int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
MeshReaderH2D mloader;
mloader.load(mesh_file.c_str(), &mesh);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Solution variables.
Solution<double> sln1, sln2, sln3, sln4;
Hermes::vector<Solution<double>*> solutions(&sln1, &sln2, &sln3, &sln4);
// Define initial conditions.
Hermes::Mixins::Loggable::Static::info("Setting initial conditions.");
ConstantSolution<double> iter1(&mesh, 1.00), iter2(&mesh, 1.00), iter3(&mesh, 1.00), iter4(&mesh, 1.00);
Hermes::vector<MeshFunction<double>*> iterates(&iter1, &iter2, &iter3, &iter4);
// Create H1 spaces with default shapesets.
H1Space<double> space1(&mesh, P_INIT_1);
H1Space<double> space2(&mesh, P_INIT_2);
H1Space<double> space3(&mesh, P_INIT_3);
H1Space<double> space4(&mesh, P_INIT_4);
Hermes::vector<const Space<double>* > spaces(&space1, &space2, &space3, &space4);
int ndof = Space<double>::get_num_dofs(spaces);
Hermes::Mixins::Loggable::Static::info("ndof = %d", ndof);
// Initialize views.
ScalarView view1("Neutron flux 1", new WinGeom(0, 0, 320, 600));
ScalarView view2("Neutron flux 2", new WinGeom(350, 0, 320, 600));
ScalarView view3("Neutron flux 3", new WinGeom(700, 0, 320, 600));
ScalarView view4("Neutron flux 4", new WinGeom(1050, 0, 320, 600));
// Do not show meshes, set 3D mode.
view1.show_mesh(false); view1.set_3d_mode(true);
view2.show_mesh(false); view2.set_3d_mode(true);
view3.show_mesh(false); view3.set_3d_mode(true);
view4.show_mesh(false); view4.set_3d_mode(true);
// Load physical data of the problem for the 4 energy groups.
Hermes::Hermes2D::WeakFormsNeutronics::Multigroup::MaterialProperties::Diffusion::MaterialPropertyMaps matprop(4);
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();
// Printing table of material properties.
std::cout << matprop;
// Initialize the weak formulation.
CustomWeakForm wf(matprop, iterates, k_eff, bdy_vacuum);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, spaces);
// Initialize Newton solver.
NewtonSolver<double> newton(&dp);
// Time measurement.
Hermes::Mixins::TimeMeasurable cpu_time;
// Main power iteration loop:
int it = 1; bool done = false;
do
{
Hermes::Mixins::Loggable::Static::info("------------ Power iteration %d:", it);
Hermes::Mixins::Loggable::Static::info("Newton's method.");
// Perform Newton's iteration.
try
{
newton.set_newton_max_iter(NEWTON_MAX_ITER);
newton.set_newton_tol(NEWTON_TOL);
newton.solve_keep_jacobian();
}
catch(Hermes::Exceptions::Exception e)
{
e.printMsg();
throw Hermes::Exceptions::Exception("Newton's iteration failed.");
}
// Debug.
//printf("\n=================================================\n");
//for (int d = 0; d < ndof; d++) printf("%g ", newton.get_sln_vector()[d]);
// Translate the resulting coefficient vector into a Solution.
Solution<double>::vector_to_solutions(newton.get_sln_vector(), spaces, solutions);
// Show intermediate solutions.
view1.show(&sln1);
view2.show(&sln2);
view3.show(&sln3);
view4.show(&sln4);
// Compute eigenvalue.
SourceFilter source(solutions, &matprop, core);
SourceFilter source_prev(iterates, &matprop, core);
double k_new = k_eff * (integrate(&source, core) / integrate(&source_prev, core));
Hermes::Mixins::Loggable::Static::info("Largest eigenvalue: %.8g, rel. difference from previous it.: %g", k_new, fabs((k_eff - k_new) / k_new));
// Stopping criterion.
if (fabs((k_eff - k_new) / k_new) < ERROR_STOP) done = true;
// Update eigenvalue.
k_eff = k_new;
wf.update_keff(k_eff);
if (!done)
{
// Save solutions for the next iteration.
iter1.copy(&sln1);
iter2.copy(&sln2);
iter3.copy(&sln3);
iter4.copy(&sln4);
it++;
}
}
while (!done);
// Time measurement.
cpu_time.tick();
// Show solutions.
view1.show(&sln1);
view2.show(&sln2);
view3.show(&sln3);
view4.show(&sln4);
// Skip visualization time.
cpu_time.tick(Hermes::Mixins::TimeMeasurable::HERMES_SKIP);
// Print timing information.
Hermes::Mixins::Loggable::Static::info("Total running time: %g s", cpu_time.accumulated());
// Wait for all views to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("reactor.mesh", &mesh);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Solution variables.
Solution sln1, sln2, sln3, sln4;
Solution iter1, iter2, iter3, iter4;
Hermes::Tuple<Solution*> solutions(&sln1, &sln2, &sln3, &sln4);
// Define initial conditions.
info("Setting initial conditions.");
iter1.set_const(&mesh, 1.00);
iter2.set_const(&mesh, 1.00);
iter3.set_const(&mesh, 1.00);
iter4.set_const(&mesh, 1.00);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_neumann(BDY_SYM);
bc_types.add_bc_newton(BDY_VACUUM);
// Create H1 spaces with default shapesets.
H1Space space1(&mesh, &bc_types, P_INIT_1);
H1Space space2(&mesh, &bc_types, P_INIT_2);
H1Space space3(&mesh, &bc_types, P_INIT_3);
H1Space space4(&mesh, &bc_types, P_INIT_4);
Hermes::Tuple<Space*> spaces(&space1, &space2, &space3, &space4);
int ndof = Space::get_num_dofs(Hermes::Tuple<Space*>(&space1, &space2, &space3, &space4));
info("ndof = %d.", ndof);
// Initialize views.
ScalarView view1("Neutron flux 1", new WinGeom(0, 0, 320, 600));
ScalarView view2("Neutron flux 2", new WinGeom(350, 0, 320, 600));
ScalarView view3("Neutron flux 3", new WinGeom(700, 0, 320, 600));
ScalarView view4("Neutron flux 4", new WinGeom(1050, 0, 320, 600));
// Do not show meshes.
view1.show_mesh(false); view1.set_3d_mode(true);
view2.show_mesh(false); view2.set_3d_mode(true);
view3.show_mesh(false); view3.set_3d_mode(true);
view4.show_mesh(false); view4.set_3d_mode(true);
// Initialize the weak formulation.
WeakForm wf(4);
wf.add_matrix_form(0, 0, callback(biform_0_0), HERMES_SYM);
wf.add_matrix_form(1, 1, callback(biform_1_1), HERMES_SYM);
wf.add_matrix_form(1, 0, callback(biform_1_0));
wf.add_matrix_form(2, 2, callback(biform_2_2), HERMES_SYM);
wf.add_matrix_form(2, 1, callback(biform_2_1));
wf.add_matrix_form(3, 3, callback(biform_3_3), HERMES_SYM);
wf.add_matrix_form(3, 2, callback(biform_3_2));
wf.add_vector_form(0, callback(liform_0), marker_core, Hermes::Tuple<MeshFunction*>(&iter1, &iter2, &iter3, &iter4));
wf.add_vector_form(1, callback(liform_1), marker_core, Hermes::Tuple<MeshFunction*>(&iter1, &iter2, &iter3, &iter4));
wf.add_vector_form(2, callback(liform_2), marker_core, Hermes::Tuple<MeshFunction*>(&iter1, &iter2, &iter3, &iter4));
wf.add_vector_form(3, callback(liform_3), marker_core, Hermes::Tuple<MeshFunction*>(&iter1, &iter2, &iter3, &iter4));
wf.add_matrix_form_surf(0, 0, callback(biform_surf_0_0), BDY_VACUUM);
wf.add_matrix_form_surf(1, 1, callback(biform_surf_1_1), BDY_VACUUM);
wf.add_matrix_form_surf(2, 2, callback(biform_surf_2_2), BDY_VACUUM);
wf.add_matrix_form_surf(3, 3, callback(biform_surf_3_3), BDY_VACUUM);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, spaces, is_linear);
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
if (matrix_solver == SOLVER_AZTECOO)
{
((AztecOOSolver*) solver)->set_solver(iterative_method);
((AztecOOSolver*) solver)->set_precond(preconditioner);
// Using default iteration parameters (see solver/aztecoo.h).
}
// Time measurement.
TimePeriod cpu_time, solver_time;
// Main power iteration loop:
int iter = 1; bool done = false;
bool rhs_only = false;
solver->set_factorization_scheme(HERMES_REUSE_FACTORIZATION_COMPLETELY);
do
{
info("------------ Power iteration %d:", iter);
info("Assembling the stiffness matrix and right-hand side vector.");
dp.assemble(matrix, rhs, rhs_only);
/*
// Testing the factorization reuse schemes for direct solvers.
if (iter == 10)
solver->set_factorization_scheme(HERMES_REUSE_MATRIX_REORDERING);
if (iter == 20)
solver->set_factorization_scheme(HERMES_REUSE_MATRIX_REORDERING_AND_SCALING);
if (iter == 30)
solver->set_factorization_scheme(HERMES_REUSE_FACTORIZATION_COMPLETELY);
*/
info("Solving the matrix problem by %s.", MatrixSolverNames[matrix_solver].c_str());
solver_time.tick(HERMES_SKIP);
bool solved = solver->solve();
solver_time.tick();
if(solved)
Solution::vector_to_solutions(solver->get_solution(), spaces, solutions);
else
error ("Matrix solver failed.\n");
// Show intermediate solutions.
// view1.show(&sln1);
// view2.show(&sln2);
// view3.show(&sln3);
// view4.show(&sln4);
SimpleFilter source(source_fn, Hermes::Tuple<MeshFunction*>(&sln1, &sln2, &sln3, &sln4));
SimpleFilter source_prev(source_fn, Hermes::Tuple<MeshFunction*>(&iter1, &iter2, &iter3, &iter4));
// Compute eigenvalue.
double k_new = k_eff * (integrate(&source, marker_core) / integrate(&source_prev, marker_core));
info("Largest eigenvalue: %.8g, rel. difference from previous it.: %g", k_new, fabs((k_eff - k_new) / k_new));
// Stopping criterion.
if (fabs((k_eff - k_new) / k_new) < ERROR_STOP) done = true;
// Update eigenvalue.
k_eff = k_new;
if (!done)
{
// Save solutions for the next iteration.
iter1.copy(&sln1);
iter2.copy(&sln2);
iter3.copy(&sln3);
iter4.copy(&sln4);
// Don't need to reassemble the system matrix in further iterations,
// only the rhs changes to reflect the progressively updated source.
rhs_only = true;
iter++;
}
}
while (!done);
// Time measurement.
cpu_time.tick();
solver_time.tick(HERMES_SKIP);
// Print timing information.
verbose("Average solver time for one power iteration: %g s", solver_time.accumulated() / iter);
// Clean up.
delete matrix;
delete rhs;
delete solver;
// Show solutions.
view1.show(&sln1);
view2.show(&sln2);
view3.show(&sln3);
view4.show(&sln4);
// Skip visualization time.
cpu_time.tick(HERMES_SKIP);
// Print timing information.
verbose("Total running time: %g s", cpu_time.accumulated());
// 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;
}
main(int argc, char *argv[]) {
char name[256];
int i,j,k,squareSize,maxCZ;
double radiusL,radiusC,num;
double x1,y1,z1,xy1;
double x2,y2,z2,xy2;
double x3,y3,z3,xy3;
GraphicsSpace space1("lightTest1.ppm");
space1.createImage(301,301);
space1.addSphere(100,100,0, 45, 255,0,0, 1,.5,.5,30);
space1.addSphere(0,100,0, 45, 255,255,0, 1,1,1,30);
space1.addSphere(-100,100,0, 45, 255,255,255, 1,.5,.5,30);
space1.addSphere(-100,0,0, 45, 0,255,255, 1,1,1,30);
space1.addSphere(-100,-100,0, 45, 0,255,0, 1,.5,.5,30);
space1.addSphere(0,-100,0, 45, 255,0,255, 1,1,1,30);
space1.addSphere(100,-100,0, 45, 0,0,255, 1,.5,.5,30);
space1.addSphere(100,0,0, 45, 128,128,255, 1,1,1,30);
//lighting
space1.addLightAmbient(.5);
//space1.addLightPoint(0,0,-100, 1, 255,255,255);
space1.setCamera(0,0,-600);
space1.setViewPlaneCenter(0,0,-30);
space1.setViewPlaneNormal(1,1,1);//not important right now
//render image
space1.render();
space1.writeImage();
//image 2
GraphicsSpace space2("lightTest2.ppm");
space2.createImage(301,301);
// space2.setBackground(255,255,255);
space2.addSphere(100,100,0, 45, 255,0,0, 1,.5,.5,30);
space2.addSphere(0,100,0, 45, 255,255,0, 1,1,1,30);
space2.addSphere(-100,100,0, 45, 255,255,255, 1,.5,.5,30);
space2.addSphere(-100,0,0, 45, 0,255,255, 1,1,1,30);
space2.addSphere(-100,-100,0, 45, 0,255,0, 1,.5,.5,30);
space2.addSphere(0,-100,0, 45, 255,0,255, 1,1,1,30);
space2.addSphere(100,-100,0, 45, 0,0,255, 1,.5,.5,30);
space2.addSphere(100,0,0, 45, 128,128,255, 1,1,1,30);
//lighting
//space2.addLightAmbient(.5);
space2.addLightPoint(0,0,-100, 1, 255,255,255);
space2.setCamera(0,0,-600);
space2.setViewPlaneCenter(0,0,-30);
space2.setViewPlaneNormal(1,1,1);//not important right now
//render image
space2.render();
space2.writeImage();
GraphicsSpace space4("lightTest4.ppm");
space4.createImage(501,501);
for (i=-250;i<=250;i+=100)
for (j=-250;j<=250;j+=100){
space4.addSphere(i,j,0, 30, 0,255,0, 1,1,.5,30);
}
space4.addPlane(0,0,50, 0,0,1, 0,0,255, 1,.8,1,30);
//lighting
space4.addLightAmbient(.1);
space4.addLightPoint(50,50,-200, 1, 255,255,255);
space4.setCamera(0,0,-600);
space4.setViewPlaneCenter(0,0,-30);
space4.setViewPlaneNormal(1,1,1);//not important right now
//render image
space4.render();
space4.writeImage();
GraphicsSpace space5("lightTest5.ppm");
space5.createImage(501,501);
space5.addPlane(0,0,-100, 0,0,1, 100,100,100, 1,.8,1,30);
space5.addSphere(300,0,0, 100, 255,0,0, 1,1,1,30);
//pyramid
space5.addTriangle(-100,-100,-100, -100,100,-100, 0,0,100, 0,255,0, 1,1,1,30);
space5.addTriangle(-100,-100,-100, 100,-100,-100, 0,0,100, 0,255,0, 1,1,1,30);
space5.addTriangle(100,100,-100, -100,100,-100, 0,0,100, 0,255,0, 1,1,1,30);
space5.addTriangle(100,100,-100, 100,-100,-100, 0,0,100, 0,255,0, 1,1,1,30);
//cube
////base top
space5.addTriangle(-200,-100,-100, -200,100,-100, -400,-100,-100, 0,0,255, 1,1,1,30);
space5.addTriangle(-400,100,-100, -200,100,-100, -400,-100,-100, 0,0,255, 1,1,1,30);
space5.addTriangle(-200,-100,100, -200,100,100, -400,-100,100, 0,0,255, 1,1,1,30);
space5.addTriangle(-400,100,100, -200,100,100, -400,-100,100, 0,0,255, 1,1,1,30);
////left right
space5.addTriangle(-400,100,-100, -400,100,100, -200,100,100, 0,0,255, 1,1,1,30);
space5.addTriangle(-400,100,-100, -200,100,-100, -200,100,100, 0,0,255, 1,1,1,30);
space5.addTriangle(-400,-100,-100, -400,-100,100, -200,-100,100, 0,0,255, 1,1,1,30);
space5.addTriangle(-400,-100,-100, -200,-100,-100, -200,-100,100, 0,0,255, 1,1,1,30);
////other left right
space5.addTriangle(-200,-100,-100, -200,100,100, -200,-100,100, 0,0,255, 1,1,1,30);
space5.addTriangle(-200,-100,-100, -200,100,100, -200,100,-100, 0,0,255, 1,1,1,30);
space5.addTriangle(-400,-100,-100, -400,100,100, -400,-100,100, 0,0,255, 1,1,1,30);
space5.addTriangle(-400,-100,-100, -400,100,100, -400,100,-100, 0,0,255, 1,1,1,30);
//lighting
space5.addLightAmbient(.1);
space5.addLightPoint(0,300,400, 1, 100,100,100);
space5.addLightPoint(-500,300,400, 1, 50,50,50);
space5.setCamera(0,0,900);
space5.setViewPlaneCenter(0,0,300);
space5.setViewPlaneNormal(1,1,1);//not important right now
//render image
space5.render();
space5.writeImage();
//image 3
GraphicsSpace space3("lightTest3.ppm");
space3.createImage(501,501);
// create edge planes
space3.addPlane(300,0,0, 1,0,0, 255,255,255, 1,.8,1,30);
space3.addPlane(-300,0,0, 1,0,0, 255,255,255, 1,.8,1,30);
space3.addPlane(0,300,0, 0,1,0, 255,255,255, 1,.8,1,30);
space3.addPlane(0,-300,0, 0,1,0, 255,255,255, 1,.8,1,30);
radiusL=200;
radiusC=50;
num=12;
// create outside circles
for (i=0;i<360;i+=360/num){
x1=radiusL*cos((double)i*PI/180.0);
y1=radiusL*sin((double)i*PI/180.0);
space3.addSphere(x1,y1,60, radiusC, 255,0,0, 1,(double)i/360+1/num,(double)i/360+1/num,((double)i/360+1/num)*30);
}
// //
// //create center circle with triangles
num=24;
radiusC=100;
for (k=0;k<num/2;k++){
z1=radiusC*cos((double)k*PI*360/(num*180.0));
xy1=radiusC*sin((double)k*PI*360/(num*180.0));
z2=radiusC*cos((double)(k+1)*PI*360/(num*180.0));
xy2=radiusC*sin((double)(k+1)*PI*360/(num*180.0));
z3=radiusC*cos((double)(k+1)*PI*360/(num*180.0));
xy3=radiusC*sin((double)(k+1)*PI*360/(num*180.0));
if (k%2==1){
for (i=0;i<num;i++){
x1=xy1*cos((double)i*PI*360/(num*180));
y1=xy1*sin((double)i*PI*360/(num*180));
x2=xy2*cos(((double)i-.5)*PI*360/(num*180));
y2=xy2*sin(((double)i-.5)*PI*360/(num*180));
x3=xy3*cos(((double)i+.5)*PI*360/(num*180));
y3=xy3*sin(((double)i+.5)*PI*360/(num*180));
space3.addTriangle(z1,y1,x1,z2,y2,x2,z3,y3,x3, 0,0,255, 1,1,1,30);
}
} else {
for (i=0;i<num;i++){
x1=xy1*cos(((double)i+.5)*PI*360/(num*180));
y1=xy1*sin(((double)i+.5)*PI*360/(num*180));
x2=xy2*cos(((double)i)*PI*360/(num*180));
y2=xy2*sin(((double)i)*PI*360/(num*180));
x3=xy3*cos(((double)i+1)*PI*360/(num*180));
y3=xy3*sin(((double)i+1)*PI*360/(num*180));
space3.addTriangle(z1,y1,x1,z2,y2,x2,z3,y3,x3, 0,0,255, 1,1,1,30);
}
}
if (k>0){
z1=radiusC*cos((double)(k+1)*PI*360/(num*180.0));
xy1=radiusC*sin((double)(k+1)*PI*360/(num*180.0));
z2=radiusC*cos((double)(k)*PI*360/(num*180.0));
xy2=radiusC*sin((double)(k)*PI*360/(num*180.0));
z3=radiusC*cos((double)(k)*PI*360/(num*180.0));
xy3=radiusC*sin((double)(k)*PI*360/(num*180.0));
if (k%2==0){
for (i=0;i<num;i++){
x1=xy1*cos((double)i*PI*360/(num*180));
y1=xy1*sin((double)i*PI*360/(num*180));
x2=xy2*cos(((double)i-.5)*PI*360/(num*180));
y2=xy2*sin(((double)i-.5)*PI*360/(num*180));
x3=xy3*cos(((double)i+.5)*PI*360/(num*180));
y3=xy3*sin(((double)i+.5)*PI*360/(num*180));
space3.addTriangle(z1,y1,x1,z2,y2,x2,z3,y3,x3, 0,0,255, 1,1,1,30);
}
} else {
for (i=0;i<num;i++){
x1=xy1*cos(((double)i+.5)*PI*360/(num*180));
y1=xy1*sin(((double)i+.5)*PI*360/(num*180));
x2=xy2*cos(((double)i)*PI*360/(num*180));
y2=xy2*sin(((double)i)*PI*360/(num*180));
x3=xy3*cos(((double)i+1)*PI*360/(num*180));
y3=xy3*sin(((double)i+1)*PI*360/(num*180));
space3.addTriangle(z1,y1,x1,z2,y2,x2,z3,y3,x3, 0,0,255, 1,1,1,30);
}
}
}
}
//
//lighting
space3.addLightPoint(0,0,-200, 1, 255,255,255);
space3.setCamera(0,0,-600);
space3.setViewPlaneCenter(0,0,-30);
space3.setViewPlaneNormal(1,1,1);//not important right now
//render image
space3.render();
space3.writeImage();
}
void X86_Stm_print (S s)
{
Assert_ASSERT(s);
switch (s->kind){
case X86_STM_MOVERR:
space4 ();
print ("movl ");
X86_Register_print (s->u.moverr.src);
print (", ");
X86_Register_print (s->u.moverr.dest);
break;
case X86_STM_MOVERI:
space4 ();
print ("movl $");
print (Int_toString (s->u.moveri.src));
print (", ");
X86_Register_print (s->u.moveri.dest);
break;
case X86_STM_LOAD:
space4 ();
print ("movl ");
X86_Operand_print (s->u.load.src);
print (", ");
X86_Register_print (s->u.load.dest);
break;
case X86_STM_STORE:
space4 ();
print ("movl ");
X86_Register_print (s->u.store.src);
print (", ");
X86_Operand_print (s->u.store.dest);
break;
case X86_STM_BOP:
space4 ();
X86_Operator_print (s->u.bop.op);
X86_Register_print (s->u.bop.src);
print (", ");
X86_Register_print (s->u.bop.dest);
break;
case X86_STM_UOP:
space4 ();
X86_Operator_print (s->u.uop.op);
X86_Register_print (s->u.uop.dest);
break;
case X86_STM_CALL:
space4 ();
print ("call ");
print (Id_toString (s->u.call.name));
break;
case X86_STM_CMP:
space4 ();
print ("cmpl ");
X86_Register_print (s->u.cmp.src);
print (", ");
X86_Register_print (s->u.cmp.dest);
break;
case X86_STM_LABEL:
space2();
print (Label_toString (s->u.label));
print (":");
break;
case X86_STM_JE:
space4 ();
print ("je ");
print (Label_toString (s->u.je));
break;
case X86_STM_JL:
space4 ();
print ("jl ");
print (Label_toString (s->u.je));
break;
case X86_STM_JUMP:
space4 ();
print ("jmp ");
print (Label_toString (s->u.jump));
break;
case X86_STM_PUSH:
space4 ();
print ("pushl ");
X86_Register_print (s->u.push);
break;
case X86_STM_NEG:
space4 ();
print ("negl ");
X86_Register_print (s->u.neg);
break;
case X86_STM_SETL:
space4 ();
print ("setl ");
X86_Register_print (s->u.setAny);
break;
case X86_STM_SETLE:
space4 ();
print ("setle ");
X86_Register_print (s->u.setAny);
break;
case X86_STM_SETG:
space4 ();
print ("setg ");
X86_Register_print (s->u.setAny);
break;
case X86_STM_SETGE:
space4 ();
print ("setge ");
X86_Register_print (s->u.setAny);
break;
case X86_STM_SETE:
space4 ();
print ("sete ");
X86_Register_print (s->u.setAny);
break;
case X86_STM_SETNE:
space4 ();
print ("setne ");
X86_Register_print (s->u.setAny);
break;
case X86_STM_XOR:
space4 ();
print ("xorl ");
X86_Register_print (s->u.xor.src);
print (", ");
X86_Register_print (s->u.xor.dest);
break;
case X86_STM_EXTENDAL:
space4 ();
print ("cbtw\n");
space4 ();
print ("cwtl");
break;
case X86_STM_NOT:{
space4 ();
print ("notl ");
X86_Register_print (s->u.not);
break;
}
case X86_STM_RETURN:
space4 ();
print ("leave\n\tret");
break;
case X86_STM_CLTD:
space4 ();
print ("cltd");
break;
case X86_STM_INC:
space4 ();
print ("incl ");
X86_Register_print (s->u.inc);
break;
default:
Error_impossible();
break;
}
print ("\n");
return;
}
int main(int argc, char* argv[])
{
// Instantiate a class with global functions.
Hermes2D hermes2d;
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("reactor.mesh", &mesh);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Solution variables.
Solution sln1, sln2, sln3, sln4;
Hermes::vector<Solution*> solutions(&sln1, &sln2, &sln3, &sln4);
// Define initial conditions.
info("Setting initial conditions.");
Solution iter1, iter2, iter3, iter4;
iter1.set_const(&mesh, 1.00);
iter2.set_const(&mesh, 1.00);
iter3.set_const(&mesh, 1.00);
iter4.set_const(&mesh, 1.00);
Hermes::vector<MeshFunction*> iterates(&iter1, &iter2, &iter3, &iter4);
// Create H1 spaces with default shapesets.
H1Space space1(&mesh, P_INIT_1);
H1Space space2(&mesh, P_INIT_2);
H1Space space3(&mesh, P_INIT_3);
H1Space space4(&mesh, P_INIT_4);
Hermes::vector<Space*> spaces(&space1, &space2, &space3, &space4);
int ndof = Space::get_num_dofs(spaces);
info("ndof = %d.", ndof);
// Initialize views.
ScalarView view1("Neutron flux 1", new WinGeom(0, 0, 320, 600));
ScalarView view2("Neutron flux 2", new WinGeom(350, 0, 320, 600));
ScalarView view3("Neutron flux 3", new WinGeom(700, 0, 320, 600));
ScalarView view4("Neutron flux 4", new WinGeom(1050, 0, 320, 600));
// Do not show meshes.
view1.show_mesh(false); view1.set_3d_mode(true);
view2.show_mesh(false); view2.set_3d_mode(true);
view3.show_mesh(false); view3.set_3d_mode(true);
view4.show_mesh(false); view4.set_3d_mode(true);
// Load physical data of the problem for the 4 energy groups.
MaterialPropertyMaps matprop(4);
matprop.set_D(D);
matprop.set_Sigma_r(Sr);
matprop.set_Sigma_s(Ss);
matprop.set_Sigma_s_nnz_structure(Ss_nnz);
matprop.set_Sigma_a(Sa);
matprop.set_Sigma_f(Sf);
matprop.set_nu(nu);
matprop.set_chi(chi);
matprop.validate();
std::cout << matprop;
// Initialize the weak formulation.
CustomWeakForm wf(matprop, iterates, k_eff, bdy_vacuum);
// Initialize the FE problem.
DiscreteProblem dp(&wf, spaces);
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
if (matrix_solver == SOLVER_AZTECOO)
{
((AztecOOSolver*) solver)->set_solver(iterative_method);
((AztecOOSolver*) solver)->set_precond(preconditioner);
// Using default iteration parameters (see solver/aztecoo.h).
}
// Time measurement.
TimePeriod cpu_time, solver_time;
// Initial coefficient vector for the Newton's method.
scalar* coeff_vec = new scalar[ndof];
// Force the Jacobian assembling in the first iteration.
bool Jacobian_changed = true;
// In the following iterations, Jacobian will not be changing; its LU factorization
// may be reused.
solver->set_factorization_scheme(HERMES_REUSE_FACTORIZATION_COMPLETELY);
// Main power iteration loop:
int it = 1; bool done = false;
do
{
info("------------ Power iteration %d:", it);
info("Newton's method (matrix problem solved by %s).", MatrixSolverNames[matrix_solver].c_str());
memset(coeff_vec, 0.0, ndof*sizeof(scalar)); //TODO: Why it doesn't work without zeroing coeff_vec in each iteration?
solver_time.tick(HERMES_SKIP);
if (!hermes2d.solve_newton(coeff_vec, &dp, solver, matrix, rhs, Jacobian_changed, 1e-8, 10, true))
error("Newton's iteration failed.");
solver_time.tick();
Solution::vector_to_solutions(solver->get_solution(), spaces, solutions);
// Show intermediate solutions.
view1.show(&sln1);
view2.show(&sln2);
view3.show(&sln3);
view4.show(&sln4);
// Compute eigenvalue.
SourceFilter source(solutions, matprop);
SourceFilter source_prev(iterates, matprop);
double k_new = k_eff * (integrate(&source, core) / integrate(&source_prev, core));
info("Largest eigenvalue: %.8g, rel. difference from previous it.: %g", k_new, fabs((k_eff - k_new) / k_new));
// Stopping criterion.
if (fabs((k_eff - k_new) / k_new) < ERROR_STOP) done = true;
// Update eigenvalue.
k_eff = k_new;
wf.update_keff(k_eff);
if (!done)
{
// Save solutions for the next iteration.
iter1.copy(&sln1);
iter2.copy(&sln2);
iter3.copy(&sln3);
iter4.copy(&sln4);
// Don't need to reassemble the system matrix in further iterations,
// only the rhs changes to reflect the progressively updated source.
Jacobian_changed = false;
it++;
}
}
while (!done);
delete [] coeff_vec;
// Time measurement.
cpu_time.tick();
solver_time.tick(HERMES_SKIP);
// Print timing information.
verbose("Average solver time for one power iteration: %g s", solver_time.accumulated() / it);
// Clean up.
delete matrix;
delete rhs;
delete solver;
// Show solutions.
view1.show(&sln1);
view2.show(&sln2);
view3.show(&sln3);
view4.show(&sln4);
// Skip visualization time.
cpu_time.tick(HERMES_SKIP);
// Print timing information.
verbose("Total running time: %g s", cpu_time.accumulated());
// Wait for all views to be closed.
View::wait();
return 0;
}
