Hermes::vector<Space<Scalar>*> CalculationContinuity<Scalar>::Record::load_spaces(Hermes::vector<Mesh*> meshes, Hermes::vector<Shapeset*> shapesets)
{
Hermes::vector<Space<Scalar>*> spaces;
if(shapesets == Hermes::vector<Shapeset*>())
for(unsigned int i = 0; i < meshes.size(); i++)
shapesets.push_back(NULL);
for(unsigned int i = 0; i < meshes.size(); i++)
{
std::stringstream filename;
filename << CalculationContinuity<Scalar>::space_file_name << i << '_' << (std::string)"t = " << this->time << (std::string)"n = " << this->number << (std::string)".h2d";
try
{
spaces.push_back(Space<Scalar>::load(filename.str().c_str(), meshes[i], false, NULL, shapesets[i]));
}
catch(Hermes::Exceptions::SpaceLoadFailureException& e)
{
throw IOCalculationContinuityException(CalculationContinuityException::spaces, IOCalculationContinuityException::input, filename.str().c_str(), e.what());
}
catch(std::exception& e)
{
throw IOCalculationContinuityException(CalculationContinuityException::spaces, IOCalculationContinuityException::input, filename.str().c_str(), e.what());
}
}
}
Adapt<Scalar>::Adapt(Hermes::vector<Space<Scalar>*> spaces,
Hermes::vector<ProjNormType> proj_norms) :
spaces(spaces),
num_act_elems(-1),
have_errors(false),
have_coarse_solutions(false),
have_reference_solutions(false)
{
// sanity check
if (proj_norms.size() > 0 && spaces.size() != proj_norms.size())
error("Mismatched numbers of spaces and projection types in Adapt<Scalar>::Adapt().");
this->num = spaces.size();
// sanity checks
error_if(this->num <= 0, "Too few components (%d), only %d supported.", this->num, H2D_MAX_COMPONENTS);
error_if(this->num > H2D_MAX_COMPONENTS, "Too many components (%d), only %d supported.", this->num, H2D_MAX_COMPONENTS);
// reset values
memset(errors, 0, sizeof(errors));
memset(sln, 0, sizeof(sln));
memset(rsln, 0, sizeof(rsln));
// if norms were not set by the user, set them to defaults
// according to spaces
if (proj_norms.size() == 0)
{
for (int i = 0; i < this->num; i++)
{
switch (spaces[i]->get_type())
{
case HERMES_H1_SPACE: proj_norms.push_back(HERMES_H1_NORM); break;
case HERMES_HCURL_SPACE: proj_norms.push_back(HERMES_HCURL_NORM); break;
case HERMES_HDIV_SPACE: proj_norms.push_back(HERMES_HDIV_NORM); break;
case HERMES_L2_SPACE: proj_norms.push_back(HERMES_L2_NORM); break;
default: error("Unknown space type in Adapt<Scalar>::Adapt().");
}
}
}
// assign norm weak forms according to norms selection
for (int i = 0; i < this->num; i++)
for (int j = 0; j < this->num; j++)
{
error_form[i][j] = NULL;
norm_form[i][j] = NULL;
}
for (int i = 0; i < this->num; i++)
{
error_form[i][i] = new MatrixFormVolError(proj_norms[i]);
norm_form[i][i] = error_form[i][i];
}
}
MeshFunction<double>* FilterVectorPotential::clone()
{
Hermes::vector<MeshFunction<double>*> fns;
Hermes::vector<int> items;
for(int i = 0; i < this->num; i++)
{
fns.push_back(this->sln[i]->clone());
items.push_back(item[i]);
}
return new FilterVectorPotential(fns, items);
}
// Set Dirichlet boundary values.
void ModuleBasic::set_dirichlet_values(const std::vector<int> &bdy_markers_dirichlet,
const std::vector<double> &bdy_values_dirichlet)
{
Hermes::vector<int> tm;
for (unsigned int i = 0; i < bdy_markers_dirichlet.size(); i++) {
tm.push_back(bdy_markers_dirichlet[i]);
}
Hermes::vector<double> tv;
for (unsigned int i = 0; i < bdy_values_dirichlet.size(); i++) {
tv.push_back(bdy_values_dirichlet[i]);
}
if (tm.size() != tv.size()) error("Mismatched numbers of Dirichlet boundary markers and values.");
for (unsigned int i = 0; i < tm.size(); i++) this->bc_values.add_const(tm[i], tv[i]);
}
void SimpleFilter::precalculate(int order, int mask)
{
if (mask & (H2D_FN_DX | H2D_FN_DY | H2D_FN_DXX | H2D_FN_DYY | H2D_FN_DXY))
error("Filter not defined for derivatives.");
Quad2D* quad = quads[cur_quad];
int np = quad->get_num_points(order);
Node* node = new_node(H2D_FN_VAL, np);
// precalculate all solutions
for (int i = 0; i < num; i++)
sln[i]->set_quad_order(order, item[i]);
for (int j = 0; j < num_components; j++)
{
// obtain corresponding tables
scalar* tab[10];
for (int i = 0; i < num; i++)
{
int a = 0, b = 0, mask = item[i];
if (mask >= 0x40) { a = 1; mask >>= 6; }
while (!(mask & 1)) { mask >>= 1; b++; }
tab[i] = sln[i]->get_values(num_components == 1 ? a : j, b);
if (tab[i] == NULL) error("Value of 'item%d' is incorrect in filter definition.", i+1);
}
Hermes::vector<scalar*> values;
for(int i = 0; i < this->num; i++)
values.push_back(tab[i]);
// apply the filter
filter_fn(np, values, node->values[j][0]);
}
MeshFunction<double>* FilterFluxDensity::clone()
{
Hermes::vector<MeshFunction<double>*> fns;
for(int i = 0; i < this->num; i++)
fns.push_back(this->sln[i]->clone());
return new FilterFluxDensity(fns);
}
void SimpleFilter<Scalar>::precalculate(int order, int mask)
{
if(mask & (H2D_FN_DX | H2D_FN_DY | H2D_FN_DXX | H2D_FN_DYY | H2D_FN_DXY))
throw Hermes::Exceptions::Exception("Filter not defined for derivatives.");
Quad2D* quad = this->quads[this->cur_quad];
int np = quad->get_num_points(order, this->element->get_mode());
struct Function<Scalar>::Node* node = this->new_node(H2D_FN_VAL, np);
// precalculate all solutions
for (int i = 0; i < this->num; i++)
this->sln[i]->set_quad_order(order, item[i]);
for (int j = 0; j < this->num_components; j++)
{
// obtain corresponding tables
Scalar* tab[H2D_MAX_COMPONENTS];
for (int i = 0; i < this->num; i++)
{
int a = 0, b = 0, mask = item[i];
if(mask >= 0x40) { a = 1; mask >>= 6; }
while (!(mask & 1)) { mask >>= 1; b++; }
tab[i] = this->sln[i]->get_values(this->num_components == 1 ? a : j, b);
if(tab[i] == nullptr) throw Hermes::Exceptions::Exception("Value of 'item%d' is incorrect in filter definition.", i + 1);
}
Hermes::vector<Scalar*> values;
for(int i = 0; i < this->num; i++)
values.push_back(tab[i]);
// apply the filter
filter_fn(np, values, node->values[j][0]);
}
void Continuity<Scalar>::Record::load_spaces(Hermes::vector<Space<Scalar>*> spaces, Hermes::vector<SpaceType> space_types, Hermes::vector<Mesh*> meshes, Hermes::vector<Shapeset*> shapesets)
{
if(shapesets == Hermes::vector<Shapeset*>())
for(unsigned int i = 0; i < spaces.size(); i++)
shapesets.push_back(NULL);
for(unsigned int i = 0; i < spaces.size(); i++)
{
std::stringstream filename;
filename << Continuity<Scalar>::spaceFileName << i << '_' << (std::string)"t = " << this->time << (std::string)"n = " << this->number << (std::string)".h2d";
spaces[i]->free();
switch(space_types[i])
{
case HERMES_H1_SPACE:
dynamic_cast<H1Space<Scalar>*>(spaces[i])->load(filename.str().c_str(), meshes[i], shapesets[i]);
break;
case HERMES_HCURL_SPACE:
dynamic_cast<HcurlSpace<Scalar>*>(spaces[i])->load(filename.str().c_str(), meshes[i], shapesets[i]);
break;
case HERMES_HDIV_SPACE:
dynamic_cast<HdivSpace<Scalar>*>(spaces[i])->load(filename.str().c_str(), meshes[i], shapesets[i]);
break;
case HERMES_L2_SPACE:
dynamic_cast<L2Space<Scalar>*>(spaces[i])->load(filename.str().c_str(), meshes[i], shapesets[i]);
break;
}
}
}
// Set material markers, and check compatibility with mesh file.
void ModuleBasic::set_material_markers(const std::vector<int> &m_markers)
{
this->mat_markers = m_markers;
// FIXME: these global arrays need to be removed.
for (unsigned int i = 0; i < m_markers.size(); i++) {
_global_mat_markers.push_back(m_markers[i]);;
}
}
// Set Dirichlet boundary markers.
void ModuleBasic::set_dirichlet_markers(const std::vector<int> &bdy_markers_dirichlet)
{
//this->bdy_markers_dirichlet = bdy_markers_dirichlet;
Hermes::vector<int> t;
for (unsigned int i = 0; i < bdy_markers_dirichlet.size(); i++) {
t.push_back(bdy_markers_dirichlet[i]);
}
this->bc_types.add_bc_dirichlet(t);
}
// Set Newton boundary markers.
void ModuleBasic::set_newton_markers(const std::vector<int> &bdy_markers_newton)
{
this->bdy_markers_newton = bdy_markers_newton;
Hermes::vector<int> t;
for (unsigned int i = 0; i < bdy_markers_newton.size(); i++) {
t.push_back(bdy_markers_newton[i]);
}
this->bc_types.add_bc_newton(t);
}
void WeakForm<Scalar>::cloneMembers(const WeakForm<Scalar>* otherWf)
{
this->mfvol.clear();
this->mfsurf.clear();
this->mfDG.clear();
this->vfvol.clear();
this->vfsurf.clear();
this->vfDG.clear();
this->forms.clear();
this->ext.clear();
for(unsigned int i = 0; i < otherWf->forms.size(); i++)
{
if(dynamic_cast<MatrixFormVol<Scalar>*>(otherWf->forms[i]) != NULL)
this->forms.push_back((dynamic_cast<MatrixFormVol<Scalar>*>(otherWf->forms[i]))->clone());
if(dynamic_cast<MatrixFormSurf<Scalar>*>(otherWf->forms[i]) != NULL)
this->forms.push_back((dynamic_cast<MatrixFormSurf<Scalar>*>(otherWf->forms[i]))->clone());
if(dynamic_cast<MatrixFormDG<Scalar>*>(otherWf->forms[i]) != NULL)
this->forms.push_back((dynamic_cast<MatrixFormDG<Scalar>*>(otherWf->forms[i]))->clone());
if(dynamic_cast<VectorFormVol<Scalar>*>(otherWf->forms[i]) != NULL)
this->forms.push_back((dynamic_cast<VectorFormVol<Scalar>*>(otherWf->forms[i]))->clone());
if(dynamic_cast<VectorFormSurf<Scalar>*>(otherWf->forms[i]) != NULL)
this->forms.push_back((dynamic_cast<VectorFormSurf<Scalar>*>(otherWf->forms[i]))->clone());
if(dynamic_cast<VectorFormDG<Scalar>*>(otherWf->forms[i]) != NULL)
this->forms.push_back((dynamic_cast<VectorFormDG<Scalar>*>(otherWf->forms[i]))->clone());
Hermes::vector<MeshFunction<Scalar>*> newExt;
for(unsigned int ext_i = 0; ext_i < otherWf->forms[i]->ext.size(); ext_i++)
newExt.push_back(otherWf->forms[i]->ext[ext_i]->clone());
this->forms.back()->set_ext(newExt);
this->forms.back()->wf = this;
if(dynamic_cast<MatrixFormVol<Scalar>*>(otherWf->forms[i]) != NULL)
this->mfvol.push_back(dynamic_cast<MatrixFormVol<Scalar>*>(this->forms.back()));
if(dynamic_cast<MatrixFormSurf<Scalar>*>(otherWf->forms[i]) != NULL)
this->mfsurf.push_back(dynamic_cast<MatrixFormSurf<Scalar>*>(this->forms.back()));
if(dynamic_cast<MatrixFormDG<Scalar>*>(otherWf->forms[i]) != NULL)
this->mfDG.push_back(dynamic_cast<MatrixFormDG<Scalar>*>(this->forms.back()));
if(dynamic_cast<VectorFormVol<Scalar>*>(otherWf->forms[i]) != NULL)
this->vfvol.push_back(dynamic_cast<VectorFormVol<Scalar>*>(this->forms.back()));
if(dynamic_cast<VectorFormSurf<Scalar>*>(otherWf->forms[i]) != NULL)
this->vfsurf.push_back(dynamic_cast<VectorFormSurf<Scalar>*>(this->forms.back()));
if(dynamic_cast<VectorFormDG<Scalar>*>(otherWf->forms[i]) != NULL)
this->vfDG.push_back(dynamic_cast<VectorFormDG<Scalar>*>(this->forms.back()));
}
for(unsigned int i = 0; i < otherWf->ext.size(); i++)
{
this->ext.push_back(otherWf->ext[i]->clone());
if(dynamic_cast<Solution<Scalar>*>(otherWf->ext[i]) != NULL)
{
dynamic_cast<Solution<Scalar>*>(this->ext.back())->set_type(dynamic_cast<Solution<Scalar>*>(otherWf->ext[i])->get_type());
}
}
}
// Calculate norm of a (possibly vector-valued) solution.
// Take norm from spaces where these solutions belong.
double calc_norms(Hermes::vector<Solution*> slns)
{
// Calculate norms for all solutions.
Hermes::vector<double> norms;
int n = slns.size();
for (int i=0; i<n; i++) {
switch (slns[i]->get_space_type()) {
case HERMES_H1_SPACE: norms.push_back(calc_norm(slns[i], HERMES_H1_NORM)); break;
case HERMES_HCURL_SPACE: norms.push_back(calc_norm(slns[i], HERMES_HCURL_NORM)); break;
case HERMES_HDIV_SPACE: norms.push_back(calc_norm(slns[i], HERMES_HDIV_NORM)); break;
case HERMES_L2_SPACE: norms.push_back(calc_norm(slns[i], HERMES_L2_NORM)); break;
default: error("Internal in calc_norms(): unknown space type.");
}
}
// Calculate the resulting norm.
double result = 0;
for (int i=0; i<n; i++) result += norms[i]*norms[i];
return sqrt(result);
}
Hermes::vector<Cand> create_candidates(Element* e, int quad_order)
{
Hermes::vector<Cand> candidates;
// Get the current order range.
int current_min_order, current_max_order;
this->get_current_order_range(e, current_min_order, current_max_order);
int order_h = H2D_GET_H_ORDER(quad_order), order_v = H2D_GET_V_ORDER(quad_order);
if(current_max_order < std::max(order_h, order_v))
current_max_order = std::max(order_h, order_v);
int last_order_h = std::min(current_max_order, order_h + 1), last_order_v = std::min(current_max_order, order_v + 1);
int last_order = H2D_MAKE_QUAD_ORDER(last_order_h, last_order_v);
switch(strategy)
{
case(hORpSelectionBasedOnDOFs):
{
candidates.push_back(Cand(H2D_REFINEMENT_P, quad_order));
}
case(hXORpSelectionBasedOnError):
{
candidates.push_back(Cand(H2D_REFINEMENT_P, last_order));
candidates.push_back(Cand(H2D_REFINEMENT_H, quad_order, quad_order, quad_order, quad_order));
return candidates;
}
break;
case(isoHPSelectionBasedOnDOFs):
{
this->cand_list = H2D_HP_ISO;
return H1ProjBasedSelector<complex>::create_candidates(e, quad_order);
}
break;
case(anisoHPSelectionBasedOnDOFs):
{
this->cand_list = H2D_HP_ANISO;
return H1ProjBasedSelector<complex>::create_candidates(e, quad_order);
}
break;
}
}
MeshFunctionSharedPtr<Scalar> Limiter<Scalar>::get_solution()
{
// A check.
warn_if(this->component_count > 1, "One solution asked from a Limiter, but multiple solutions exist for limiting.");
MeshFunctionSharedPtr<Scalar> solution(new Solution<Scalar>());
Hermes::vector<MeshFunctionSharedPtr<Scalar> > solutions;
solutions.push_back(solution);
this->get_solutions(solutions);
return solutions.back();
}
void OGProjection<Scalar>::project_global(Space<Scalar>* space, MeshFunction<Scalar>* source_meshfn,
Scalar* target_vec, Hermes::MatrixSolverType matrix_solver_type,
ProjNormType proj_norm)
{
Hermes::vector<Space<Scalar>*> spaces;
spaces.push_back(space);
Hermes::vector<MeshFunction<Scalar>*> source_meshfns;
source_meshfns.push_back(source_meshfn);
Hermes::vector<ProjNormType> proj_norms;
proj_norms.push_back(proj_norm);
project_global(spaces, source_meshfns, target_vec, matrix_solver_type, proj_norms);
}
bool calc_errors(Hermes::vector<Solution* > left, Hermes::vector<Solution *> right, Hermes::vector<double> & err_abs, Hermes::vector<double> & norm_vals,
double & err_abs_total, double & norm_total, double & err_rel_total, Hermes::vector<ProjNormType> norms)
{
bool default_norms = false;
// Checks.
if(left.size() != right.size())
return false;
if (norms != Hermes::vector<ProjNormType>())
{
if(left.size() != norms.size())
return false;
}
else
default_norms = true;
// Zero the resulting Tuples.
err_abs.clear();
norm_vals.clear();
// Zero the sums.
err_abs_total = 0;
norm_total = 0;
err_rel_total = 0;
// Calculation.
for(unsigned int i = 0; i < left.size(); i++)
{
err_abs.push_back(calc_abs_error(left[i], right[i], default_norms ? HERMES_H1_NORM : norms[i]));
norm_vals.push_back(calc_norm(right[i], default_norms ? HERMES_H1_NORM : norms[i]));
err_abs_total += err_abs[i] * err_abs[i];
norm_total += norm_vals[i] * norm_vals[i];
}
err_abs_total = sqrt(err_abs_total);
norm_total = sqrt(norm_total);
err_rel_total = err_abs_total / norm_total * 100.;
// Everything went well, return appropriate flag.
return true;
}
Hermes::vector<unsigned int> NeighborSearch<Scalar>::get_transforms(uint64_t sub_idx) const
{
Hermes::vector<unsigned int> transformations_backwards;
while (sub_idx > 0)
{
transformations_backwards.push_back((sub_idx - 1) & 7);
sub_idx = (sub_idx - 1) >> 3;
}
Hermes::vector<unsigned int> transformations;
for(unsigned int i = 0; i < transformations_backwards.size(); i++)
transformations.push_back(transformations_backwards[transformations_backwards.size() - 1 - i]);
return transformations;
}
void OGProjection<Scalar>::project_global(Space<Scalar>* space,
Solution<Scalar>* sol_src, Solution<Scalar>* sol_dest,
Hermes::MatrixSolverType matrix_solver_type,
ProjNormType proj_norm)
{
Hermes::vector<Space<Scalar>*> spaces;
spaces.push_back(space);
Hermes::vector<Solution<Scalar>*> sols_src;
sols_src.push_back(sol_src);
Hermes::vector<Solution<Scalar>*> sols_dest;
sols_dest.push_back(sol_dest);
Hermes::vector<ProjNormType> proj_norms;
if(proj_norm != HERMES_UNSET_NORM)
proj_norms.push_back(proj_norm);
project_global(spaces, sols_src, sols_dest, matrix_solver_type, proj_norms);
}
void CalculationContinuity<Scalar>::Record::load_spaces(Hermes::vector<Space<Scalar>*> spaces, Hermes::vector<SpaceType> space_types, Hermes::vector<Mesh*> meshes, Hermes::vector<Shapeset*> shapesets)
{
if(shapesets == Hermes::vector<Shapeset*>())
for(unsigned int i = 0; i < spaces.size(); i++)
shapesets.push_back(NULL);
for(unsigned int i = 0; i < spaces.size(); i++)
{
std::stringstream filename;
filename << CalculationContinuity<Scalar>::spaceFileName << i << '_' << (std::string)"t = " << this->time << (std::string)"n = " << this->number << (std::string)".h2d";
spaces[i]->free();
try
{
switch(space_types[i])
{
case HERMES_H1_SPACE:
dynamic_cast<H1Space<Scalar>*>(spaces[i])->load(filename.str().c_str(), meshes[i], shapesets[i]);
break;
case HERMES_HCURL_SPACE:
dynamic_cast<HcurlSpace<Scalar>*>(spaces[i])->load(filename.str().c_str(), meshes[i], shapesets[i]);
break;
case HERMES_HDIV_SPACE:
dynamic_cast<HdivSpace<Scalar>*>(spaces[i])->load(filename.str().c_str(), meshes[i], shapesets[i]);
break;
case HERMES_L2_SPACE:
dynamic_cast<L2Space<Scalar>*>(spaces[i])->load(filename.str().c_str(), meshes[i], shapesets[i]);
break;
}
}
catch(Hermes::Exceptions::SpaceLoadFailureException& e)
{
throw IOCalculationContinuityException(CalculationContinuityException::spaces, IOCalculationContinuityException::input, filename.str().c_str(), e.what());
}
catch(std::exception& e)
{
throw IOCalculationContinuityException(CalculationContinuityException::spaces, IOCalculationContinuityException::input, filename.str().c_str(), e.what());
}
}
}
KellyTypeAdapt::KellyTypeAdapt(Hermes::vector< Space* > spaces_,
Hermes::vector< ProjNormType > norms_,
bool ignore_visited_segments_,
Hermes::vector<interface_estimator_scaling_fn_t> interface_scaling_fns_)
: Adapt(spaces_, norms_)
{
error_estimators_surf.reserve(num);
error_estimators_vol.reserve(num);
if (interface_scaling_fns_.size() == 0)
{
interface_scaling_fns_.reserve(num);
for (int i = 0; i < num; i++)
interface_scaling_fns_.push_back(scale_by_element_diameter);
}
use_aposteriori_interface_scaling = true;
interface_scaling_fns = interface_scaling_fns_;
interface_scaling_const = boundary_scaling_const = volumetric_scaling_const = 1.0;
ignore_visited_segments = ignore_visited_segments_;
element_markers_conversion = spaces_[0]->get_mesh()->element_markers_conversion;
boundary_markers_conversion = spaces_[0]->get_mesh()->boundary_markers_conversion;
}
int main(int argc, char* argv[])
{
if (NUMBER_OF_EIGENVALUES > 6) error("Maximum number of eigenvalues is 6.");
info("Desired number of eigenvalues: %d.", NUMBER_OF_EIGENVALUES);
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinements (optional).
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Enter boundary markers.
// Note: "essential" means that solution value is prescribed.
BCTypes bc_types;
bc_types.add_bc_dirichlet(Hermes::vector<int>(BDY_BOTTOM, BDY_RIGHT, BDY_TOP, BDY_LEFT));
// Enter Dirichlet boudnary values.
BCValues bc_values;
bc_values.add_zero(Hermes::vector<int>(BDY_BOTTOM, BDY_RIGHT, BDY_TOP, BDY_LEFT));
// Create an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
// Initialize the weak formulation for the left hand side i.e. H
WeakForm wf_left, wf_right;
wf_left.add_matrix_form(callback(bilinear_form_left));
wf_right.add_matrix_form(callback(bilinear_form_right));
// Initialize refinement selector.
H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Initialize views.
ScalarView sview_1("", new WinGeom(0, 0, 350, 250));
sview_1.show_mesh(false);
sview_1.fix_scale_width(60);
ScalarView sview_2("", new WinGeom(360, 0, 350, 250));
sview_2.show_mesh(false);
sview_2.fix_scale_width(60);
ScalarView sview_3("", new WinGeom(720, 0, 350, 250));
sview_3.show_mesh(false);
sview_3.fix_scale_width(60);
ScalarView sview_4("", new WinGeom(0, 305, 350, 250));
sview_4.show_mesh(false);
sview_4.fix_scale_width(60);
ScalarView sview_5("", new WinGeom(360, 305, 350, 250));
sview_5.show_mesh(false);
sview_5.fix_scale_width(60);
ScalarView sview_6("", new WinGeom(720, 305, 350, 250));
sview_6.show_mesh(false);
sview_6.fix_scale_width(60);
OrderView oview("Polynomial orders", new WinGeom(1080, 0, 410, 350));
// DOF and CPU convergence graphs.
SimpleGraph graph_dof_est, graph_cpu_est;
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
Solution sln[NUMBER_OF_EIGENVALUES], ref_sln[NUMBER_OF_EIGENVALUES];
// Adaptivity loop:
int as = 1;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
info("Solving on reference mesh.");
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = construct_refined_space(&space);
int ref_ndof = Space::get_num_dofs(ref_space);
info("ref_ndof: %d.", ref_ndof);
// Initialize matrices and matrix solver on referenc emesh.
SparseMatrix* matrix_left = create_matrix(matrix_solver);
SparseMatrix* matrix_right = create_matrix(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix_left);
// Assemble the matrices on reference mesh.
bool is_linear = true;
DiscreteProblem* dp_left = new DiscreteProblem(&wf_left, ref_space, is_linear);
dp_left->assemble(matrix_left);
DiscreteProblem* dp_right = new DiscreteProblem(&wf_right, ref_space, is_linear);
dp_right->assemble(matrix_right);
// Time measurement.
cpu_time.tick();
// Write matrix_left in MatrixMarket format.
write_matrix_mm("mat_left.mtx", matrix_left);
// Write matrix_left in MatrixMarket format.
write_matrix_mm("mat_right.mtx", matrix_right);
// Time measurement.
cpu_time.tick(HERMES_SKIP);
// Calling Python eigensolver. Solution will be written to "eivecs.dat".
info("Calling Pysparse...");
char call_cmd[255];
sprintf(call_cmd, "python solveGenEigenFromMtx.py mat_left.mtx mat_right.mtx %g %d %g %d",
TARGET_VALUE, NUMBER_OF_EIGENVALUES, TOL, MAX_ITER);
system(call_cmd);
info("Pysparse finished.");
// Initializing solution vector, solution and ScalarView.
double* ref_coeff_vec = new double[ref_ndof];
//Solution sln[NUMBER_OF_EIGENVALUES], ref_sln[NUMBER_OF_EIGENVALUES];
//ScalarView view("Solution", new WinGeom(0, 0, 440, 350));
// Reading solution vectors from file and visualizing.
double eigenval[NUMBER_OF_EIGENVALUES];
FILE *file = fopen("eivecs.dat", "r");
char line [64]; // Maximum line size.
fgets(line, sizeof line, file); // ref_ndof
int n = atoi(line);
if (n != ref_ndof) error("Mismatched ndof in the eigensolver output file.");
fgets(line, sizeof line, file); // Number of eigenvectors in the file.
int neig = atoi(line);
if (neig != NUMBER_OF_EIGENVALUES) error("Mismatched number of eigenvectors in the eigensolver output file.");
for (int ieig = 0; ieig < NUMBER_OF_EIGENVALUES; ieig++) {
// Get next eigenvalue from the file
fgets(line, sizeof line, file); // eigenval
eigenval[ieig] = atof(line);
// Get the corresponding eigenvector.
for (int i = 0; i < ref_ndof; i++) {
fgets(line, sizeof line, file);
ref_coeff_vec[i] = atof(line);
}
// Convert coefficient vector into a Solution.
Solution::vector_to_solution(ref_coeff_vec, ref_space, &(ref_sln[ieig]));
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution %d on coarse mesh.", ieig);
OGProjection::project_global(&space, &(ref_sln[ieig]), &(sln[ieig]), matrix_solver);
}
fclose(file);
delete [] ref_coeff_vec;
// FIXME: Below, the adaptivity is done for the last eigenvector only,
// this needs to be changed to take into account all eigenvectors.
// View the coarse mesh solution and polynomial orders.
char title[100];
if (NUMBER_OF_EIGENVALUES > 0) {
sprintf(title, "Solution 0, val = %g", eigenval[0]);
sview_1.set_title(title);
sview_1.show(&(sln[0]));
}
if (NUMBER_OF_EIGENVALUES > 1) {
sprintf(title, "Solution 1, val = %g", eigenval[1]);
sview_2.set_title(title);
sview_2.show(&(sln[1]));
}
if (NUMBER_OF_EIGENVALUES > 2) {
sprintf(title, "Solution 2, val = %g", eigenval[2]);
sview_3.set_title(title);
sview_3.show(&(sln[2]));
}
if (NUMBER_OF_EIGENVALUES > 3) {
sprintf(title, "Solution 3, val = %g", eigenval[3]);
sview_4.set_title(title);
sview_4.show(&(sln[3]));
}
if (NUMBER_OF_EIGENVALUES > 4) {
sprintf(title, "Solution 4, val = %g", eigenval[4]);
sview_5.set_title(title);
sview_5.show(&(sln[4]));
}
if (NUMBER_OF_EIGENVALUES > 5) {
sprintf(title, "Solution 5, val = %g", eigenval[5]);
sview_6.set_title(title);
sview_6.show(&(sln[5]));
}
oview.show(&space);
// Calculate element errors and total error estimate.
info("Calculating error estimate.");
Hermes::vector<Space *> spaces;
for(int i = 0; i < NUMBER_OF_EIGENVALUES; i++) spaces.push_back(&space);
Adapt* adaptivity = new Adapt(spaces);
Hermes::vector<Solution *> slns;
if (NUMBER_OF_EIGENVALUES > 0) slns.push_back(&sln[0]);
if (NUMBER_OF_EIGENVALUES > 1) slns.push_back(&sln[1]);
if (NUMBER_OF_EIGENVALUES > 2) slns.push_back(&sln[2]);
if (NUMBER_OF_EIGENVALUES > 3) slns.push_back(&sln[3]);
if (NUMBER_OF_EIGENVALUES > 4) slns.push_back(&sln[4]);
if (NUMBER_OF_EIGENVALUES > 5) slns.push_back(&sln[5]);
Hermes::vector<Solution *> ref_slns;
if (NUMBER_OF_EIGENVALUES > 0) ref_slns.push_back(&ref_sln[0]);
if (NUMBER_OF_EIGENVALUES > 1) ref_slns.push_back(&ref_sln[1]);
if (NUMBER_OF_EIGENVALUES > 2) ref_slns.push_back(&ref_sln[2]);
if (NUMBER_OF_EIGENVALUES > 3) ref_slns.push_back(&ref_sln[3]);
if (NUMBER_OF_EIGENVALUES > 4) ref_slns.push_back(&ref_sln[4]);
if (NUMBER_OF_EIGENVALUES > 5) ref_slns.push_back(&ref_sln[5]);
Hermes::vector<double> component_errors;
double err_est_rel = adaptivity->calc_err_est(slns, ref_slns, &component_errors) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d.", Space::get_num_dofs(&space), Space::get_num_dofs(ref_space));
if (NUMBER_OF_EIGENVALUES > 0) info("err_est_rel[0]: %g%%", component_errors[0] * 100);
if (NUMBER_OF_EIGENVALUES > 1) info("err_est_rel[1]: %g%%", component_errors[1] * 100);
if (NUMBER_OF_EIGENVALUES > 2) info("err_est_rel[2]: %g%%", component_errors[2] * 100);
if (NUMBER_OF_EIGENVALUES > 3) info("err_est_rel[3]: %g%%", component_errors[3] * 100);
if (NUMBER_OF_EIGENVALUES > 4) info("err_est_rel[4]: %g%%", component_errors[4] * 100);
if (NUMBER_OF_EIGENVALUES > 5) info("err_est_rel[5]: %g%%", component_errors[5] * 100);
// Time measurement.
cpu_time.tick();
// Add entry to DOF and CPU convergence graphs.
graph_dof_est.add_values(Space::get_num_dofs(&space), err_est_rel);
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu_est.save("conv_cpu_est.dat");
// If err_est too large, adapt the mesh.
if (err_est_rel < ERR_STOP) done = true;
else
{
info("Adapting coarse mesh.");
Hermes::vector<RefinementSelectors::Selector *> selectors;
for(int i = 0; i < NUMBER_OF_EIGENVALUES; i++)
selectors.push_back(&selector);
done = adaptivity->adapt(selectors, THRESHOLD, STRATEGY, MESH_REGULARITY);
// Increase the counter of performed adaptivity steps.
if (done == false) as++;
}
if (Space::get_num_dofs(&space) >= NDOF_STOP) done = true;
// Clean up.
delete solver;
delete matrix_left;
delete matrix_right;
delete adaptivity;
if(done == false) delete ref_space->get_mesh();
delete ref_space;
delete dp_left;
delete dp_right;
}
while (done == false);
// Wait for all views to be closed.
View::wait();
return 0;
};
int main(int argc, char* argv[])
{
// Time measurement.
Hermes::Mixins::TimeMeasurable cpu_time;
cpu_time.tick();
// Load physical data of the problem.
MaterialPropertyMaps matprop(N_GROUPS);
matprop.set_D(D);
matprop.set_Sigma_r(Sr);
matprop.set_Sigma_s(Ss);
matprop.set_Sigma_a(Sa);
matprop.set_Sigma_f(Sf);
matprop.set_nu(nu);
matprop.set_chi(chi);
matprop.validate();
std::cout << matprop;
// Use multimesh, i.e. create one mesh for each energy group.
Hermes::vector<Mesh *> meshes;
for (unsigned int g = 0; g < matprop.get_G(); g++)
meshes.push_back(new Mesh());
// Load the mesh for the 1st group.
MeshReaderH2D mloader;
mloader.load(mesh_file.c_str(), meshes[0]);
for (unsigned int g = 1; g < matprop.get_G(); g++)
{
// Obtain meshes for the 2nd to 4th group by cloning the mesh loaded for the 1st group.
meshes[g]->copy(meshes[0]);
// Initial uniform refinements.
for (int i = 0; i < INIT_REF_NUM[g]; i++)
meshes[g]->refine_all_elements();
}
for (int i = 0; i < INIT_REF_NUM[0]; i++)
meshes[0]->refine_all_elements();
// Create pointers to solutions on coarse and fine meshes and from the latest power iteration, respectively.
Hermes::vector<Solution<double>*> coarse_solutions, fine_solutions;
Hermes::vector<MeshFunction<double>*> power_iterates;
// Initialize all the new solution variables.
for (unsigned int g = 0; g < matprop.get_G(); g++)
{
coarse_solutions.push_back(new Solution<double>());
fine_solutions.push_back(new Solution<double>());
power_iterates.push_back(new ConstantSolution<double>(meshes[g], 1.0));
}
// Create the approximation spaces with the default shapeset.
H1Space<double> space1(meshes[0], P_INIT[0]);
H1Space<double> space2(meshes[1], P_INIT[1]);
H1Space<double> space3(meshes[2], P_INIT[2]);
H1Space<double> space4(meshes[3], P_INIT[3]);
Hermes::vector<const Space<double>*> const_spaces(&space1, &space2, &space3, &space4);
Hermes::vector<Space<double>*> spaces(&space1, &space2, &space3, &space4);
// Initialize the weak formulation.
CustomWeakForm wf(matprop, power_iterates, k_eff, bdy_vacuum);
// Initialize the discrete algebraic representation of the problem and its solver.
//
// Create the matrix and right-hand side vector for the solver.
SparseMatrix<double>* mat = create_matrix<double>();
Vector<double>* rhs = create_vector<double>();
// Instantiate the solver itself.
LinearMatrixSolver<double>* solver = create_linear_solver<double>( mat, rhs);
// Initialize views.
/* for 1280x800 display */
ScalarView view1("Neutron flux 1", new WinGeom(0, 0, 320, 400));
ScalarView view2("Neutron flux 2", new WinGeom(330, 0, 320, 400));
ScalarView view3("Neutron flux 3", new WinGeom(660, 0, 320, 400));
ScalarView view4("Neutron flux 4", new WinGeom(990, 0, 320, 400));
OrderView oview1("Mesh for group 1", new WinGeom(0, 450, 320, 500));
OrderView oview2("Mesh for group 2", new WinGeom(330, 450, 320, 500));
OrderView oview3("Mesh for group 3", new WinGeom(660, 450, 320, 500));
OrderView oview4("Mesh for group 4", new WinGeom(990, 450, 320, 500));
/* for adjacent 1280x800 and 1680x1050 displays
ScalarView view1("Neutron flux 1", new WinGeom(0, 0, 640, 480));
ScalarView view2("Neutron flux 2", new WinGeom(650, 0, 640, 480));
ScalarView view3("Neutron flux 3", new WinGeom(1300, 0, 640, 480));
ScalarView view4("Neutron flux 4", new WinGeom(1950, 0, 640, 480));
OrderView oview1("Mesh for group 1", new WinGeom(1300, 500, 340, 500));
OrderView oview2("Mesh for group 2", new WinGeom(1650, 500, 340, 500));
OrderView oview3("Mesh for group 3", new WinGeom(2000, 500, 340, 500));
OrderView oview4("Mesh for group 4", new WinGeom(2350, 500, 340, 500));
*/
Hermes::vector<ScalarView *> sviews(&view1, &view2, &view3, &view4);
Hermes::vector<OrderView *> oviews(&oview1, &oview2, &oview3, &oview4);
for (unsigned int g = 0; g < matprop.get_G(); g++)
{
sviews[g]->show_mesh(false);
sviews[g]->set_3d_mode(true);
}
// DOF and CPU convergence graphs
GnuplotGraph graph_dof("Error convergence", "NDOF", "log(error)");
graph_dof.add_row("H1 err. est. [%]", "r", "-", "o");
graph_dof.add_row("L2 err. est. [%]", "g", "-", "s");
graph_dof.add_row("Keff err. est. [milli-%]", "b", "-", "d");
graph_dof.set_log_y();
graph_dof.show_legend();
graph_dof.show_grid();
GnuplotGraph graph_dof_evol("Evolution of NDOF", "Adaptation step", "NDOF");
graph_dof_evol.add_row("group 1", "r", "-", "o");
graph_dof_evol.add_row("group 2", "g", "-", "x");
graph_dof_evol.add_row("group 3", "b", "-", "+");
graph_dof_evol.add_row("group 4", "m", "-", "*");
graph_dof_evol.set_log_y();
graph_dof_evol.set_legend_pos("bottom right");
graph_dof_evol.show_grid();
GnuplotGraph graph_cpu("Error convergence", "CPU time [s]", "log(error)");
graph_cpu.add_row("H1 err. est. [%]", "r", "-", "o");
graph_cpu.add_row("L2 err. est. [%]", "g", "-", "s");
graph_cpu.add_row("Keff err. est. [milli-%]", "b", "-", "d");
graph_cpu.set_log_y();
graph_cpu.show_legend();
graph_cpu.show_grid();
// Initialize the refinement selectors.
H1ProjBasedSelector<double> selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
Hermes::vector<RefinementSelectors::Selector<double>*> selectors;
for (unsigned int g = 0; g < matprop.get_G(); g++)
selectors.push_back(&selector);
Hermes::vector<MatrixFormVol<double>*> projection_jacobian;
Hermes::vector<VectorFormVol<double>*> projection_residual;
for (unsigned int g = 0; g < matprop.get_G(); g++)
{
projection_jacobian.push_back(new H1AxisymProjectionJacobian(g));
projection_residual.push_back(new H1AxisymProjectionResidual(g, power_iterates[g]));
}
Hermes::vector<ProjNormType> proj_norms_h1, proj_norms_l2;
for (unsigned int g = 0; g < matprop.get_G(); g++)
{
proj_norms_h1.push_back(HERMES_H1_NORM);
proj_norms_l2.push_back(HERMES_L2_NORM);
}
// Initial power iteration to obtain a coarse estimate of the eigenvalue and the fission source.
Hermes::Mixins::Loggable::Static::info("Coarse mesh power iteration, %d + %d + %d + %d = %d ndof:", report_num_dofs(spaces));
power_iteration(matprop, const_spaces, &wf, power_iterates, core, TOL_PIT_CM, matrix_solver);
// Adaptivity loop:
int as = 1; bool done = false;
do
{
Hermes::Mixins::Loggable::Static::info("---- Adaptivity step %d:", as);
// Construct globally refined meshes and setup reference spaces on them.
Hermes::vector<const Space<double>*> ref_spaces_const;
Hermes::vector<Mesh *> ref_meshes;
for (unsigned int g = 0; g < matprop.get_G(); g++)
{
ref_meshes.push_back(new Mesh());
Mesh *ref_mesh = ref_meshes.back();
ref_mesh->copy(spaces[g]->get_mesh());
ref_mesh->refine_all_elements();
int order_increase = 1;
ref_spaces_const.push_back(spaces[g]->dup(ref_mesh, order_increase));
}
#ifdef WITH_PETSC
// PETSc assembling is currently slow for larger matrices, so we switch to
// UMFPACK when matrices of order >8000 start to appear.
if (Space<double>::get_num_dofs(ref_spaces_const) > 8000 && matrix_solver == SOLVER_PETSC)
{
// Delete the old solver.
delete mat;
delete rhs;
delete solver;
// Create a new one.
matrix_solver = SOLVER_UMFPACK;
mat = create_matrix<double>();
rhs = create_vector<double>();
solver = create_linear_solver<double>( mat, rhs);
}
#endif
// Solve the fine mesh problem.
Hermes::Mixins::Loggable::Static::info("Fine mesh power iteration, %d + %d + %d + %d = %d ndof:", report_num_dofs(ref_spaces_const));
power_iteration(matprop, ref_spaces_const, &wf, power_iterates, core, TOL_PIT_RM, matrix_solver);
// Store the results.
for (unsigned int g = 0; g < matprop.get_G(); g++)
fine_solutions[g]->copy((static_cast<Solution<double>*>(power_iterates[g])));
Hermes::Mixins::Loggable::Static::info("Projecting fine mesh solutions on coarse meshes.");
// This is commented out as the appropriate method was deleted in the commit
// "Cleaning global projections" (b282194946225014faa1de37f20112a5a5d7ab5a).
//OGProjection<double> ogProjection; ogProjection.project_global(spaces, projection_jacobian, projection_residual, coarse_solutions);
// Time measurement.
cpu_time.tick();
// View the coarse mesh solution and meshes.
for (unsigned int g = 0; g < matprop.get_G(); g++)
{
sviews[g]->show(coarse_solutions[g]);
oviews[g]->show(spaces[g]);
}
// Skip visualization time.
cpu_time.tick(Hermes::Mixins::TimeMeasurable::HERMES_SKIP);
// Report the number of negative eigenfunction values.
Hermes::Mixins::Loggable::Static::info("Num. of negative values: %d, %d, %d, %d",
get_num_of_neg(coarse_solutions[0]), get_num_of_neg(coarse_solutions[1]),
get_num_of_neg(coarse_solutions[2]), get_num_of_neg(coarse_solutions[3]));
// Calculate element errors and total error estimate.
Adapt<double> adapt_h1(spaces);
Adapt<double> adapt_l2(spaces);
for (unsigned int g = 0; g < matprop.get_G(); g++)
{
adapt_h1.set_error_form(g, g, new ErrorForm(proj_norms_h1[g]));
adapt_l2.set_error_form(g, g, new ErrorForm(proj_norms_l2[g]));
}
// Calculate element errors and error estimates in H1 and L2 norms. Use the H1 estimate to drive adaptivity.
Hermes::Mixins::Loggable::Static::info("Calculating errors.");
Hermes::vector<double> h1_group_errors, l2_group_errors;
double h1_err_est = adapt_h1.calc_err_est(coarse_solutions, fine_solutions, &h1_group_errors) * 100;
double l2_err_est = adapt_l2.calc_err_est(coarse_solutions, fine_solutions, &l2_group_errors, false) * 100;
// Time measurement.
cpu_time.tick();
double cta = cpu_time.accumulated();
// Report results.
Hermes::Mixins::Loggable::Static::info("ndof_coarse: %d + %d + %d + %d = %d", report_num_dofs(spaces));
// Millipercent eigenvalue error w.r.t. the reference value (see physical_parameters.cpp).
double keff_err = 1e5*fabs(wf.get_keff() - REF_K_EFF)/REF_K_EFF;
Hermes::Mixins::Loggable::Static::info("per-group err_est_coarse (H1): %g%%, %g%%, %g%%, %g%%", report_errors(h1_group_errors));
Hermes::Mixins::Loggable::Static::info("per-group err_est_coarse (L2): %g%%, %g%%, %g%%, %g%%", report_errors(l2_group_errors));
Hermes::Mixins::Loggable::Static::info("total err_est_coarse (H1): %g%%", h1_err_est);
Hermes::Mixins::Loggable::Static::info("total err_est_coarse (L2): %g%%", l2_err_est);
Hermes::Mixins::Loggable::Static::info("k_eff err: %g milli-percent", keff_err);
// Add entry to DOF convergence graph.
int ndof_coarse = spaces[0]->get_num_dofs() + spaces[1]->get_num_dofs()
+ spaces[2]->get_num_dofs() + spaces[3]->get_num_dofs();
graph_dof.add_values(0, ndof_coarse, h1_err_est);
graph_dof.add_values(1, ndof_coarse, l2_err_est);
graph_dof.add_values(2, ndof_coarse, keff_err);
// Add entry to CPU convergence graph.
graph_cpu.add_values(0, cta, h1_err_est);
graph_cpu.add_values(1, cta, l2_err_est);
graph_cpu.add_values(2, cta, keff_err);
for (unsigned int g = 0; g < matprop.get_G(); g++)
graph_dof_evol.add_values(g, as, Space<double>::get_num_dofs(spaces[g]));
cpu_time.tick(Hermes::Mixins::TimeMeasurable::HERMES_SKIP);
// If err_est too large, adapt the mesh (L2 norm chosen since (weighted integrals of) solution values
// are more important for further analyses than the derivatives.
if (l2_err_est < ERR_STOP)
done = true;
else
{
Hermes::Mixins::Loggable::Static::info("Adapting the coarse mesh.");
done = adapt_h1.adapt(selectors, THRESHOLD, STRATEGY, MESH_REGULARITY);
if (spaces[0]->get_num_dofs() + spaces[1]->get_num_dofs()
+ spaces[2]->get_num_dofs() + spaces[3]->get_num_dofs() >= NDOF_STOP)
done = true;
}
// Free reference meshes and spaces.
for (unsigned int g = 0; g < matprop.get_G(); g++)
{
delete ref_spaces_const[g];
delete ref_meshes[g];
}
as++;
if (as >= MAX_ADAPT_NUM) done = true;
}
while(done == false);
Hermes::Mixins::Loggable::Static::info("Total running time: %g s", cpu_time.accumulated());
for (unsigned int g = 0; g < matprop.get_G(); g++)
{
delete spaces[g]; delete meshes[g];
delete coarse_solutions[g], delete fine_solutions[g]; delete power_iterates[g];
}
delete mat;
delete rhs;
delete solver;
graph_dof.save("conv_dof.gp");
graph_cpu.save("conv_cpu.gp");
graph_dof_evol.save("dof_evol.gp");
// Wait for all views to be closed.
View::wait();
return 0;
}
bool NewtonSolver<Scalar>::solve_keep_jacobian(Scalar* coeff_vec, double newton_tol, int newton_max_iter, bool residual_as_function)
{
// Obtain the number of degrees of freedom.
int ndof = this->dp->get_num_dofs();
// The Newton's loop.
double residual_norm;
int it = 1;
while (1)
{
// Assemble the residual vector.
this->dp->assemble(coeff_vec, residual);
// Measure the residual norm.
if (residual_as_function)
{
// Prepare solutions for measuring residual norm.
Hermes::vector<Solution<Scalar>*> solutions;
Hermes::vector<bool> dir_lift_false;
for (unsigned int i = 0; i < static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_spaces().size(); i++) {
solutions.push_back(new Solution<Scalar>());
dir_lift_false.push_back(false);
}
Solution<Scalar>::vector_to_solutions(residual, static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_spaces(), solutions, dir_lift_false);
// Calculate the norm.
residual_norm = Global<Scalar>::calc_norms(solutions);
// Clean up.
for (unsigned int i = 0; i < static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_spaces().size(); i++)
delete solutions[i];
}
else
{
// Calculate the l2-norm of residual vector, this is the traditional way.
residual_norm = Global<Scalar>::get_l2_norm(residual);
}
// Info for the user.
if(it == 1)
{
if(this->verbose_output)
info("---- Newton initial residual norm: %g", residual_norm);
}
else
if(this->verbose_output)
info("---- Newton iter %d, residual norm: %g", it - 1, residual_norm);
// If maximum allowed residual norm is exceeded, fail.
if (residual_norm > max_allowed_residual_norm)
{
if (this->verbose_output)
{
info("Current residual norm: %g", residual_norm);
info("Maximum allowed residual norm: %g", max_allowed_residual_norm);
info("Newton solve not successful, returning false.");
}
break;
}
// If residual norm is within tolerance, return 'true'.
// This is the only correct way of ending.
if (residual_norm < newton_tol && it > 1) {
// We want to return the solution in a different structure.
this->sln_vector = new Scalar[ndof];
for (int i = 0; i < ndof; i++)
this->sln_vector[i] = coeff_vec[i];
return true;
}
// Assemble and keep the jacobian if this has not been done before.
// Also declare that LU-factorization in case of a direct solver will be done only once and reused afterwards.
if(kept_jacobian == NULL) {
kept_jacobian = create_matrix<Scalar>(this->matrix_solver_type);
// Give the matrix solver the correct Jacobian. NOTE: It would be cleaner if the whole decision whether to keep
// Jacobian or not was made in the constructor.
//
// Delete the matrix solver created in the constructor.
delete linear_solver;
// Create new matrix solver with correct matrix.
linear_solver = create_linear_solver<Scalar>(this->matrix_solver_type, kept_jacobian, residual);
this->dp->assemble(coeff_vec, kept_jacobian);
linear_solver->set_factorization_scheme(HERMES_REUSE_FACTORIZATION_COMPLETELY);
}
// Multiply the residual vector with -1 since the matrix
// equation reads J(Y^n) \deltaY^{n+1} = -F(Y^n).
residual->change_sign();
// Solve the linear system.
if(!linear_solver->solve()) {
if (this->verbose_output)
info ("Matrix<Scalar> solver failed. Returning false.\n");
break;
}
// Add \deltaY^{n+1} to Y^n.
for (int i = 0; i < ndof; i++)
coeff_vec[i] += linear_solver->get_sln_vector()[i];
// Increase the number of iterations and test if we are still under the limit.
if (it++ >= newton_max_iter)
{
if (this->verbose_output)
info("Maximum allowed number of Newton iterations exceeded, returning false.");
break;
}
}
// Return false.
// All 'bad' situations end here.
return false;
}
bool NewtonSolver<Scalar>::solve(Scalar* coeff_vec, double newton_tol, int newton_max_iter, bool residual_as_function)
{
// Delete the old solution vector, if there is any.
if(this->sln_vector != NULL)
{
delete [] this->sln_vector;
this->sln_vector = NULL;
}
// Obtain the number of degrees of freedom.
int ndof = this->dp->get_num_dofs();
// The Newton's loop.
double residual_norm;
int it = 1;
bool delete_timer = false;
if (this->timer == NULL)
{
this->timer = new TimePeriod;
delete_timer = true;
}
this->timer->tick();
setup_time += this->timer->last();
while (1)
{
// Assemble just the residual vector.
if(it > 1)
static_cast<DiscreteProblem<Scalar>*>(this->dp)->temp_disable_adaptivity_cache();
this->dp->assemble(coeff_vec, residual);
this->timer->tick();
assemble_time += this->timer->last();
// Measure the residual norm.
if (residual_as_function)
{
// Prepare solutions for measuring residual norm.
Hermes::vector<Solution<Scalar>*> solutions;
Hermes::vector<bool> dir_lift_false;
for (unsigned int i = 0; i < static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_spaces().size(); i++) {
solutions.push_back(new Solution<Scalar>());
dir_lift_false.push_back(false);
}
Solution<Scalar>::vector_to_solutions(residual, static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_spaces(), solutions, dir_lift_false);
// Calculate the norm.
residual_norm = Global<Scalar>::calc_norms(solutions);
// Clean up.
for (unsigned int i = 0; i < static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_spaces().size(); i++)
delete solutions[i];
}
else
{
// Calculate the l2-norm of residual vector, this is the traditional way.
residual_norm = Global<Scalar>::get_l2_norm(residual);
}
// Info for the user.
if(it == 1) {
if(this->verbose_output)
info("---- Newton initial residual norm: %g", residual_norm);
}
else
if(this->verbose_output)
info("---- Newton iter %d, residual norm: %g", it - 1, residual_norm);
// If maximum allowed residual norm is exceeded, fail.
if (residual_norm > max_allowed_residual_norm)
{
if (this->verbose_output)
{
info("Current residual norm: %g", residual_norm);
info("Maximum allowed residual norm: %g", max_allowed_residual_norm);
info("Newton solve not successful, returning false.");
}
break;
}
// If residual norm is within tolerance, return 'true'.
// This is the only correct way of ending.
if (residual_norm < newton_tol && it > 1) {
// We want to return the solution in a different structure.
this->sln_vector = new Scalar[ndof];
for (int i = 0; i < ndof; i++)
this->sln_vector[i] = coeff_vec[i];
this->timer->tick();
solve_time += this->timer->last();
if (delete_timer)
{
delete this->timer;
this->timer = NULL;
}
static_cast<DiscreteProblem<Scalar>*>(this->dp)->temp_enable_adaptivity_cache();
return true;
}
this->timer->tick();
solve_time += this->timer->last();
// Assemble just the jacobian.
this->dp->assemble(coeff_vec, jacobian);
this->timer->tick();
assemble_time += this->timer->last();
// Multiply the residual vector with -1 since the matrix
// equation reads J(Y^n) \deltaY^{n+1} = -F(Y^n).
residual->change_sign();
// Solve the linear system.
if(!linear_solver->solve()) {
if (this->verbose_output)
info ("Matrix<Scalar> solver failed. Returning false.\n");
break;
}
// Add \deltaY^{n+1} to Y^n.
for (int i = 0; i < ndof; i++)
coeff_vec[i] += linear_solver->get_sln_vector()[i];
// Increase the number of iterations and test if we are still under the limit.
if (it++ >= newton_max_iter)
{
if (this->verbose_output)
info("Maximum allowed number of Newton iterations exceeded, returning false.");
break;
}
this->timer->tick();
solve_time += this->timer->last();
}
// Return false.
// All 'bad' situations end here.
if (delete_timer)
{
delete this->timer;
this->timer = NULL;
}
return false;
}
double KellyTypeAdapt::eval_interface_estimator(KellyTypeAdapt::ErrorEstimatorForm* err_est_form,
RefMap *rm, SurfPos* surf_pos,
LightArray<NeighborSearch*>& neighbor_searches, int neighbor_index)
{
NeighborSearch* nbs = neighbor_searches.get(neighbor_index);
Hermes::vector<MeshFunction*> slns;
for (int i = 0; i < num; i++)
slns.push_back(this->sln[i]);
// Determine integration order.
ExtData<Ord>* fake_ui = dp.init_ext_fns_ord(slns, neighbor_searches);
// Order of additional external functions.
// ExtData<Ord>* fake_ext = dp.init_ext_fns_ord(err_est_form->ext, nbs);
// Order of geometric attributes (eg. for multiplication of a solution with coordinates, normals, etc.).
Geom<Ord>* fake_e = new InterfaceGeom<Ord>(init_geom_ord(), nbs->neighb_el->marker, nbs->neighb_el->id, nbs->neighb_el->get_diameter());
double fake_wt = 1.0;
Ord o = err_est_form->ord(1, &fake_wt, fake_ui->fn, fake_ui->fn[err_est_form->i], fake_e, NULL);
int order = rm->get_inv_ref_order();
order += o.get_order();
limit_order(order);
// Clean up.
if (fake_ui != NULL)
{
for (int i = 0; i < num; i++)
delete fake_ui->fn[i];
fake_ui->free_ord();
delete fake_ui;
}
delete fake_e;
//delete fake_ext;
Quad2D* quad = this->sln[err_est_form->i]->get_quad_2d();
int eo = quad->get_edge_points(surf_pos->surf_num, order);
int np = quad->get_num_points(eo);
double3* pt = quad->get_points(eo);
// Init geometry and jacobian*weights (do not use the NeighborSearch caching mechanism).
double3* tan = rm->get_tangent(surf_pos->surf_num, eo);
double* jwt = new double[np];
for(int i = 0; i < np; i++)
jwt[i] = pt[i][2] * tan[i][2];
Geom<double>* e = new InterfaceGeom<double>(init_geom_surf(rm, surf_pos, eo),
nbs->neighb_el->marker,
nbs->neighb_el->id,
nbs->neighb_el->get_diameter());
// function values
ExtData<scalar>* ui = dp.init_ext_fns(slns, neighbor_searches, order);
//ExtData<scalar>* ext = dp.init_ext_fns(err_est_form->ext, nbs);
scalar res = interface_scaling_const *
err_est_form->value(np, jwt, ui->fn, ui->fn[err_est_form->i], e, NULL);
if (ui != NULL) { ui->free(); delete ui; }
//if (ext != NULL) { ext->free(); delete ext; }
e->free(); delete e;
delete [] jwt;
return std::abs(0.5*res); // Edges are parameterized from 0 to 1 while integration weights
// are defined in (-1, 1). Thus multiplying with 0.5 to correct
// the weights.
}
Adapt::Adapt(Hermes::vector< Space* > spaces_,
Hermes::vector<ProjNormType> proj_norms) :
num_act_elems(-1),
have_errors(false),
have_coarse_solutions(false),
have_reference_solutions(false)
{
// sanity check
if (proj_norms.size() > 0 && spaces_.size() != proj_norms.size())
error("Mismatched numbers of spaces and projection types in Adapt::Adapt().");
this->num = spaces_.size();
// sanity checks
error_if(this->num <= 0, "Too few components (%d), only %d supported.", this->num, H2D_MAX_COMPONENTS);
error_if(this->num > H2D_MAX_COMPONENTS, "Too many components (%d), only %d supported.", this->num, H2D_MAX_COMPONENTS);
for (int i = 0; i < this->num; i++) {
if (spaces_[i] == NULL) error("spaces[%d] is NULL in Adapt::Adapt().", i);
this->spaces.push_back(spaces_[i]);
}
// reset values
memset(errors, 0, sizeof(errors));
memset(error_form, 0, sizeof(error_form));
memset(error_ord, 0, sizeof(error_ord));
memset(sln, 0, sizeof(sln));
memset(rsln, 0, sizeof(rsln));
// if norms were not set by the user, set them to defaults
// according to spaces
if (proj_norms.size() == 0) {
for (int i = 0; i < this->num; i++) {
switch (spaces[i]->get_type()) {
case HERMES_H1_SPACE: proj_norms.push_back(HERMES_H1_NORM); break;
case HERMES_HCURL_SPACE: proj_norms.push_back(HERMES_HCURL_NORM); break;
case HERMES_HDIV_SPACE: proj_norms.push_back(HERMES_HDIV_NORM); break;
case HERMES_L2_SPACE: proj_norms.push_back(HERMES_L2_NORM); break;
default: error("Unknown space type in Adapt::Adapt().");
}
}
}
// assign norm weak forms according to norms selection
for (int i = 0; i < this->num; i++) {
switch (proj_norms[i]) {
case HERMES_H1_NORM:
error_form[i][i] = h1_error_form<double, scalar>; error_ord[i][i] = h1_error_form<Ord, Ord>;
//printf("H1 norm.\n");
break;
case HERMES_H1_SEMINORM:
error_form[i][i] = h1_error_semi_form<double, scalar>; error_ord[i][i] = h1_error_semi_form<Ord, Ord>;
//printf("H1 semi norm.\n");
break;
case HERMES_HCURL_NORM:
error_form[i][i] = hcurl_error_form<double, scalar>; error_ord[i][i] = hcurl_error_form<Ord, Ord>;
//printf("Hcurl norm.\n");
break;
case HERMES_HDIV_NORM:
error_form[i][i] = hdiv_error_form<double, scalar>; error_ord[i][i] = hdiv_error_form<Ord, Ord>;
//printf("Hdiv norm.\n");
break;
case HERMES_L2_NORM:
error_form[i][i] = l2_error_form<double, scalar>; error_ord[i][i] = l2_error_form<Ord, Ord>;
//printf("L2 norm.\n");
break;
default: error("Unknown projection type in Adapt::Adapt().");
}
}
}
void Adapt::fix_shared_mesh_refinements(Mesh** meshes, Hermes::vector<ElementToRefine>& elems_to_refine,
int** idx, Hermes::vector<RefinementSelectors::Selector *> refinement_selectors) {
int num_elem_to_proc = elems_to_refine.size();
for(int inx = 0; inx < num_elem_to_proc; inx++) {
ElementToRefine& elem_ref = elems_to_refine[inx];
int current_quad_order = this->spaces[elem_ref.comp]->get_element_order(elem_ref.id);
Element* current_elem = meshes[elem_ref.comp]->get_element(elem_ref.id);
//select a refinement used by all components that share a mesh which is about to be refined
int selected_refinement = elem_ref.split;
for (int j = 0; j < this->num; j++)
{
if (selected_refinement == H2D_REFINEMENT_H) break; // iso refinement is max what can be recieved
if (j != elem_ref.comp && meshes[j] == meshes[elem_ref.comp]) { // if a mesh is shared
int ii = idx[elem_ref.id][j];
if (ii >= 0) { // and the sample element is about to be refined by another compoment
const ElementToRefine& elem_ref_ii = elems_to_refine[ii];
if (elem_ref_ii.split != selected_refinement && elem_ref_ii.split != H2D_REFINEMENT_P) { //select more complicated refinement
if ((elem_ref_ii.split == H2D_REFINEMENT_ANISO_H || elem_ref_ii.split == H2D_REFINEMENT_ANISO_V) && selected_refinement == H2D_REFINEMENT_P)
selected_refinement = elem_ref_ii.split;
else
selected_refinement = H2D_REFINEMENT_H;
}
}
}
}
//fix other refinements according to the selected refinement
if (selected_refinement != H2D_REFINEMENT_P)
{
//get suggested orders for the selected refinement
const int* suggested_orders = NULL;
if (selected_refinement == H2D_REFINEMENT_H)
suggested_orders = elem_ref.q;
//update orders
for (int j = 0; j < this->num; j++) {
if (j != elem_ref.comp && meshes[j] == meshes[elem_ref.comp]) { // if components share the mesh
// change currently processed refinement
if (elem_ref.split != selected_refinement) {
elem_ref.split = selected_refinement;
refinement_selectors[j]->generate_shared_mesh_orders(current_elem, current_quad_order, elem_ref.split, elem_ref.p, suggested_orders);
}
// change other refinements
int ii = idx[elem_ref.id][j];
if (ii >= 0) {
ElementToRefine& elem_ref_ii = elems_to_refine[ii];
if (elem_ref_ii.split != selected_refinement) {
elem_ref_ii.split = selected_refinement;
refinement_selectors[j]->generate_shared_mesh_orders(current_elem, current_quad_order, elem_ref_ii.split, elem_ref_ii.p, suggested_orders);
}
}
else { // element (of the other comp.) not refined at all: assign refinement
ElementToRefine elem_ref_new(elem_ref.id, j);
elem_ref_new.split = selected_refinement;
refinement_selectors[j]->generate_shared_mesh_orders(current_elem, current_quad_order, elem_ref_new.split, elem_ref_new.p, suggested_orders);
elems_to_refine.push_back(elem_ref_new);
}
}
}
}
}
}
int main(int argc, char* argv[])
{
if (NUMBER_OF_EIGENVALUES > 6) error("Maximum number of eigenvalues is 6.");
info("Desired number of eigenvalues: %d.", NUMBER_OF_EIGENVALUES);
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("../domain.mesh", &mesh);
// Perform initial mesh refinements (optional).
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Initialize boundary conditions.
DefaultEssentialBCConst bc_essential(Hermes::vector<std::string>(BDY_BOTTOM, BDY_RIGHT, BDY_TOP, BDY_LEFT), 0.0);
EssentialBCs bcs(&bc_essential);
// Create an H1 space with default shapeset.
H1Space space(&mesh, &bcs, P_INIT);
// Initialize the weak formulation.
WeakFormEigenLeft wf_left;
WeakFormEigenRight wf_right;
// Initialize refinement selector.
H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Initialize views.
ScalarView sview_1("", new WinGeom(0, 0, 400, 360));
sview_1.show_mesh(false);
sview_1.fix_scale_width(60);
ScalarView sview_2("", new WinGeom(405, 0, 400, 360));
sview_2.show_mesh(false);
sview_2.fix_scale_width(60);
ScalarView sview_3("", new WinGeom(810, 0, 400, 360));
sview_3.show_mesh(false);
sview_3.fix_scale_width(60);
ScalarView sview_4("", new WinGeom(0, 410, 400, 360));
sview_4.show_mesh(false);
sview_4.fix_scale_width(60);
ScalarView sview_5("", new WinGeom(405, 410, 400, 360));
sview_5.show_mesh(false);
sview_5.fix_scale_width(60);
ScalarView sview_6("", new WinGeom(810, 410, 400, 360));
sview_6.show_mesh(false);
sview_6.fix_scale_width(60);
OrderView oview("Polynomial orders", new WinGeom(1215, 0, 400, 360));
// DOF and CPU convergence graphs.
SimpleGraph graph_dof_est, graph_cpu_est;
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
Solution sln[NUMBER_OF_EIGENVALUES], ref_sln[NUMBER_OF_EIGENVALUES];
// Adaptivity loop:
int as = 1;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
info("Solving on reference mesh.");
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = Space::construct_refined_space(&space);
int ref_ndof = Space::get_num_dofs(ref_space);
info("ref_ndof: %d.", ref_ndof);
// Initialize matrices and matrix solver on referenc emesh.
RCP<SparseMatrix> matrix_left = rcp(new CSCMatrix());
RCP<SparseMatrix> matrix_right = rcp(new CSCMatrix());
Solver* solver = create_linear_solver(matrix_solver, matrix_left.get());
// Assemble the matrices on reference mesh.
DiscreteProblem* dp_left = new DiscreteProblem(&wf_left, ref_space);
dp_left->assemble(matrix_left.get());
DiscreteProblem* dp_right = new DiscreteProblem(&wf_right, ref_space);
dp_right->assemble(matrix_right.get());
// Time measurement.
cpu_time.tick();
// Time measurement.
cpu_time.tick(HERMES_SKIP);
EigenSolver es(matrix_left, matrix_right);
info("Calling Pysparse...");
es.solve(NUMBER_OF_EIGENVALUES, TARGET_VALUE, TOL, MAX_ITER);
info("Pysparse finished.");
es.print_eigenvalues();
// Initializing solution vector, solution and ScalarView.
double* ref_coeff_vec;
//Solution sln[NUMBER_OF_EIGENVALUES], ref_sln[NUMBER_OF_EIGENVALUES];
//ScalarView view("Solution", new WinGeom(0, 0, 440, 350));
// Reading solution vectors from file and visualizing.
double eigenval[NUMBER_OF_EIGENVALUES];
int neig = es.get_n_eigs();
if (neig != NUMBER_OF_EIGENVALUES) error("Mismatched number of eigenvectors in the eigensolver output file.");
for (int ieig = 0; ieig < NUMBER_OF_EIGENVALUES; ieig++) {
eigenval[ieig] = es.get_eigenvalue(ieig);
int n;
es.get_eigenvector(ieig, &ref_coeff_vec, &n);
// Convert coefficient vector into a Solution.
Solution::vector_to_solution(ref_coeff_vec, ref_space, &(ref_sln[ieig]));
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution %d on coarse mesh.", ieig);
OGProjection::project_global(&space, &(ref_sln[ieig]), &(sln[ieig]), matrix_solver);
}
// FIXME: Below, the adaptivity is done for the last eigenvector only,
// this needs to be changed to take into account all eigenvectors.
// View the coarse mesh solution and polynomial orders.
//char title[100];
//if (NUMBER_OF_EIGENVALUES > 0) {
// sprintf(title, "Solution 0, val = %g", eigenval[0]);
// sview_1.set_title(title);
// sview_1.show(&(sln[0]));
//}
//if (NUMBER_OF_EIGENVALUES > 1) {
// sprintf(title, "Solution 1, val = %g", eigenval[1]);
// sview_2.set_title(title);
// sview_2.show(&(sln[1]));
//}
//if (NUMBER_OF_EIGENVALUES > 2) {
// sprintf(title, "Solution 2, val = %g", eigenval[2]);
// sview_3.set_title(title);
// sview_3.show(&(sln[2]));
//}
//if (NUMBER_OF_EIGENVALUES > 3) {
// sprintf(title, "Solution 3, val = %g", eigenval[3]);
// sview_4.set_title(title);
// sview_4.show(&(sln[3]));
//}
//if (NUMBER_OF_EIGENVALUES > 4) {
// sprintf(title, "Solution 4, val = %g", eigenval[4]);
// sview_5.set_title(title);
// sview_5.show(&(sln[4]));
//}
//if (NUMBER_OF_EIGENVALUES > 5) {
// sprintf(title, "Solution 5, val = %g", eigenval[5]);
// sview_6.set_title(title);
// sview_6.show(&(sln[5]));
//}
//oview.show(&space);
// Calculate element errors and total error estimate.
info("Calculating error estimate.");
Hermes::vector<Space *> spaces;
for(int i = 0; i < NUMBER_OF_EIGENVALUES; i++) spaces.push_back(&space);
Adapt* adaptivity = new Adapt(spaces);
Hermes::vector<Solution *> slns;
if (NUMBER_OF_EIGENVALUES > 0) slns.push_back(&sln[0]);
if (NUMBER_OF_EIGENVALUES > 1) slns.push_back(&sln[1]);
if (NUMBER_OF_EIGENVALUES > 2) slns.push_back(&sln[2]);
if (NUMBER_OF_EIGENVALUES > 3) slns.push_back(&sln[3]);
if (NUMBER_OF_EIGENVALUES > 4) slns.push_back(&sln[4]);
if (NUMBER_OF_EIGENVALUES > 5) slns.push_back(&sln[5]);
Hermes::vector<Solution *> ref_slns;
if (NUMBER_OF_EIGENVALUES > 0) ref_slns.push_back(&ref_sln[0]);
if (NUMBER_OF_EIGENVALUES > 1) ref_slns.push_back(&ref_sln[1]);
if (NUMBER_OF_EIGENVALUES > 2) ref_slns.push_back(&ref_sln[2]);
if (NUMBER_OF_EIGENVALUES > 3) ref_slns.push_back(&ref_sln[3]);
if (NUMBER_OF_EIGENVALUES > 4) ref_slns.push_back(&ref_sln[4]);
if (NUMBER_OF_EIGENVALUES > 5) ref_slns.push_back(&ref_sln[5]);
Hermes::vector<double> component_errors;
double err_est_rel = adaptivity->calc_err_est(slns, ref_slns, &component_errors) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d.", Space::get_num_dofs(&space), Space::get_num_dofs(ref_space));
if (NUMBER_OF_EIGENVALUES > 0) info("err_est_rel[0]: %g%%", component_errors[0] * 100);
if (NUMBER_OF_EIGENVALUES > 1) info("err_est_rel[1]: %g%%", component_errors[1] * 100);
if (NUMBER_OF_EIGENVALUES > 2) info("err_est_rel[2]: %g%%", component_errors[2] * 100);
if (NUMBER_OF_EIGENVALUES > 3) info("err_est_rel[3]: %g%%", component_errors[3] * 100);
if (NUMBER_OF_EIGENVALUES > 4) info("err_est_rel[4]: %g%%", component_errors[4] * 100);
if (NUMBER_OF_EIGENVALUES > 5) info("err_est_rel[5]: %g%%", component_errors[5] * 100);
// Time measurement.
cpu_time.tick();
// Add entry to DOF and CPU convergence graphs.
graph_dof_est.add_values(Space::get_num_dofs(&space), err_est_rel);
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu_est.save("conv_cpu_est.dat");
// Wait for keypress.
//View::wait(HERMES_WAIT_KEYPRESS);
// If err_est too large, adapt the mesh.
if (err_est_rel < ERR_STOP) done = true;
else
{
info("Adapting coarse mesh.");
Hermes::vector<RefinementSelectors::Selector *> selectors;
for(int i = 0; i < NUMBER_OF_EIGENVALUES; i++)
selectors.push_back(&selector);
done = adaptivity->adapt(selectors, THRESHOLD, STRATEGY, MESH_REGULARITY);
// Increase the counter of performed adaptivity steps.
if (done == false) as++;
}
if (Space::get_num_dofs(&space) >= NDOF_STOP) done = true;
// Clean up.
delete solver;
delete adaptivity;
if(done == false) delete ref_space->get_mesh();
delete ref_space;
delete dp_left;
delete dp_right;
}
while (done == false);
int ndof = Space::get_num_dofs(&space);
if (ndof < 450) { // Was 401 when this test was created.
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}
bool rk_time_step(double current_time, double time_step, ButcherTable* const bt,
scalar* coeff_vec, scalar* err_vec, DiscreteProblem* dp, MatrixSolverType matrix_solver,
bool verbose, bool is_linear, double newton_tol, int newton_max_iter,
double newton_damping_coeff, double newton_max_allowed_residual_norm)
{
// Check for not implemented features.
if (matrix_solver != SOLVER_UMFPACK)
error("Sorry, rk_time_step() still only works with UMFpack.");
if (dp->get_weak_formulation()->get_neq() > 1)
error("Sorry, rk_time_step() does not work with systems yet.");
// Get number of stages from the Butcher's table.
int num_stages = bt->get_size();
// Check whether the user provided a second B-row if he wants
// err_vec.
if(err_vec != NULL) {
double b2_coeff_sum = 0;
for (int i=0; i < num_stages; i++) b2_coeff_sum += fabs(bt->get_B2(i));
if (b2_coeff_sum < 1e-10)
error("err_vec != NULL but the B2 row in the Butcher's table is zero in rk_time_step().");
}
// Matrix for the time derivative part of the equation (left-hand side).
UMFPackMatrix* matrix_left = new UMFPackMatrix();
// Matrix and vector for the rest (right-hand side).
UMFPackMatrix* matrix_right = new UMFPackMatrix();
UMFPackVector* vector_right = new UMFPackVector();
// Create matrix solver.
Solver* solver = create_linear_solver(matrix_solver, matrix_right, vector_right);
// Get original space, mesh, and ndof.
dp->get_space(0);
Mesh* mesh = dp->get_space(0)->get_mesh();
int ndof = dp->get_space(0)->get_num_dofs();
// Create spaces for stage solutions. This is necessary
// to define a num_stages x num_stages block weak formulation.
Hermes::vector<Space*> stage_spaces;
stage_spaces.push_back(dp->get_space(0));
for (int i = 1; i < num_stages; i++) {
stage_spaces.push_back(dp->get_space(0)->dup(mesh));
}
Space::assign_dofs(stage_spaces);
// Create a multistage weak formulation.
WeakForm stage_wf_left; // For the matrix M (size ndof times ndof).
WeakForm stage_wf_right(num_stages); // For the rest of equation (written on the right),
// size num_stages*ndof times num_stages*ndof.
create_stage_wf(current_time, time_step, bt, dp, &stage_wf_left, &stage_wf_right);
// Initialize discrete problems for the assembling of the
// matrix M and the stage Jacobian matrix and residual.
DiscreteProblem stage_dp_left(&stage_wf_left, dp->get_space(0));
DiscreteProblem stage_dp_right(&stage_wf_right, stage_spaces);
// Vector K_vector of length num_stages * ndof. will represent
// the 'k_i' vectors in the usual R-K notation.
scalar* K_vector = new scalar[num_stages*ndof];
memset(K_vector, 0, num_stages * ndof * sizeof(scalar));
// Vector u_prev_vec will represent y_n + h \sum_{j=1}^s a_{ij}k_i
// in the usual R-K notation.
scalar* u_prev_vec = new scalar[num_stages*ndof];
// Vector for the left part of the residual.
scalar* vector_left = new scalar[num_stages*ndof];
// Prepare residuals of stage solutions.
Hermes::vector<Solution*> residuals;
Hermes::vector<bool> add_dir_lift;
for (int i = 0; i < num_stages; i++) {
residuals.push_back(new Solution(mesh));
add_dir_lift.push_back(false);
}
// Assemble the block-diagonal mass matrix M of size ndof times ndof.
// The corresponding part of the global residual vector is obtained
// just by multiplication.
stage_dp_left.assemble(matrix_left);
// The Newton's loop.
double residual_norm;
int it = 1;
while (true)
{
// Prepare vector Y_n + h\sum_{j=1}^s a_{ij} K_j.
for (int i = 0; i < num_stages; i++) { // block row
for (int idx = 0; idx < ndof; idx++) {
scalar increment = 0;
for (int j = 0; j < num_stages; j++) {
increment += bt->get_A(i, j) * K_vector[j*ndof + idx];
}
u_prev_vec[i*ndof + idx] = coeff_vec[idx] + time_step * increment;
}
}
multiply_as_diagonal_block_matrix(matrix_left, num_stages,
K_vector, vector_left);
// Assemble the block Jacobian matrix of the stationary residual F
// Diagonal blocks are created even if empty, so that matrix_left
// can be added later.
bool rhs_only = false;
bool force_diagonal_blocks = true;
stage_dp_right.assemble(u_prev_vec, matrix_right, vector_right,
rhs_only, force_diagonal_blocks);
matrix_right->add_to_diagonal_blocks(num_stages, matrix_left);
vector_right->add_vector(vector_left);
// Multiply the residual vector with -1 since the matrix
// equation reads J(Y^n) \deltaY^{n+1} = -F(Y^n).
vector_right->change_sign();
// Measure the residual norm.
if (HERMES_RESIDUAL_AS_VECTOR_RK) {
// Calculate the l2-norm of residual vector.
residual_norm = get_l2_norm(vector_right);
}
else {
// Translate residual vector into residual functions.
Solution::vector_to_solutions(vector_right, stage_dp_right.get_spaces(),
residuals, add_dir_lift);
residual_norm = calc_norms(residuals);
}
// Info for the user.
if (verbose) info("---- Newton iter %d, ndof %d, residual norm %g",
it, ndof, residual_norm);
// If maximum allowed residual norm is exceeded, fail.
if (residual_norm > newton_max_allowed_residual_norm) {
if (verbose) {
info("Current residual norm: %g", residual_norm);
info("Maximum allowed residual norm: %g", newton_max_allowed_residual_norm);
info("Newton solve not successful, returning false.");
}
return false;
}
// If residual norm is within tolerance, or the maximum number
// of iteration has been reached, or the problem is linear, then quit.
if ((residual_norm < newton_tol || it > newton_max_iter) && it > 1) break;
// Solve the linear system.
if(!solver->solve()) error ("Matrix solver failed.\n");
// Add \deltaY^{n+1} to Y^n.
for (int i = 0; i < num_stages*ndof; i++) {
K_vector[i] += newton_damping_coeff * solver->get_solution()[i];
}
// If the problem is linear, quit.
if (is_linear) {
if (verbose) {
info("Terminating Newton's loop as problem is linear.");
}
break;
}
// Increase iteration counter.
it++;
}
// If max number of iterations was exceeded, fail.
if (it >= newton_max_iter) {
if (verbose) info("Maximum allowed number of Newton iterations exceeded, returning false.");
return false;
}
// Calculate the vector \sum_{j=1}^s b_j k_j.
Vector* rk_increment_vector = create_vector(matrix_solver);
rk_increment_vector->alloc(ndof);
for (int i = 0; i < ndof; i++) {
rk_increment_vector->set(i, 0);
for (int j = 0; j < num_stages; j++) {
rk_increment_vector->add(i, bt->get_B(j) * K_vector[j*ndof + i]);
}
}
// Calculate Y^{n+1} = Y^n + h \sum_{j=1}^s b_j k_j.
for (int i = 0; i < ndof; i++) coeff_vec[i] += time_step * rk_increment_vector->get(i);
// If err_vec is not NULL, use the second B-row in the Butcher's
// table to calculate the second approximation Y_{n+1}. Then
// subtract the original one from it, and return this as an
// error vector err_vec.
if (err_vec != NULL) {
for (int i = 0; i < ndof; i++) {
rk_increment_vector->set(i, 0);
for (int j = 0; j < num_stages; j++) {
rk_increment_vector->add(i, bt->get_B2(j) * K_vector[j*ndof + i]);
}
}
for (int i = 0; i < ndof; i++) err_vec[i] = time_step * rk_increment_vector->get(i);
for (int i = 0; i < ndof; i++) err_vec[i] = err_vec[i] - coeff_vec[i];
}
// Clean up.
delete matrix_left;
delete matrix_right;
delete vector_right;
delete solver;
delete rk_increment_vector;
// Delete stage spaces, but not the first (original) one.
for (int i = 1; i < num_stages; i++) delete stage_spaces[i];
// Delete all residuals.
for (int i = 0; i < num_stages; i++) delete residuals[i];
// TODO: Delete stage_wf, in particular its external solutions
// stage_time_sol[i], i = 0, 1, ..., num_stages-1.
// Delete stage_vec and u_prev_vec.
delete [] K_vector;
delete [] u_prev_vec;
// debug
delete [] vector_left;
return true;
}