need to turn off or limit the
// maximum level of our adaptivity eventually
error_estimator.reset(new KellyErrorEstimator);
}
// Calculate error
std::vector<Real> weights(3,1.0);
// Keep the same default norm type.
std::vector<FEMNormType>
norms(1, error_estimator->error_norm.type(0));
error_estimator->error_norm = SystemNorm(norms, weights);
error_estimator->estimate_error(system, error);
// Print out status at each adaptive step.
Real global_error = error.l2_norm();
std::cout << "Adaptive step " << a_step << ": " << std::endl;
if (global_tolerance != 0.)
std::cout << "Global_error = " << global_error
<< std::endl;
if (global_tolerance != 0.)
std::cout << "Worst element error = " << error.maximum()
<< ", mean = " << error.mean() << std::endl;
if (global_tolerance != 0.)
{
// If we've reached our desired tolerance, we
// don't need any more adaptive steps
if (global_error < global_tolerance)
break;
mesh_refinement.flag_elements_by_error_tolerance(error);
}
else
{
// If flag_elements_by_nelem_target returns true, this
// should be our last adaptive step.
if (mesh_refinement.flag_elements_by_nelem_target(error))
{
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
a_step = max_adaptivesteps;
break;
}
}
// Carry out the adaptive mesh refinement/coarsening
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
std::cout << "Refined mesh to "
<< mesh.n_active_elem()
<< " active elements and "
<< equation_systems.n_active_dofs()
<< " active dofs." << std::endl;
}
// Do one last solve if necessary
if (a_step == max_adaptivesteps)
{
using std::chrono::duration_cast;
using std::chrono::milliseconds;
typedef std::chrono::high_resolution_clock clock;
auto start = clock::now();
system.solve();
auto end = clock::now();
std::cout << "\n Solve took " << duration_cast<milliseconds>(end-start).count() << " ms\n" << std::endl;
system.postprocess();
Number QoI_computed = system.get_QoI_value("computed", 0);
std::cout<< "Computed QoI is " << std::setprecision(17) << QoI_computed << std::endl;
}
// Advance to the next timestep in a transient problem
system.time_solver->advance_timestep();
#ifdef LIBMESH_HAVE_EXODUS_API
// Write out this timestep if we're requested to
if ((t_step+1)%write_interval == 0)
{
std::ostringstream file_name;
// We write the file in the ExodusII format.
file_name << "out_"
<< std::setw(3)
<< std::setfill('0')
<< std::right
<< t_step+1
<< ".e";
ExodusII_IO(mesh).write_timestep(file_name.str(),
equation_systems,
1, /* This number indicates how many time steps
are being written to the file */
system.time);
equation_systems.write("invHF.xda", WRITE, EquationSystems::WRITE_DATA |
EquationSystems::WRITE_ADDITIONAL_DATA);
}
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
}
// All done.
return 0;
} //end main
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 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 assemble_and_solve(MeshBase & mesh,
EquationSystems & equation_systems)
{
mesh.print_info();
LinearImplicitSystem & system =
equation_systems.add_system<LinearImplicitSystem> ("Poisson");
unsigned int u_var = system.add_variable("u", FIRST, LAGRANGE);
system.attach_assemble_function (assemble_poisson);
// the cube has boundaries IDs 0, 1, 2, 3, 4 and 5
std::set<boundary_id_type> boundary_ids;
for (int j = 0; j<6; ++j)
boundary_ids.insert(j);
// Create a vector storing the variable numbers which the BC applies to
std::vector<unsigned int> variables(1);
variables[0] = u_var;
ZeroFunction<> zf;
DirichletBoundary dirichlet_bc(boundary_ids,
variables,
&zf);
system.get_dof_map().add_dirichlet_boundary(dirichlet_bc);
equation_systems.init();
equation_systems.print_info();
#ifdef LIBMESH_ENABLE_AMR
MeshRefinement mesh_refinement(mesh);
mesh_refinement.refine_fraction() = 0.7;
mesh_refinement.coarsen_fraction() = 0.3;
mesh_refinement.max_h_level() = 5;
const unsigned int max_r_steps = 2;
for (unsigned int r_step=0; r_step<=max_r_steps; r_step++)
{
system.solve();
if (r_step != max_r_steps)
{
ErrorVector error;
KellyErrorEstimator error_estimator;
error_estimator.estimate_error(system, error);
libMesh::out << "Error estimate\nl2 norm = "
<< error.l2_norm()
<< "\nmaximum = "
<< error.maximum()
<< std::endl;
mesh_refinement.flag_elements_by_error_fraction (error);
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
}
}
#else
system.solve();
#endif
}
int main(int argc, char** argv)
{
// Initialize the library. This is necessary because the library
// may depend on a number of other libraries (i.e. MPI and PETSc)
// that require initialization before use. When the LibMeshInit
// object goes out of scope, other libraries and resources are
// finalized.
LibMeshInit init (argc, argv);
// Skip adaptive examples on a non-adaptive libMesh build
#ifndef LIBMESH_ENABLE_AMR
libmesh_example_requires(false, "--enable-amr");
#else
// Create a mesh, with dimension to be overridden later, on the
// default MPI communicator.
Mesh mesh(init.comm());
GetPot command_line (argc, argv);
int n = 4;
if ( command_line.search(1, "-n") )
n = command_line.next(n);
// Build a 1D mesh with 4 elements from x=0 to x=1, using
// EDGE3 (i.e. quadratic) 1D elements. They are called EDGE3 elements
// because a quadratic element contains 3 nodes.
MeshTools::Generation::build_line(mesh,n,0.,1.,EDGE3);
// Define the equation systems object and the system we are going
// to solve. See Introduction Example 2 for more details.
EquationSystems equation_systems(mesh);
LinearImplicitSystem& system = equation_systems.add_system
<LinearImplicitSystem>("1D");
// Add a variable "u" to the system, using second-order approximation
system.add_variable("u",SECOND);
// Give the system a pointer to the matrix assembly function. This
// will be called when needed by the library.
system.attach_assemble_function(assemble_1D);
// Define the mesh refinement object that takes care of adaptively
// refining the mesh.
MeshRefinement mesh_refinement(mesh);
// These parameters determine the proportion of elements that will
// be refined and coarsened. Any element within 30% of the maximum
// error on any element will be refined, and any element within 30%
// of the minimum error on any element might be coarsened
mesh_refinement.refine_fraction() = 0.7;
mesh_refinement.coarsen_fraction() = 0.3;
// We won't refine any element more than 5 times in total
mesh_refinement.max_h_level() = 5;
// Initialize the data structures for the equation system.
equation_systems.init();
// Refinement parameters
const unsigned int max_r_steps = 5; // Refine the mesh 5 times
// Define the refinement loop
for(unsigned int r_step=0; r_step<=max_r_steps; r_step++)
{
// Solve the equation system
equation_systems.get_system("1D").solve();
// We need to ensure that the mesh is not refined on the last iteration
// of this loop, since we do not want to refine the mesh unless we are
// going to solve the equation system for that refined mesh.
if(r_step != max_r_steps)
{
// Error estimation objects, see Adaptivity Example 2 for details
ErrorVector error;
KellyErrorEstimator error_estimator;
// Compute the error for each active element
error_estimator.estimate_error(system, error);
// Output error estimate magnitude
libMesh::out << "Error estimate\nl2 norm = " << error.l2_norm() <<
"\nmaximum = " << error.maximum() << std::endl;
// Flag elements to be refined and coarsened
mesh_refinement.flag_elements_by_error_fraction (error);
// Perform refinement and coarsening
mesh_refinement.refine_and_coarsen_elements();
// Reinitialize the equation_systems object for the newly refined
// mesh. One of the steps in this is project the solution onto the
// new mesh
equation_systems.reinit();
}
}
// Construct gnuplot plotting object, pass in mesh, title of plot
// and boolean to indicate use of grid in plot. The grid is used to
// show the edges of each element in the mesh.
GnuPlotIO plot(mesh,"Adaptivity Example 1", GnuPlotIO::GRID_ON);
// Write out script to be called from within gnuplot:
// Load gnuplot, then type "call 'gnuplot_script'" from gnuplot prompt
plot.write_equation_systems("gnuplot_script",equation_systems);
#endif // #ifndef LIBMESH_ENABLE_AMR
// All done. libMesh objects are destroyed here. Because the
// LibMeshInit object was created first, its destruction occurs
// last, and it's destructor finalizes any external libraries and
// checks for leaked memory.
return 0;
}
int main(int argc, char** argv)
{
// Initialize libMesh.
LibMeshInit init (argc, argv);
// Skip adaptive examples on a non-adaptive libMesh build
#ifndef LIBMESH_ENABLE_AMR
libmesh_example_assert(false, "--enable-amr");
#else
// Parse the input file
GetPot input_file("adaptivity_ex3.in");
// Read in parameters from the input file
const unsigned int max_r_steps = input_file("max_r_steps", 3);
const unsigned int max_r_level = input_file("max_r_level", 3);
const Real refine_percentage = input_file("refine_percentage", 0.5);
const Real coarsen_percentage = input_file("coarsen_percentage", 0.5);
const unsigned int uniform_refine = input_file("uniform_refine",0);
const std::string refine_type = input_file("refinement_type", "h");
const std::string approx_type = input_file("approx_type", "LAGRANGE");
const unsigned int approx_order = input_file("approx_order", 1);
const std::string element_type = input_file("element_type", "tensor");
const int extra_error_quadrature = input_file("extra_error_quadrature", 0);
const int max_linear_iterations = input_file("max_linear_iterations", 5000);
const bool output_intermediate = input_file("output_intermediate", false);
dim = input_file("dimension", 2);
const std::string indicator_type = input_file("indicator_type", "kelly");
singularity = input_file("singularity", true);
// Skip higher-dimensional examples on a lower-dimensional libMesh build
libmesh_example_assert(dim <= LIBMESH_DIM, "2D/3D support");
// Output file for plotting the error as a function of
// the number of degrees of freedom.
std::string approx_name = "";
if (element_type == "tensor")
approx_name += "bi";
if (approx_order == 1)
approx_name += "linear";
else if (approx_order == 2)
approx_name += "quadratic";
else if (approx_order == 3)
approx_name += "cubic";
else if (approx_order == 4)
approx_name += "quartic";
std::string output_file = approx_name;
output_file += "_";
output_file += refine_type;
if (uniform_refine == 0)
output_file += "_adaptive.m";
else
output_file += "_uniform.m";
std::ofstream out (output_file.c_str());
out << "% dofs L2-error H1-error" << std::endl;
out << "e = [" << std::endl;
// Create a mesh.
Mesh mesh;
// Read in the mesh
if (dim == 1)
MeshTools::Generation::build_line(mesh,1,-1.,0.);
else if (dim == 2)
mesh.read("lshaped.xda");
else
mesh.read("lshaped3D.xda");
// Use triangles if the config file says so
if (element_type == "simplex")
MeshTools::Modification::all_tri(mesh);
// We used first order elements to describe the geometry,
// but we may need second order elements to hold the degrees
// of freedom
if (approx_order > 1 || refine_type != "h")
mesh.all_second_order();
// Mesh Refinement object
MeshRefinement mesh_refinement(mesh);
mesh_refinement.refine_fraction() = refine_percentage;
mesh_refinement.coarsen_fraction() = coarsen_percentage;
mesh_refinement.max_h_level() = max_r_level;
// Create an equation systems object.
EquationSystems equation_systems (mesh);
// Declare the system and its variables.
// Creates a system named "Laplace"
LinearImplicitSystem& system =
equation_systems.add_system<LinearImplicitSystem> ("Laplace");
// Adds the variable "u" to "Laplace", using
// the finite element type and order specified
// in the config file
system.add_variable("u", static_cast<Order>(approx_order),
Utility::string_to_enum<FEFamily>(approx_type));
// Give the system a pointer to the matrix assembly
// function.
system.attach_assemble_function (assemble_laplace);
// Initialize the data structures for the equation system.
equation_systems.init();
// Set linear solver max iterations
equation_systems.parameters.set<unsigned int>("linear solver maximum iterations")
= max_linear_iterations;
// Linear solver tolerance.
equation_systems.parameters.set<Real>("linear solver tolerance") =
std::pow(TOLERANCE, 2.5);
// Prints information about the system to the screen.
equation_systems.print_info();
// Construct ExactSolution object and attach solution functions
ExactSolution exact_sol(equation_systems);
exact_sol.attach_exact_value(exact_solution);
exact_sol.attach_exact_deriv(exact_derivative);
// Use higher quadrature order for more accurate error results
exact_sol.extra_quadrature_order(extra_error_quadrature);
// A refinement loop.
for (unsigned int r_step=0; r_step<max_r_steps; r_step++)
{
std::cout << "Beginning Solve " << r_step << std::endl;
// Solve the system "Laplace", just like example 2.
system.solve();
std::cout << "System has: " << equation_systems.n_active_dofs()
<< " degrees of freedom."
<< std::endl;
std::cout << "Linear solver converged at step: "
<< system.n_linear_iterations()
<< ", final residual: "
<< system.final_linear_residual()
<< std::endl;
#ifdef LIBMESH_HAVE_EXODUS_API
// After solving the system write the solution
// to a ExodusII-formatted plot file.
if (output_intermediate)
{
OStringStream outfile;
outfile << "lshaped_" << r_step << ".e";
ExodusII_IO (mesh).write_equation_systems (outfile.str(),
equation_systems);
}
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
// Compute the error.
exact_sol.compute_error("Laplace", "u");
// Print out the error values
std::cout << "L2-Error is: "
<< exact_sol.l2_error("Laplace", "u")
<< std::endl;
std::cout << "H1-Error is: "
<< exact_sol.h1_error("Laplace", "u")
<< std::endl;
// Print to output file
out << equation_systems.n_active_dofs() << " "
<< exact_sol.l2_error("Laplace", "u") << " "
<< exact_sol.h1_error("Laplace", "u") << std::endl;
// Possibly refine the mesh
if (r_step+1 != max_r_steps)
{
std::cout << " Refining the mesh..." << std::endl;
if (uniform_refine == 0)
{
// The \p ErrorVector is a particular \p StatisticsVector
// for computing error information on a finite element mesh.
ErrorVector error;
if (indicator_type == "exact")
{
// The \p ErrorEstimator class interrogates a
// finite element solution and assigns to each
// element a positive error value.
// This value is used for deciding which elements to
// refine and which to coarsen.
// For these simple test problems, we can use
// numerical quadrature of the exact error between
// the approximate and analytic solutions.
// However, for real problems, we would need an error
// indicator which only relies on the approximate
// solution.
ExactErrorEstimator error_estimator;
error_estimator.attach_exact_value(exact_solution);
error_estimator.attach_exact_deriv(exact_derivative);
// We optimize in H1 norm, the default
// error_estimator.error_norm = H1;
// Compute the error for each active element using
// the provided indicator. Note in general you
// will need to provide an error estimator
// specifically designed for your application.
error_estimator.estimate_error (system, error);
}
else if (indicator_type == "patch")
{
// The patch recovery estimator should give a
// good estimate of the solution interpolation
// error.
PatchRecoveryErrorEstimator error_estimator;
error_estimator.estimate_error (system, error);
}
else if (indicator_type == "uniform")
{
// Error indication based on uniform refinement
// is reliable, but very expensive.
UniformRefinementEstimator error_estimator;
error_estimator.estimate_error (system, error);
}
else
{
libmesh_assert_equal_to (indicator_type, "kelly");
// The Kelly error estimator is based on
// an error bound for the Poisson problem
// on linear elements, but is useful for
// driving adaptive refinement in many problems
KellyErrorEstimator error_estimator;
error_estimator.estimate_error (system, error);
}
// Write out the error distribution
OStringStream ss;
ss << r_step;
#ifdef LIBMESH_HAVE_EXODUS_API
std::string error_output = "error_"+ss.str()+".e";
#else
std::string error_output = "error_"+ss.str()+".gmv";
#endif
error.plot_error( error_output, mesh );
// This takes the error in \p error and decides which elements
// will be coarsened or refined. Any element within 20% of the
// maximum error on any element will be refined, and any
// element within 10% of the minimum error on any element might
// be coarsened. Note that the elements flagged for refinement
// will be refined, but those flagged for coarsening _might_ be
// coarsened.
mesh_refinement.flag_elements_by_error_fraction (error);
// If we are doing adaptive p refinement, we want
// elements flagged for that instead.
if (refine_type == "p")
mesh_refinement.switch_h_to_p_refinement();
// If we are doing "matched hp" refinement, we
// flag elements for both h and p
if (refine_type == "matchedhp")
mesh_refinement.add_p_to_h_refinement();
// If we are doing hp refinement, we
// try switching some elements from h to p
if (refine_type == "hp")
{
HPCoarsenTest hpselector;
hpselector.select_refinement(system);
}
// If we are doing "singular hp" refinement, we
// try switching most elements from h to p
if (refine_type == "singularhp")
{
// This only differs from p refinement for
// the singular problem
libmesh_assert (singularity);
HPSingularity hpselector;
// Our only singular point is at the origin
hpselector.singular_points.push_back(Point());
hpselector.select_refinement(system);
}
// This call actually refines and coarsens the flagged
// elements.
mesh_refinement.refine_and_coarsen_elements();
}
else if (uniform_refine == 1)
{
if (refine_type == "h" || refine_type == "hp" ||
refine_type == "matchedhp")
mesh_refinement.uniformly_refine(1);
if (refine_type == "p" || refine_type == "hp" ||
refine_type == "matchedhp")
mesh_refinement.uniformly_p_refine(1);
}
// This call reinitializes the \p EquationSystems object for
// the newly refined mesh. One of the steps in the
// reinitialization is projecting the \p solution,
// \p old_solution, etc... vectors from the old mesh to
// the current one.
equation_systems.reinit ();
}
}
#ifdef LIBMESH_HAVE_EXODUS_API
// Write out the solution
// After solving the system write the solution
// to a ExodusII-formatted plot file.
ExodusII_IO (mesh).write_equation_systems ("lshaped.e",
equation_systems);
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
// Close up the output file.
out << "];" << std::endl;
out << "hold on" << std::endl;
out << "plot(e(:,1), e(:,2), 'bo-');" << std::endl;
out << "plot(e(:,1), e(:,3), 'ro-');" << std::endl;
// out << "set(gca,'XScale', 'Log');" << std::endl;
// out << "set(gca,'YScale', 'Log');" << std::endl;
out << "xlabel('dofs');" << std::endl;
out << "title('" << approx_name << " elements');" << std::endl;
out << "legend('L2-error', 'H1-error');" << std::endl;
// out << "disp('L2-error linear fit');" << std::endl;
// out << "polyfit(log10(e(:,1)), log10(e(:,2)), 1)" << std::endl;
// out << "disp('H1-error linear fit');" << std::endl;
// out << "polyfit(log10(e(:,1)), log10(e(:,3)), 1)" << std::endl;
#endif // #ifndef LIBMESH_ENABLE_AMR
// All done.
return 0;
}