int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr mesh(new Mesh);
if (USE_XML_FORMAT == true)
{
MeshReaderH2DXML mloader;
Hermes::Mixins::Loggable::Static::info("Reading mesh in XML format.");
try
{
mloader.load("domain.xml", mesh);
}
catch(Hermes::Exceptions::Exception& e)
{
e.print_msg();
}
}
else
{
MeshReaderH2D mloader;
Hermes::Mixins::Loggable::Static::info("Reading mesh in original format.");
mloader.load("domain.mesh", mesh);
}
// Perform initial mesh refinements (optional).
for (int i = 0; i < INIT_REF_NUM; i++)
mesh->refine_all_elements();
// Initialize the weak formulation.
CustomWeakFormPoisson wf("Aluminum", new Hermes1DFunction<double>(LAMBDA_AL),
"Copper", new Hermes1DFunction<double>(LAMBDA_CU),
new Hermes2DFunction<double>(-VOLUME_HEAT_SRC));
// Initialize essential boundary conditions.
DefaultEssentialBCConst<double> bc_essential(
Hermes::vector<std::string>("Bottom", "Inner", "Outer", "Left"), FIXED_BDY_TEMP);
EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
SpaceSharedPtr<double> space(new H1Space<double>(mesh, &bcs, P_INIT));
int ndof = space->get_num_dofs();
Hermes::Mixins::Loggable::Static::info("ndof = %d", ndof);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, space);
// Initialize Newton solver.
NewtonSolver<double> newton(&dp);
// Perform Newton's iteration.
try
{
// When newton.solve() is used without any parameters, this means that the initial coefficient
// vector will be the zero vector, tolerance will be 1e-8, maximum allowed number of iterations
// will be 100, and residual will be measured using Euclidean vector norm.
newton.solve();
}
catch(std::exception& e)
{
std::cout << e.what();
}
// Translate the resulting coefficient vector into a Solution.
MeshFunctionSharedPtr<double> sln(new Solution<double>);
Solution<double>::vector_to_solution(newton.get_sln_vector(), space, sln);
// VTK output.
if (VTK_VISUALIZATION)
{
// Output solution in VTK format.
Linearizer lin;
bool mode_3D = true;
lin.save_solution_vtk(sln, "sln.vtk", "Temperature", mode_3D);
Hermes::Mixins::Loggable::Static::info("Solution in VTK format saved to file %s.", "sln.vtk");
// Output mesh and element orders in VTK format.
Orderizer ord;
ord.save_orders_vtk(space, "ord.vtk");
Hermes::Mixins::Loggable::Static::info("Element orders in VTK format saved to file %s.", "ord.vtk");
}
// Visualize the solution.
if (HERMES_VISUALIZATION)
{
ScalarView view("Solution", new WinGeom(0, 0, 440, 350));
// Hermes uses adaptive FEM to approximate higher-order FE solutions with linear
// triangles for OpenGL. The second parameter of View::show() sets the error
// tolerance for that. Options are HERMES_EPS_LOW, HERMES_EPS_NORMAL (default),
// HERMES_EPS_HIGH and HERMES_EPS_VERYHIGH. The size of the graphics file grows
// considerably with more accurate representation, so use it wisely.
view.show(sln, HERMES_EPS_HIGH);
View::wait();
}
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("motor.mesh", &mesh);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(Hermes::vector<int>(OUTER_BDY, STATOR_BDY));
// Enter Dirichlet boundary values.
BCValues bc_values;
bc_values.add_const(STATOR_BDY, VOLTAGE);
bc_values.add_const(OUTER_BDY, 0.0);
// Create an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
// Initialize the weak formulation.
int adapt_order_increase = 1;
double adapt_rel_error_tol = 1e1;
WeakForm wf;
if (ADAPTIVE_QUADRATURE) {
info("Adaptive quadrature ON.");
wf.add_matrix_form(biform1, HERMES_SYM, MATERIAL_1,
Hermes::vector<MeshFunction*>(),
adapt_order_increase, adapt_rel_error_tol);
wf.add_matrix_form(biform2, HERMES_SYM, MATERIAL_2,
Hermes::vector<MeshFunction*>(),
adapt_order_increase, adapt_rel_error_tol);
}
else {
info("Adaptive quadrature OFF.");
wf.add_matrix_form(callback(biform1), HERMES_SYM, MATERIAL_1);
wf.add_matrix_form(callback(biform2), HERMES_SYM, MATERIAL_2);
}
// Initialize coarse and reference mesh solution.
Solution sln, ref_sln;
// Initialize refinement selector.
H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Initialize views.
ScalarView sview("Solution", new WinGeom(0, 0, 410, 600));
sview.fix_scale_width(50);
sview.show_mesh(false);
OrderView oview("Polynomial orders", new WinGeom(420, 0, 400, 600));
// DOF and CPU convergence graphs initialization.
SimpleGraph graph_dof, graph_cpu;
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Adaptivity loop:
int as = 1;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = construct_refined_space(&space);
// Initialize matrix solver.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Assemble reference problem.
info("Solving on reference mesh.");
bool is_linear = true;
DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space, is_linear);
dp->assemble(matrix, rhs);
// Time measurement.
cpu_time.tick();
// Solve the linear system of the reference problem.
// If successful, obtain the solution.
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), ref_space, &ref_sln);
else error ("Matrix solver failed.\n");
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution on coarse mesh.");
OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);
// Time measurement.
cpu_time.tick();
// VTK output.
if (VTK_OUTPUT) {
// Output solution in VTK format.
Linearizer lin;
char* title = new char[100];
sprintf(title, "sln-%d.vtk", as);
lin.save_solution_vtk(&sln, title, "Potential", false);
info("Solution in VTK format saved to file %s.", title);
// Output mesh and element orders in VTK format.
Orderizer ord;
sprintf(title, "ord-%d.vtk", as);
ord.save_orders_vtk(&space, title);
info("Element orders in VTK format saved to file %s.", title);
}
// View the coarse mesh solution and polynomial orders.
if (HERMES_VISUALIZATION) {
sview.show(&sln);
oview.show(&space);
}
// Skip visualization time.
cpu_time.tick(HERMES_SKIP);
// Calculate element errors and total error estimate.
info("Calculating error estimate.");
Adapt* adaptivity = new Adapt(&space);
bool solutions_for_adapt = true;
// In the following function, the Boolean parameter "solutions_for_adapt" determines whether
// the calculated errors are intended for use with adaptivity (this may not be the case, for example,
// when error wrt. an exact solution is calculated). The default value is solutions_for_adapt = true,
// The last parameter "error_flags" determine whether the total and element errors are treated as
// absolute or relative. Its default value is error_flags = HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL.
// In subsequent examples and benchmarks, these two parameters will be often used with
// their default values, and thus they will not be present in the code explicitly.
double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln, solutions_for_adapt,
HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%",
Space::get_num_dofs(&space), Space::get_num_dofs(ref_space), err_est_rel);
// Time measurement.
cpu_time.tick();
// Add entry to DOF and CPU convergence graphs.
graph_dof.add_values(Space::get_num_dofs(&space), err_est_rel);
graph_dof.save("conv_dof_est.dat");
graph_cpu.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu.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.");
done = adaptivity->adapt(&selector, 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;
delete rhs;
delete adaptivity;
if(done == false) delete ref_space->get_mesh();
delete ref_space;
delete dp;
}
while (done == false);
verbose("Total running time: %g s", cpu_time.accumulated());
// Show the reference solution - the final result.
sview.set_title("Fine mesh solution");
sview.show_mesh(false);
sview.show(&ref_sln);
// Wait for all views to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
if (USE_XML_FORMAT == true)
{
MeshReaderH2DXML mloader;
info("Reading mesh in XML format.");
mloader.load("domain.xml", &mesh);
}
else
{
MeshReaderH2D mloader;
info("Reading mesh in original format.");
mloader.load("domain.mesh", &mesh);
}
// Perform initial mesh refinements.
for(int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_essential("Bottom", T1);
EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
H1Space<double> space(&mesh, &bcs, P_INIT);
int ndof = space.get_num_dofs();
info("ndof = %d", ndof);
// Initialize the weak formulation.
CustomWeakFormPoissonNewton wf(LAMBDA, ALPHA, T0, "Heat_flux");
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, &space);
// Initial coefficient vector for the Newton's method.
double* coeff_vec = new double[ndof];
memset(coeff_vec, 0, ndof*sizeof(double));
// Initialize Newton solver.
NewtonSolver<double> newton(&dp, matrix_solver);
// Perform Newton's iteration.
try
{
newton.solve(coeff_vec);
}
catch(Hermes::Exceptions::Exception e)
{
e.printMsg();
error("Newton's iteration failed.");
}
// Translate the resulting coefficient vector into a Solution.
Solution<double> sln;
Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);
// VTK output.
if (VTK_VISUALIZATION)
{
// Output solution in VTK format.
Linearizer lin;
bool mode_3D = true;
lin.save_solution_vtk(&sln, "sln.vtk", "Temperature", mode_3D);
info("Solution in VTK format saved to file %s.", "sln.vtk");
// Output mesh and element orders in VTK format.
Orderizer ord;
ord.save_orders_vtk(&space, "ord.vtk");
info("Element orders in VTK format saved to file %s.", "ord.vtk");
}
// Visualize the solution.
if (HERMES_VISUALIZATION)
{
ScalarView view("Solution", new WinGeom(0, 0, 440, 350));
// Hermes uses adaptive FEM to approximate higher-order FE solutions with linear
// triangles for OpenGL. The second parameter of View::show() sets the error
// tolerance for that. Options are HERMES_EPS_LOW, HERMES_EPS_NORMAL (default),
// HERMES_EPS_HIGH and HERMES_EPS_VERYHIGH. The size of the graphics file grows
// considerably with more accurate representation, so use it wisely.
view.show(&sln, HERMES_EPS_HIGH);
View::wait();
}
// Clean up.
delete [] coeff_vec;
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh, basemesh;
MeshReaderH2D mloader;
mloader.load("domain.mesh", &basemesh);
/* MeshView meshview("mesh", new WinGeom(0, 0, 500, 400));
meshview.show(&basemesh);
View::wait();*/
// Perform initial mesh refinements (optional).
for (int i=0; i < INIT_REF_NUM; i++) basemesh.refine_all_elements();
mesh.copy(&basemesh);
// Initialize boundary conditions.
DefaultEssentialBCConst<double> bc_essential(BDY_IN, 0.0);
EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
H1Space<double> space(&mesh, &bcs, P_INIT);
// Initialize solution of lower & higher order
Solution<double> low_sln, ref_sln, high_sln, sln;
PrevSolution u_prev_time;
// Previous time level solution (initialized by the initial condition).
CustomInitialCondition initial_condition(&mesh);
// Initialize the weak formulation.
CustomWeakFormMassmatrix massmatrix(time_step);
CustomWeakFormConvection convection;
// Initialize views.
ScalarView sview("Solution", new WinGeom(0, 500, 500, 400));
OrderView mview("mesh", new WinGeom(0, 0, 500, 400));
OrderView ref_mview("ref_mesh", new WinGeom(500, 0, 500, 400));
char title[100];
// Output solution in VTK format.
Linearizer lin;
Orderizer ord;
bool mode_3D = true;
// Create a refinement selector.
H1ProjBasedSelector<double> selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
//Initialize
UMFPackMatrix<double> * mass_matrix = new UMFPackMatrix<double> ; //M_c/tau
UMFPackMatrix<double> * conv_matrix = new UMFPackMatrix<double> ; //K
double* u_L = NULL;
double* u_H =NULL;
double* ref_sln_double =NULL;
int ref_ndof, ndof; double err_est_rel_total;
Adapt<double> adaptivity(&space, HERMES_L2_NORM);
OGProjection<double> ogProjection;
Lumped_Projection lumpedProjection;
Low_Order lowOrder(theta);
High_Order highOrd(theta);
Flux_Correction fluxCorrection(theta);
Regularity_Estimator regEst(EPS_smooth);
DiscreteProblem<double> dp_mass(&massmatrix, &space);
DiscreteProblem<double> dp_convection(&convection, &space);
// Time stepping loop:
double current_time = 0.0;
int ts = 1;
do
{
Hermes::Mixins::Loggable::Static::info("Time step %d, time %3.5f", ts, current_time);
Hermes::Hermes2D::Hermes2DApi.set_integral_param_value(Hermes::Hermes2D::numThreads,1);
// Periodic global derefinement.
if ((ts > 1 && ts % UNREF_FREQ == 0)||(space.get_num_dofs() >= NDOF_STOP))
{
Hermes::Mixins::Loggable::Static::info("Global mesh derefinement.");
switch (UNREF_METHOD) {
case 1: mesh.copy(&basemesh);
space.set_uniform_order(P_INIT);
break;
case 2: mesh.unrefine_all_elements();
space.set_uniform_order(P_INIT);
break;
case 3: mesh.unrefine_all_elements();
space.adjust_element_order(-1, -1, P_INIT, P_INIT);
break;
default: Exceptions::Exception("Wrong global derefinement method.");
}
}
bool done = false; int as = 1;
do
{
Hermes::Mixins::Loggable::Static::info("Time step %i, adap_step %i", ts, as);
ndof = space.get_num_dofs();
//Unrefinement step
/* if(as==1)
{
double* coeff_vec_smooth = new double[ndof];
if(ts==1)
ogProjection.project_global(&space,&initial_condition, coeff_vec_smooth, HERMES_L2_NORM);
else
ogProjection.project_global(&space,&u_prev_time, coeff_vec_smooth, HERMES_L2_NORM);
Solution<double>::vector_to_solution(coeff_vec_smooth, &space, &low_sln);
// Calculate element errors and total error estimate.
if(ts==1)
err_est_rel_total = adaptivity.calc_err_est(&low_sln, &initial_condition) * 100;
else
err_est_rel_total = adaptivity.calc_err_est(&low_sln, &u_prev_time) * 100;
adaptivity.unrefine(THRESHOLD_UNREF);
delete [] coeff_vec_smooth;
// Visualize the solution.
if(HERMES_VISUALIZATION)
{
sprintf(title, "unrefined Mesh: Time %3.2f,timestep %i", current_time,ts);
mview.set_title(title);
mview.show(&space);
}
} */
ndof = space.get_num_dofs();
double* coeff_vec_smooth = new double[ndof];
int* smooth_elem_ref;
//smoothness-check for projected data
Hermes::Mixins::Loggable::Static::info("Projecting...");
if(ts==1)
ogProjection.project_global(&space,&initial_condition, coeff_vec_smooth, HERMES_L2_NORM);
else
ogProjection.project_global(&space,&u_prev_time, coeff_vec_smooth, HERMES_L2_NORM);
Hermes::Mixins::Loggable::Static::info("Calling get_smooth_elems()...");
smooth_elem_ref = regEst.get_smooth_elems(&space,coeff_vec_smooth);
// Construct reference mesh and setup reference space.
Mesh* ref_mesh = new Mesh;
ref_mesh->copy(space.get_mesh());
Space<double>::ReferenceSpaceCreator ref_space_creator(&space, ref_mesh, 0);
Space<double>* ref_space = ref_space_creator.create_ref_space();
HPAdapt * adapting = new HPAdapt(ref_space, HERMES_L2_NORM);
// increase p in smooth regions, h refine in non-smooth regions
Hermes::Mixins::Loggable::Static::info("Calling adapt_smooth()...");
if(adapting->adapt_smooth(smooth_elem_ref, P_MAX)==false)
throw Exceptions::Exception("reference space couldn't be constructed");
delete adapting;
delete [] coeff_vec_smooth;
ref_ndof = ref_space->get_num_dofs();
Hermes::Mixins::Loggable::Static::info("Visualization...");
if(HERMES_VISUALIZATION)
{
sprintf(title, "Ref_Mesh: Time %3.2f,timestep %i,as=%i,", current_time,ts,as);
ref_mview.set_title(title);
ref_mview.show(ref_space);
}
dp_mass.set_space(ref_space);
dp_convection.set_space(ref_space);
fluxCorrection.init(ref_space);
double* coeff_vec = new double[ref_ndof];
double* coeff_vec_2 = new double[ref_ndof];
double* limited_flux = new double[ref_ndof];
dp_mass.assemble(mass_matrix); //M_c/tau
dp_convection.assemble(conv_matrix, NULL,true); //K
//----------------------MassLumping & Artificial Diffusion --------------------------------------------------------------------
UMFPackMatrix<double>* lumped_matrix = fluxCorrection.massLumping(mass_matrix); // M_L/tau
UMFPackMatrix<double>* diffusion = fluxCorrection.artificialDiffusion(conv_matrix);
//-----------------Assembling of matrices ---------------------------------------------------------------------
lowOrder.assemble_Low_Order(conv_matrix,diffusion,lumped_matrix);
highOrd.assemble_High_Order(conv_matrix,mass_matrix);
mass_matrix->multiply_with_Scalar(time_step); // massmatrix = M_C
lumped_matrix->multiply_with_Scalar(time_step); // M_L
//--------- Project the previous timestep solution on the FE space (FCT is applied )----------------
// coeff_vec : FCT -Projection, coeff_vec_2: L2 Projection (ogProjection)
if(ts==1)
fluxCorrection.project_FCT(&initial_condition, coeff_vec, coeff_vec_2,mass_matrix,lumped_matrix,time_step,&ogProjection,&lumpedProjection, ®Est);
else
fluxCorrection.project_FCT(&u_prev_time, coeff_vec, coeff_vec_2,mass_matrix,lumped_matrix,time_step,&ogProjection,&lumpedProjection, ®Est);
//------------------------- lower order solution------------
u_L = lowOrder.solve_Low_Order(lumped_matrix, coeff_vec,time_step);
//-------------high order solution (standard galerkin) ------
u_H = highOrd.solve_High_Order(coeff_vec);
//------------------------------Assemble antidiffusive fluxes and limit these-----------------------------------
fluxCorrection.antidiffusiveFlux(mass_matrix,lumped_matrix,conv_matrix,diffusion,u_H, u_L,coeff_vec, limited_flux,time_step,®Est);
//-------------Compute final solution ---------------
ref_sln_double = lowOrder.explicit_Correction(limited_flux);
Solution<double> ::vector_to_solution(ref_sln_double, ref_space, &ref_sln);
// Project the fine mesh solution onto the coarse mesh.
ogProjection.project_global(&space, &ref_sln, &sln, HERMES_L2_NORM);
// Calculate element errors and total error estimate.
err_est_rel_total = adaptivity.calc_err_est(&sln, &ref_sln) * 100;
// Report results.
Hermes::Mixins::Loggable::Static::info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%", ndof,ref_ndof, err_est_rel_total);
// If err_est_rel too large, adapt the mesh.
if((err_est_rel_total < ERR_STOP)||(as>=ADAPSTEP_MAX)) done = true;
else
{
done = adaptivity.adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);
// Increase the counter of performed adaptivity steps.
if(done == false) as++;
}
if(space.get_num_dofs() >= NDOF_STOP)
done = true;
if(done)
{
u_prev_time.copy(&ref_sln);
u_prev_time.set_own_mesh(ref_mesh); //ref_mesh can be deleted
}
// Visualize the solution and mesh.
if(HERMES_VISUALIZATION)
{
sprintf(title, "Ref-Loesung: Time %3.2f,timestep %i,as=%i,", current_time,ts,as);
sview.set_title(title);
sview.show(&ref_sln);
sprintf(title, "Mesh: Time %3.2f,timestep %i,as=%i,", current_time,ts,as);
mview.set_title(title);
mview.show(&space);
}
if((VTK_VISUALIZATION) &&((done==true)&&(ts % VTK_FREQ == 0)))
{
// Output solution in VTK format.
char filename[40];
sprintf(filename, "solution-%i.vtk", ts );
lin.save_solution_vtk(&u_prev_time, filename, "solution", mode_3D);
sprintf(filename, "ref_space_order-%i.vtk", ts);
ord.save_orders_vtk(ref_space, filename);
sprintf(filename, "ref_mesh-%i.vtk", ts );
ord.save_mesh_vtk(ref_space, filename);
}
// Clean up.
delete lumped_matrix;
delete diffusion;
delete [] coeff_vec_2;
delete [] coeff_vec;
delete [] limited_flux;
delete ref_mesh;
delete ref_space;
}
while (done == false);
// Update global time.
current_time += time_step;
// Increase time step counter
ts++;
}
while (current_time < T_FINAL);
// Visualize the solution.
if(VTK_VISUALIZATION) {
lin.save_solution_vtk(&u_prev_time, "end_solution.vtk", "solution", mode_3D);
ord.save_mesh_vtk(&space, "end_mesh");
ord.save_orders_vtk(&space, "end_order.vtk");
}
delete mass_matrix;
delete conv_matrix;
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
Hermes::vector<std::string> BDY_NATURAL_CONCENTRATION;
BDY_NATURAL_CONCENTRATION.push_back("2");
std::ofstream time_step_out("time_step");
// Load the mesh.
Mesh basemesh;
H2DReader mloader;
mloader.load("GAMM-channel.mesh", &basemesh);
// Initialize the meshes.
Mesh mesh_flow, mesh_concentration;
mesh_flow.copy(&basemesh);
mesh_concentration.copy(&basemesh);
for(unsigned int i = 0; i < INIT_REF_NUM_CONCENTRATION; i++)
mesh_concentration.refine_all_elements(0, true);
mesh_concentration.refine_towards_boundary(BDY_DIRICHLET_CONCENTRATION, INIT_REF_NUM_CONCENTRATION_BDY, true);
//mesh_flow.refine_towards_boundary(BDY_DIRICHLET_CONCENTRATION, INIT_REF_NUM_CONCENTRATION_BDY);
for(unsigned int i = 0; i < INIT_REF_NUM_FLOW; i++)
mesh_flow.refine_all_elements(0, true);
// Initialize boundary condition types and spaces with default shapesets.
// For the concentration.
EssentialBCs<double> bcs_concentration;
bcs_concentration.add_boundary_condition(new ConcentrationTimedepEssentialBC(BDY_DIRICHLET_CONCENTRATION, CONCENTRATION_EXT, CONCENTRATION_EXT_STARTUP_TIME));
bcs_concentration.add_boundary_condition(new ConcentrationTimedepEssentialBC(BDY_SOLID_WALL_TOP, 0.0, CONCENTRATION_EXT_STARTUP_TIME));
bcs_concentration.add_boundary_condition(new ConcentrationTimedepEssentialBC(BDY_INLET, 0.0, CONCENTRATION_EXT_STARTUP_TIME));
L2Space<double>space_rho(&mesh_flow, P_INIT_FLOW);
L2Space<double>space_rho_v_x(&mesh_flow, P_INIT_FLOW);
L2Space<double>space_rho_v_y(&mesh_flow, P_INIT_FLOW);
L2Space<double>space_e(&mesh_flow, P_INIT_FLOW);
// Space<double> for concentration.
H1Space<double> space_c(&mesh_concentration, &bcs_concentration, P_INIT_CONCENTRATION);
int ndof = Space<double>::get_num_dofs(Hermes::vector<Space<double>*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e, &space_c));
info("ndof: %d", ndof);
// Initialize solutions, set initial conditions.
InitialSolutionEulerDensity sln_rho(&mesh_flow, RHO_EXT);
InitialSolutionEulerDensityVelX sln_rho_v_x(&mesh_flow, RHO_EXT * V1_EXT);
InitialSolutionEulerDensityVelY sln_rho_v_y(&mesh_flow, RHO_EXT * V2_EXT);
InitialSolutionEulerDensityEnergy sln_e(&mesh_flow, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
InitialSolutionConcentration sln_c(&mesh_concentration, 0.0);
InitialSolutionEulerDensity prev_rho(&mesh_flow, RHO_EXT);
InitialSolutionEulerDensityVelX prev_rho_v_x(&mesh_flow, RHO_EXT * V1_EXT);
InitialSolutionEulerDensityVelY prev_rho_v_y(&mesh_flow, RHO_EXT * V2_EXT);
InitialSolutionEulerDensityEnergy prev_e(&mesh_flow, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
InitialSolutionConcentration prev_c(&mesh_concentration, 0.0);
Solution<double> rsln_rho, rsln_rho_v_x, rsln_rho_v_y, rsln_e, rsln_c;
// Numerical flux.
OsherSolomonNumericalFlux num_flux(KAPPA);
// Initialize weak formulation.
WeakForm<double>* wf = NULL;
if(SEMI_IMPLICIT)
wf = new EulerEquationsWeakFormSemiImplicitCoupled(&num_flux, KAPPA, RHO_EXT, V1_EXT, V2_EXT, P_EXT, BDY_SOLID_WALL_BOTTOM,
BDY_SOLID_WALL_TOP, BDY_INLET, BDY_OUTLET, BDY_NATURAL_CONCENTRATION, &prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e, &prev_c, EPSILON, (P_INIT_FLOW == 0 && CAND_LIST_FLOW == H2D_H_ANISO));
else
wf = new EulerEquationsWeakFormExplicitCoupled(&num_flux, KAPPA, RHO_EXT, V1_EXT, V2_EXT, P_EXT, BDY_SOLID_WALL_BOTTOM,
BDY_SOLID_WALL_TOP, BDY_INLET, BDY_OUTLET, BDY_NATURAL_CONCENTRATION, &prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e, &prev_c, EPSILON, (P_INIT_FLOW == 0 && CAND_LIST_FLOW == H2D_H_ANISO));
// Filters for visualization of Mach number, pressure and entropy.
MachNumberFilter Mach_number(Hermes::vector<MeshFunction<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA);
PressureFilter pressure(Hermes::vector<MeshFunction<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA);
EntropyFilter entropy(Hermes::vector<MeshFunction<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA, RHO_EXT, P_EXT);
ScalarView<double> pressure_view("Pressure", new WinGeom(0, 0, 600, 400));
ScalarView<double> Mach_number_view("Mach number", new WinGeom(700, 0, 600, 400));
ScalarView<double> s5("Concentration", new WinGeom(700, 400, 600, 400));
OrderView<double> order_view_flow("Orders - flow", new WinGeom(700, 350, 600, 400));
OrderView<double> order_view_conc("Orders - concentration", new WinGeom(700, 700, 600, 400));
// Initialize refinement selector.
L2ProjBasedSelector<double> l2selector_flow(CAND_LIST_FLOW, CONV_EXP, H2DRS_DEFAULT_ORDER);
L2ProjBasedSelector<double> l2selector_concentration(CAND_LIST_CONCENTRATION, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Set up CFL calculation class.
CFLCalculation CFL(CFL_NUMBER, KAPPA);
// Set up Advection-Diffusion-Equation stability calculation class.
ADEStabilityCalculation ADES(ADVECTION_STABILITY_CONSTANT, DIFFUSION_STABILITY_CONSTANT, EPSILON);
int iteration = 0; double t = 0;
for(t = 0.0; t < 100.0; t += time_step)
{
time_step_out << time_step << std::endl;
info("---- Time step %d, time %3.5f.", iteration++, t);
if(iteration == 2) {
ERR_STOP_FLOW = 0.55;
ERR_STOP_CONCENTRATION = 8.3;
}
// Periodic global derefinements.
if (iteration > 1 && iteration % UNREF_FREQ == 0 && (REFINEMENT_COUNT_FLOW > 0 || REFINEMENT_COUNT_CONCENTRATION > 0)) {
info("Global mesh derefinement.");
if(REFINEMENT_COUNT_FLOW > 0) {
REFINEMENT_COUNT_FLOW = 0;
space_rho.unrefine_all_mesh_elements();
if(CAND_LIST_FLOW == H2D_HP_ANISO)
space_rho.adjust_element_order(-1, P_INIT_FLOW);
space_rho_v_x.copy_orders(&space_rho);
space_rho_v_y.copy_orders(&space_rho);
space_e.copy_orders(&space_rho);
}
if(REFINEMENT_COUNT_CONCENTRATION > 0) {
REFINEMENT_COUNT_CONCENTRATION = 0;
space_c.unrefine_all_mesh_elements();
space_c.adjust_element_order(-1, P_INIT_CONCENTRATION);
}
}
// Adaptivity loop:
int as = 1;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
int order_increase = 0;
if(CAND_LIST_FLOW == H2D_HP_ANISO)
order_increase = 1;
Hermes::vector<Space<double> *>* ref_spaces = Space<double>::construct_refined_spaces(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c), order_increase);
if(CAND_LIST_FLOW != H2D_HP_ANISO)
(*ref_spaces)[4]->adjust_element_order(+1, P_INIT_CONCENTRATION);
// Project the previous time level solution onto the new fine mesh.
info("Projecting the previous time level solution onto the new fine mesh.");
OGProjection<double>::project_global(*ref_spaces, Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e, &prev_c),
Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e, &prev_c), matrix_solver_type);
if(iteration == 1) {
if(CAND_LIST_FLOW == H2D_HP_ANISO)
{
prev_rho.set_const((*ref_spaces)[4]->get_mesh(), RHO_EXT);
prev_rho_v_x.set_const((*ref_spaces)[4]->get_mesh(), RHO_EXT * V1_EXT);
prev_rho_v_y.set_const((*ref_spaces)[4]->get_mesh(), RHO_EXT * V2_EXT);
prev_e.set_const((*ref_spaces)[4]->get_mesh(), QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
}
prev_c.set_const((*ref_spaces)[4]->get_mesh(), 0.0);
}
if(as > 1) {
delete rsln_rho.get_mesh();
delete rsln_rho_v_x.get_mesh();
delete rsln_rho_v_y.get_mesh();
delete rsln_e.get_mesh();
delete rsln_c.get_mesh();
}
// Report NDOFs.
info("ndof_coarse: %d, ndof_fine: %d.",
Space<double>::get_num_dofs(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c)), Space<double>::get_num_dofs(*ref_spaces));
// Very imporant, set the meshes for the flow as the same.
(*ref_spaces)[1]->get_mesh()->set_seq((*ref_spaces)[0]->get_mesh()->get_seq());
(*ref_spaces)[2]->get_mesh()->set_seq((*ref_spaces)[0]->get_mesh()->get_seq());
(*ref_spaces)[3]->get_mesh()->set_seq((*ref_spaces)[0]->get_mesh()->get_seq());
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix<double>* matrix = create_matrix<double>(matrix_solver_type);
Vector<double>* rhs = create_vector<double>(matrix_solver_type);
LinearSolver<double>* solver = create_linear_solver<double>(matrix_solver_type, matrix, rhs);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem<double> dp(wf, *ref_spaces);
if(SEMI_IMPLICIT)
static_cast<EulerEquationsWeakFormSemiImplicitCoupled*>(wf)->set_time_step(time_step);
else
static_cast<EulerEquationsWeakFormExplicitCoupled*>(wf)->set_time_step(time_step);
// Assemble stiffness matrix and rhs.
info("Assembling the stiffness matrix and right-hand side vector.");
dp.assemble(matrix, rhs);
// Solve the matrix problem.
info("Solving the matrix problem.");
if (solver->solve())
Solution<double>::vector_to_solutions(solver->get_sln_vector(), *ref_spaces,
Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e, &rsln_c));
else
error ("Matrix solver failed.\n");
Hermes::vector<Space<double>*> flow_spaces((*ref_spaces)[0], (*ref_spaces)[1], (*ref_spaces)[2], (*ref_spaces)[3]);
double* flow_solution_vector = new double[Space<double>::get_num_dofs(flow_spaces)];
OGProjection<double>::project_global(flow_spaces, Hermes::vector<MeshFunction<double> *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e), flow_solution_vector);
FluxLimiter flux_limiter(FluxLimiter::Krivodonova, flow_solution_vector, flow_spaces);
flux_limiter.limit_according_to_detector();
flux_limiter.get_limited_solutions(Hermes::vector<Solution<double> *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
if(SHOCK_CAPTURING)
flux_limiter.get_limited_solutions(Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e));
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution on coarse mesh.");
OGProjection<double>::project_global(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c), Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e, &rsln_c),
Hermes::vector<Solution<double>*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e, &sln_c), matrix_solver_type,
Hermes::vector<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM));
util_time_step = time_step;
if(SEMI_IMPLICIT)
CFL.calculate_semi_implicit(Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e), &mesh_flow, util_time_step);
else
CFL.calculate(Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e), &mesh_flow, util_time_step);
time_step = util_time_step;
ADES.calculate(Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y), &mesh_concentration, util_time_step);
// Calculate element errors and total error estimate.
info("Calculating error estimates.");
Adapt<double> adaptivity_flow(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM));
double err_est_rel_total_flow = adaptivity_flow.calc_err_est(Hermes::vector<Solution<double>*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e),
Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e)) * 100;
Adapt<double> adaptivity_concentration(&space_c, HERMES_L2_NORM);
double err_est_rel_total_concentration = adaptivity_concentration.calc_err_est(&sln_c, &rsln_c) * 100;
// Report results.
info("Error estimate for the flow part: %g%%", err_est_rel_total_flow);
info("Error estimate for the concentration part: %g%%", err_est_rel_total_concentration);
// If err_est too large, adapt the mesh.
if (err_est_rel_total_flow < ERR_STOP_FLOW && err_est_rel_total_concentration < ERR_STOP_CONCENTRATION)
{
done = true;
if(SHOCK_CAPTURING)
flux_limiter.limit_according_to_detector(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e));
}
else
{
info("Adapting coarse meshes.");
if(err_est_rel_total_flow > ERR_STOP_FLOW)
{
done = adaptivity_flow.adapt(Hermes::vector<RefinementSelectors::Selector<double> *>(&l2selector_flow, &l2selector_flow, &l2selector_flow, &l2selector_flow),
THRESHOLD, STRATEGY, MESH_REGULARITY);
REFINEMENT_COUNT_FLOW++;
}
else
done = true;
if(err_est_rel_total_concentration > ERR_STOP_CONCENTRATION)
{
if(!adaptivity_concentration.adapt(&l2selector_concentration, THRESHOLD, STRATEGY, MESH_REGULARITY))
done = false;
REFINEMENT_COUNT_CONCENTRATION++;
}
if (Space<double>::get_num_dofs(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c)) >= NDOF_STOP)
done = true;
else
// Increase the counter of performed adaptivity steps.
as++;
}
// Save orders.
if((iteration - 1) % EVERY_NTH_STEP == 0 && done)
{
if(HERMES_VISUALIZATION)
{
Hermes::vector<Space<double> *>* ref_spaces_local = Space<double>::construct_refined_spaces(Hermes::vector<Space<double> *>(&space_rho, &space_c), 0);
order_view_flow.show((*ref_spaces_local)[0]);
order_view_conc.show((*ref_spaces_local)[1]);
order_view_flow.save_numbered_screenshot("FlowMesh%i.bmp", (int)(iteration / 5), true);
order_view_conc.save_numbered_screenshot("ConcentrationMesh%i.bmp", (int)(iteration / 5), true);
for(unsigned int i = 0; i < ref_spaces_local->size(); i++) {
delete (*ref_spaces_local)[i]->get_mesh();
delete (*ref_spaces_local)[i];
}
}
if(VTK_VISUALIZATION)
{
Orderizer ord;
char filename[40];
sprintf(filename, "Flow-mesh-%i.vtk", iteration - 1);
ord.save_orders_vtk((*ref_spaces)[0], filename);
sprintf(filename, "Concentration-mesh-%i.vtk", iteration - 1);
ord.save_orders_vtk((*ref_spaces)[4], filename);
}
}
// Clean up.
delete solver;
delete matrix;
delete rhs;
for(unsigned int i = 0; i < ref_spaces->size(); i++)
delete (*ref_spaces)[i];
}
while (done == false);
// Copy the solutions into the previous time level ones.
prev_rho.copy(&rsln_rho);
prev_rho_v_x.copy(&rsln_rho_v_x);
prev_rho_v_y.copy(&rsln_rho_v_y);
prev_e.copy(&rsln_e);
prev_c.copy(&rsln_c);
delete rsln_rho.get_mesh();
delete rsln_rho_v_x.get_mesh();
delete rsln_rho_v_y.get_mesh();
delete rsln_e.get_mesh();
delete rsln_c.get_mesh();
// Visualization.
if((iteration - 1) % EVERY_NTH_STEP == 0) {
// Hermes visualization.
if(HERMES_VISUALIZATION)
{
Mach_number.reinit();
pressure.reinit();
pressure_view.show_mesh(false);
pressure_view.show(&pressure);
pressure_view.set_scale_format("%1.3f");
Mach_number_view.show_mesh(false);
Mach_number_view.set_scale_format("%1.3f");
Mach_number_view.show(&Mach_number);
s5.show_mesh(false);
s5.set_scale_format("%0.3f");
s5.show(&prev_c);
pressure_view.save_numbered_screenshot("pressure%i.bmp", (int)(iteration / 5), true);
Mach_number_view.save_numbered_screenshot("Mach_number%i.bmp", (int)(iteration / 5), true);
s5.save_numbered_screenshot("concentration%i.bmp", (int)(iteration / 5), true);
}
// Output solution in VTK format.
if(VTK_VISUALIZATION)
{
pressure.reinit();
Mach_number.reinit();
Linearizer<double> lin;
char filename[40];
//sprintf(filename, "pressure-%i.vtk", iteration - 1);
//lin.save_solution_vtk(&pressure, filename, "Pressure", false);
sprintf(filename, "pressure-3D-%i.vtk", iteration - 1);
lin.save_solution_vtk(&pressure, filename, "Pressure", true);
//sprintf(filename, "Mach number-%i.vtk", iteration - 1);
//lin.save_solution_vtk(&Mach_number, filename, "MachNumber", false);
sprintf(filename, "Mach number-3D-%i.vtk", iteration - 1);
lin.save_solution_vtk(&Mach_number, filename, "MachNumber", true);
//sprintf(filename, "Concentration-%i.vtk", iteration - 1);
//lin.save_solution_vtk(&prev_c, filename, "Concentration", true);
sprintf(filename, "Concentration-3D-%i.vtk", iteration - 1);
lin.save_solution_vtk(&prev_c, filename, "Concentration", true);
}
}
}
/*
pressure_view.close();
entropy_production_view.close();
Mach_number_view.close();
s5.close();
*/
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinements (optional).
//mesh.refine_all_elements();
// Initialize boundary conditions
DefaultEssentialBCConst bc_essential(Hermes::vector<std::string>(BDY_BOTTOM, BDY_OUTER, BDY_LEFT, BDY_INNER), 0.0);
EssentialBCs bcs(&bc_essential);
// Create an H1 space with default shapeset.
H1Space space(&mesh, &bcs, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d", ndof);
// Initialize the weak formulation. Not providing the order determination form
// (or callback) turns on adaptive numerical quadrature. The quadrature begins
// with using a first-order rule in the entire element. Then the element is split
// uniformly in space and the quadrature order is increased by "adapt_order_increase".
// Then the form is calculated again by employing the new quadrature in subelements.
// This provides a more accurate result. If relative error is less than
// "adapt_rel_error_tol", the computation stops, otherwise the same procedure is
// applied recursively to all four subelements.
int adapt_order_increase = 1;
double adapt_rel_error_tol = 1e1;
WeakFormPoisson wf(CONST_F, ADAPTIVE_QUADRATURE, adapt_order_increase, adapt_rel_error_tol);
if (ADAPTIVE_QUADRATURE)
info("Adaptive quadrature ON.");
else
info("Adaptive quadrature OFF.");
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initialize the solution.
Solution sln;
// Assemble the stiffness matrix and right-hand side vector.
info("Assembling the stiffness matrix and right-hand side vector.");
dp.assemble(matrix, rhs);
// Solve the linear system and if successful, obtain the solution.
info("Solving the matrix problem.");
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else error ("Matrix solver failed.\n");
// VTK output.
if (VTK_VISUALIZATION) {
// Output solution in VTK format.
Linearizer lin;
bool mode_3D = true;
lin.save_solution_vtk(&sln, "sln.vtk", "Temperature", mode_3D);
info("Solution in VTK format saved to file %s.", "sln.vtk");
// Output mesh and element orders in VTK format.
Orderizer ord;
ord.save_orders_vtk(&space, "ord.vtk");
info("Element orders in VTK format saved to file %s.", "ord.vtk");
}
// Visualize the solution.
if (HERMES_VISUALIZATION) {
ScalarView view("Solution", new WinGeom(0, 0, 440, 350));
view.show(&sln);
View::wait();
}
// Clean up.
delete solver;
delete matrix;
delete rhs;
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh basemesh;
H2DReader mloader;
mloader.load("domain.mesh", &basemesh);
// Initialize the meshes.
Mesh mesh_flow, mesh_concentration;
mesh_flow.copy(&basemesh);
mesh_concentration.copy(&basemesh);
for(unsigned int i = 0; i < INIT_REF_NUM_CONCENTRATION; i++)
mesh_concentration.refine_all_elements();
mesh_concentration.refine_towards_boundary(BDY_DIRICHLET_CONCENTRATION, INIT_REF_NUM_CONCENTRATION_BDY);
for(unsigned int i = 0; i < INIT_REF_NUM_FLOW; i++)
mesh_flow.refine_all_elements();
// Initialize boundary condition types and spaces with default shapesets.
// For the concentration.
EssentialBCs bcs_concentration;
bcs_concentration.add_boundary_condition(new DefaultEssentialBCConst(BDY_DIRICHLET_CONCENTRATION, CONCENTRATION_EXT));
L2Space space_rho(&mesh_flow, P_INIT_FLOW);
L2Space space_rho_v_x(&mesh_flow, P_INIT_FLOW);
L2Space space_rho_v_y(&mesh_flow, P_INIT_FLOW);
L2Space space_e(&mesh_flow, P_INIT_FLOW);
// Space for concentration.
H1Space space_c(&mesh_concentration, &bcs_concentration, P_INIT_CONCENTRATION);
int ndof = Space::get_num_dofs(Hermes::vector<Space*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e, &space_c));
info("ndof: %d", ndof);
// Initialize solutions, set initial conditions.
InitialSolutionEulerDensity sln_rho(&mesh_flow, RHO_EXT);
InitialSolutionEulerDensityVelX sln_rho_v_x(&mesh_flow, RHO_EXT * V1_EXT);
InitialSolutionEulerDensityVelY sln_rho_v_y(&mesh_flow, RHO_EXT * V2_EXT);
InitialSolutionEulerDensityEnergy sln_e(&mesh_flow, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
InitialSolutionConcentration sln_c(&mesh_concentration, 0.0);
InitialSolutionEulerDensity prev_rho(&mesh_flow, RHO_EXT);
InitialSolutionEulerDensityVelX prev_rho_v_x(&mesh_flow, RHO_EXT * V1_EXT);
InitialSolutionEulerDensityVelY prev_rho_v_y(&mesh_flow, RHO_EXT * V2_EXT);
InitialSolutionEulerDensityEnergy prev_e(&mesh_flow, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
InitialSolutionConcentration prev_c(&mesh_concentration, 0.0);
Solution rsln_rho, rsln_rho_v_x, rsln_rho_v_y, rsln_e, rsln_c;
// Numerical flux.
OsherSolomonNumericalFlux num_flux(KAPPA);
// Initialize weak formulation.
EulerEquationsWeakFormImplicitCoupled wf(&num_flux, KAPPA, RHO_EXT, V1_EXT, V2_EXT, P_EXT, BDY_SOLID_WALL,
BDY_INLET, BDY_OUTLET, BDY_NATURAL_CONCENTRATION, &prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e, &prev_c, PRECONDITIONING, EPSILON);
wf.set_time_step(time_step);
// Filters for visualization of Mach number, pressure and entropy.
MachNumberFilter Mach_number(Hermes::vector<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e), KAPPA);
PressureFilter pressure(Hermes::vector<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e), KAPPA);
EntropyFilter entropy(Hermes::vector<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e), KAPPA, RHO_EXT, P_EXT);
ScalarView pressure_view("Pressure", new WinGeom(0, 0, 600, 300));
ScalarView Mach_number_view("Mach number", new WinGeom(700, 0, 600, 300));
ScalarView entropy_production_view("Entropy estimate", new WinGeom(0, 400, 600, 300));
ScalarView s5("Concentration", new WinGeom(700, 400, 600, 300));
/*
ScalarView s1("1", new WinGeom(0, 0, 600, 300));
ScalarView s2("2", new WinGeom(700, 0, 600, 300));
ScalarView s3("3", new WinGeom(0, 400, 600, 300));
ScalarView s4("4", new WinGeom(700, 400, 600, 300));
ScalarView s5("Concentration", new WinGeom(350, 200, 600, 300));
*/
// Initialize refinement selector.
L2ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Select preconditioner.
RCP<Precond> pc = rcp(new IfpackPrecond("point-relax"));
int iteration = 0; double t = 0;
for(t = 0.0; t < 3.0; t += time_step) {
info("---- Time step %d, time %3.5f.", iteration++, t);
// Periodic global derefinements.
if (iteration > 1 && iteration % UNREF_FREQ == 0 && REFINEMENT_COUNT > 0) {
REFINEMENT_COUNT = 0;
info("Global mesh derefinement.");
mesh_flow.unrefine_all_elements();
mesh_concentration.unrefine_all_elements();
space_rho.adjust_element_order(-1, P_INIT_FLOW);
space_rho_v_x.adjust_element_order(-1, P_INIT_FLOW);
space_rho_v_y.adjust_element_order(-1, P_INIT_FLOW);
space_e.adjust_element_order(-1, P_INIT_FLOW);
space_c.adjust_element_order(-1, P_INIT_CONCENTRATION);
}
// Adaptivity loop:
int as = 1;
bool done = false;
do {
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
int order_increase = 0;
Hermes::vector<Space *>* ref_spaces = Space::construct_refined_spaces(Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c), order_increase);
// Report NDOFs.
info("ndof_coarse: %d, ndof_fine: %d.",
Space::get_num_dofs(Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c)), Space::get_num_dofs(*ref_spaces));
// Very imporant, set the meshes for the flow as the same.
(*ref_spaces)[1]->get_mesh()->set_seq((*ref_spaces)[0]->get_mesh()->get_seq());
(*ref_spaces)[2]->get_mesh()->set_seq((*ref_spaces)[0]->get_mesh()->get_seq());
(*ref_spaces)[3]->get_mesh()->set_seq((*ref_spaces)[0]->get_mesh()->get_seq());
// Project the previous time level solution onto the new fine mesh
// in order to obtain initial vector for NOX.
info("Projecting initial solution on the FE mesh.");
scalar* coeff_vec = new scalar[Space::get_num_dofs(*ref_spaces)];
OGProjection::project_global(*ref_spaces, Hermes::vector<MeshFunction *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e, &prev_c), coeff_vec);
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem dp(&wf, *ref_spaces, is_linear);
// Initialize NOX solver.
NoxSolver solver(&dp, NOX_MESSAGE_TYPE, "GMRES", "Newton", NOX_LINEAR_TOLERANCE, "None", 0, 0, 1, NOX_NONLINEAR_TOLERANCE);
solver.set_init_sln(coeff_vec);
if(PRECONDITIONING)
solver.set_precond(pc);
info("Assembling by DiscreteProblem, solving by NOX.");
if (solver.solve())
Solution::vector_to_solutions(solver.get_solution(), *ref_spaces,
Hermes::vector<Solution *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e, &rsln_c));
else
error("NOX failed.");
info("Number of nonlin iterations: %d (norm of residual: %g)",
solver.get_num_iters(), solver.get_residual());
info("Total number of iterations in linsolver: %d (achieved tolerance in the last step: %g)",
solver.get_num_lin_iters(), solver.get_achieved_tol());
if(SHOCK_CAPTURING) {
Hermes::vector<Space*> flow_spaces((*ref_spaces)[0], (*ref_spaces)[1], (*ref_spaces)[2], (*ref_spaces)[3]);
scalar* flow_solution_vector = new scalar[Space::get_num_dofs(flow_spaces)];
OGProjection::project_global(flow_spaces, Hermes::vector<MeshFunction *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e), flow_solution_vector);
DiscontinuityDetector discontinuity_detector(flow_spaces, Hermes::vector<Solution *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e));
std::set<int> discontinuous_elements = discontinuity_detector.get_discontinuous_element_ids(DISCONTINUITY_DETECTOR_PARAM);
FluxLimiter flux_limiter(flow_solution_vector, flow_spaces, Hermes::vector<Solution *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e));
flux_limiter.limit_according_to_detector(discontinuous_elements);
}
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution on coarse mesh.");
OGProjection::project_global(Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c), Hermes::vector<Solution *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e, &rsln_c),
Hermes::vector<Solution *>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e, &sln_c), matrix_solver,
Hermes::vector<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_H1_NORM));
// Calculate element errors and total error estimate.
info("Calculating error estimate.");
Adapt* adaptivity = new Adapt(Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c), Hermes::vector<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_H1_NORM));
double err_est_rel_total = adaptivity->calc_err_est(Hermes::vector<Solution *>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e, &sln_c),
Hermes::vector<Solution *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e, &rsln_c)) * 100;
// Report results.
info("err_est_rel: %g%%", err_est_rel_total);
// If err_est too large, adapt the mesh.
if (err_est_rel_total < ERR_STOP)
done = true;
else {
info("Adapting coarse mesh.");
done = adaptivity->adapt(Hermes::vector<RefinementSelectors::Selector *>(&selector, &selector, &selector, &selector, &selector),
THRESHOLD, STRATEGY, MESH_REGULARITY);
REFINEMENT_COUNT++;
if (Space::get_num_dofs(Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c)) >= NDOF_STOP)
done = true;
else
// Increase the counter of performed adaptivity steps.
as++;
}
// Save orders.
Orderizer ord;
char filename[40];
sprintf(filename, "Flow-mesh-%i-%i.vtk", iteration - 1, as - 1);
ord.save_orders_vtk((*ref_spaces)[0], filename);
sprintf(filename, "Concentration-mesh-%i-%i.vtk", iteration - 1, as - 1);
ord.save_orders_vtk((*ref_spaces)[4], filename);
// Clean up.
delete adaptivity;
if(!done)
for(unsigned int i = 0; i < ref_spaces->size(); i++)
delete (*ref_spaces)[i]->get_mesh();
for(unsigned int i = 0; i < ref_spaces->size(); i++)
delete (*ref_spaces)[i];
}
while (done == false);
// Copy the solutions into previous time level ones.
prev_rho.copy(&rsln_rho);
prev_rho_v_x.copy(&rsln_rho_v_x);
prev_rho_v_y.copy(&rsln_rho_v_y);
prev_e.copy(&rsln_e);
prev_c.copy(&rsln_c);
// Visualization.
if((iteration - 1) % EVERY_NTH_STEP == 0) {
// Hermes visualization.
if(HERMES_VISUALIZATION) {
Mach_number.reinit();
pressure.reinit();
entropy.reinit();
pressure_view.show(&pressure);
entropy_production_view.show(&entropy);
Mach_number_view.show(&Mach_number);
s5.show(&prev_c);
/*
s1.show(&prev_rho);
s2.show(&prev_rho_v_x);
s3.show(&prev_rho_v_y);
s4.show(&prev_e);
s5.show(&prev_c);
*/
}
// Output solution in VTK format.
if(VTK_VISUALIZATION) {
pressure.reinit();
Mach_number.reinit();
Linearizer lin;
char filename[40];
sprintf(filename, "pressure-%i.vtk", iteration - 1);
lin.save_solution_vtk(&pressure, filename, "Pressure", false);
sprintf(filename, "pressure-3D-%i.vtk", iteration - 1);
lin.save_solution_vtk(&pressure, filename, "Pressure", true);
sprintf(filename, "Mach number-%i.vtk", iteration - 1);
lin.save_solution_vtk(&Mach_number, filename, "MachNumber", false);
sprintf(filename, "Mach number-3D-%i.vtk", iteration - 1);
lin.save_solution_vtk(&Mach_number, filename, "MachNumber", true);
sprintf(filename, "Concentration-%i.vtk", iteration - 1);
lin.save_solution_vtk(&prev_c, filename, "Concentration", true);
sprintf(filename, "Concentration-3D-%i.vtk", iteration - 1);
lin.save_solution_vtk(&prev_c, filename, "Concentration", true);
}
}
}
pressure_view.close();
entropy_production_view.close();
Mach_number_view.close();
s5.close();
/*
s1.close();
s2.close();
s3.close();
s4.close();
*/
return 0;
}
int main(int argc, char* argv[])
{
// Instantiate a class with global functions.
Hermes2D hermes2d;
// 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 the weak formulation.
CustomWeakForm wf;
// Initialize boundary conditions.
CustomDirichletCondition bc_essential(Hermes::vector<std::string>("Bdy"),
BDY_A_PARAM, BDY_B_PARAM, BDY_C_PARAM);
EssentialBCs bcs(&bc_essential);
// Create an H1 space with default shapeset.
H1Space space(&mesh, &bcs, P_INIT);
int ndof = space.get_num_dofs();
info("ndof = %d", ndof);
// Initialize the FE problem.
DiscreteProblem dp(&wf, &space);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initial coefficient vector for the Newton's method.
scalar* coeff_vec = new scalar[ndof];
memset(coeff_vec, 0, ndof*sizeof(scalar));
// Perform Newton's iteration.
bool jacobian_changed = true;
double newton_tol = 1e-8;
int newton_max_iter = 100;
bool verbose = true;
if (!hermes2d.solve_newton(coeff_vec, &dp, solver, matrix, rhs, jacobian_changed,
newton_tol, newton_max_iter, verbose)) error("Newton's iteration failed.");
// Translate the resulting coefficient vector into the Solution sln.
Solution sln;
Solution::vector_to_solution(coeff_vec, &space, &sln);
// VTK output.
if (VTK_VISUALIZATION) {
// Output solution in VTK format.
Linearizer lin;
bool mode_3D = true;
lin.save_solution_vtk(&sln, "sln.vtk", "Temperature", mode_3D);
info("Solution in VTK format saved to file %s.", "sln.vtk");
// Output mesh and element orders in VTK format.
Orderizer ord;
ord.save_orders_vtk(&space, "ord.vtk");
info("Element orders in VTK format saved to file %s.", "ord.vtk");
}
// Visualize the solution.
if (HERMES_VISUALIZATION) {
ScalarView view("Solution", new WinGeom(0, 0, 440, 350));
view.show(&sln, HERMES_EPS_HIGH);
View::wait();
}
// Clean up.
delete solver;
delete matrix;
delete rhs;
delete [] coeff_vec;
return 0;
}
int main(int argc, char* argv[])
{
// Instantiate a class with global functions.
Hermes2D hermes2d;
// 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 the weak formulation.
CustomWeakFormPoissonDirichlet wf("Aluminum", LAMBDA_AL, "Copper",
LAMBDA_CU, VOLUME_HEAT_SRC);
// Initialize boundary conditions.
CustomDirichletCondition bc_essential(Hermes::vector<std::string>("Bottom", "Inner", "Outer", "Left"),
BDY_A_PARAM, BDY_B_PARAM, BDY_C_PARAM);
EssentialBCs bcs(&bc_essential);
// Create an H1 space with default shapeset.
H1Space space(&mesh, &bcs, P_INIT);
int ndof = space.get_num_dofs();
info("ndof = %d", ndof);
// Initialize the FE problem.
DiscreteProblem dp(&wf, &space);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initial coefficient vector for the Newton's method.
scalar* coeff_vec = new scalar[ndof];
memset(coeff_vec, 0, ndof*sizeof(scalar));
// Perform Newton's iteration.
if (!hermes2d.solve_newton(coeff_vec, &dp, solver, matrix, rhs)) error("Newton's iteration failed.");
// Translate the resulting coefficient vector into the Solution sln.
Solution sln;
Solution::vector_to_solution(coeff_vec, &space, &sln);
// VTK output.
if (VTK_VISUALIZATION) {
// Output solution in VTK format.
Linearizer lin;
bool mode_3D = true;
lin.save_solution_vtk(&sln, "sln.vtk", "Temperature", mode_3D);
info("Solution in VTK format saved to file %s.", "sln.vtk");
// Output mesh and element orders in VTK format.
Orderizer ord;
ord.save_orders_vtk(&space, "ord.vtk");
info("Element orders in VTK format saved to file %s.", "ord.vtk");
}
ndof = Space::get_num_dofs(&space);
printf("ndof = %d\n", ndof);
double sum = 0;
for (int i=0; i < ndof; i++) sum += coeff_vec[i];
printf("coefficient sum = %g\n", sum);
bool success = true;
if (fabs(sum + 4.2471) > 1e-3) success = 0;
if (success == 1) {
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}
int main(int argc, char* argv[])
{
// Instantiate a class with global functions.
Hermes2D hermes2d;
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("motor.mesh", &mesh);
// Initialize the weak formulation.
CustomWeakFormPoisson wf("Motor", EPS_MOTOR, "Air", EPS_AIR);
// Initialize boundary conditions
DefaultEssentialBCConst bc_essential_out("Outer", 0.0);
DefaultEssentialBCConst bc_essential_stator("Stator", VOLTAGE);
EssentialBCs bcs(Hermes::vector<EssentialBoundaryCondition *>(&bc_essential_out, &bc_essential_stator));
// Create an H1 space with default shapeset.
H1Space space(&mesh, &bcs, P_INIT);
// Initialize coarse and reference mesh solution.
Solution sln, ref_sln;
// Initialize refinement selector.
H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Initialize views.
ScalarView sview("Solution", new WinGeom(0, 0, 410, 600));
sview.fix_scale_width(50);
sview.show_mesh(false);
OrderView oview("Polynomial orders", new WinGeom(420, 0, 400, 600));
// DOF and CPU convergence graphs initialization.
SimpleGraph graph_dof, graph_cpu;
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Adaptivity loop:
int as = 1;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = Space::construct_refined_space(&space);
int ndof_ref = Space::get_num_dofs(ref_space);
// Initialize matrix solver.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initialize reference problem.
info("Solving on reference mesh.");
DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space);
// Time measurement.
cpu_time.tick();
// Initial coefficient vector for the Newton's method.
scalar* coeff_vec = new scalar[ndof_ref];
memset(coeff_vec, 0, ndof_ref * sizeof(scalar));
// Perform Newton's iteration.
if (!hermes2d.solve_newton(coeff_vec, dp, solver, matrix, rhs)) error("Newton's iteration failed.");
// Translate the resulting coefficient vector into the Solution sln.
Solution::vector_to_solution(coeff_vec, ref_space, &ref_sln);
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution on coarse mesh.");
OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);
// Time measurement.
cpu_time.tick();
// VTK output.
if (VTK_VISUALIZATION) {
// Output solution in VTK format.
Linearizer lin;
char* title = new char[100];
sprintf(title, "sln-%d.vtk", as);
lin.save_solution_vtk(&sln, title, "Potential", false);
info("Solution in VTK format saved to file %s.", title);
// Output mesh and element orders in VTK format.
Orderizer ord;
sprintf(title, "ord-%d.vtk", as);
ord.save_orders_vtk(&space, title);
info("Element orders in VTK format saved to file %s.", title);
}
// View the coarse mesh solution and polynomial orders.
if (HERMES_VISUALIZATION) {
sview.show(&sln);
oview.show(&space);
}
// Skip visualization time.
cpu_time.tick(HERMES_SKIP);
// Calculate element errors and total error estimate.
info("Calculating error estimate.");
Adapt* adaptivity = new Adapt(&space);
bool solutions_for_adapt = true;
// In the following function, the Boolean parameter "solutions_for_adapt" determines whether
// the calculated errors are intended for use with adaptivity (this may not be the case, for example,
// when error wrt. an exact solution is calculated). The default value is solutions_for_adapt = true,
// The last parameter "error_flags" determine whether the total and element errors are treated as
// absolute or relative. Its default value is error_flags = HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL.
// In subsequent examples and benchmarks, these two parameters will be often used with
// their default values, and thus they will not be present in the code explicitly.
double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln, solutions_for_adapt,
HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%",
Space::get_num_dofs(&space), Space::get_num_dofs(ref_space), err_est_rel);
// Time measurement.
cpu_time.tick();
// Add entry to DOF and CPU convergence graphs.
graph_dof.add_values(Space::get_num_dofs(&space), err_est_rel);
graph_dof.save("conv_dof_est.dat");
graph_cpu.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu.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.");
done = adaptivity->adapt(&selector, 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 [] coeff_vec;
delete solver;
delete matrix;
delete rhs;
delete adaptivity;
if(done == false) delete ref_space->get_mesh();
delete ref_space;
delete dp;
}
while (done == false);
verbose("Total running time: %g s", cpu_time.accumulated());
// Show the reference solution - the final result.
sview.set_title("Fine mesh solution");
sview.show_mesh(false);
sview.show(&ref_sln);
// Wait for all views to be closed.
View::wait();
return 0;
}