void Continuity<Scalar>::Record::load_mesh(Mesh* mesh)
{
MeshReaderH2DXML reader;
std::stringstream filename;
filename << Continuity<Scalar>::meshFileName << 0 << '_' << (std::string)"t = " << this->time << (std::string)"n = " << this->number << (std::string)".h2d";
reader.load(filename.str().c_str(), mesh);
}
void load_mesh(MeshSharedPtr& mesh, const char* filename, int num_initial_refinements)
{
MeshReaderH2DXML mloader;
mloader.load(filename, mesh);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++)
mesh->refine_all_elements(0, true);
}
void Continuity<Scalar>::Record::load_meshes(Hermes::vector<Mesh*> meshes)
{
MeshReaderH2DXML reader;
for(unsigned int i = 0; i < meshes.size(); i++)
{
std::stringstream filename;
filename << Continuity<Scalar>::meshFileName << i << '_' << (std::string)"t = " << this->time << (std::string)"n = " << this->number << (std::string)".h2d";
reader.load(filename.str().c_str(), meshes[i]);
}
}
void CalculationContinuity<Scalar>::Record::save_mesh(Mesh* mesh)
{
MeshReaderH2DXML reader;
std::stringstream filename;
filename << CalculationContinuity<Scalar>::mesh_file_name << 0 << '_' << (std::string)"t = " << this->time << (std::string)"n = " << this->number << (std::string)".h2d";
try
{
reader.save(filename.str().c_str(), mesh);
}
catch(std::exception& e)
{
throw IOCalculationContinuityException(CalculationContinuityException::meshes, IOCalculationContinuityException::output, filename.str().c_str(), e.what());
}
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh_whole_domain, mesh_bottom_left_corner, mesh_complement;
Hermes::vector<Mesh*> meshes (&mesh_whole_domain, &mesh_bottom_left_corner, &mesh_complement);
MeshReaderH2DXML mloader;
mloader.load("subdomains.xml", meshes);
// Perform initial mesh refinements (optional).
for(int i = 0; i < INIT_REF_NUM; i++)
for(unsigned int meshes_i = 0; meshes_i < meshes.size(); meshes_i++)
meshes[meshes_i]->refine_all_elements();
mloader.save("subdomains2.xml", meshes);
mloader.load("subdomains2.xml", meshes);
// Initialize essential boundary conditions.
DefaultEssentialBCConst<double> bc_essential_whole_domain(Hermes::vector<std::string>("Bottom Left", "Bottom Right", "Top Left", "Top Right"), 0.0);
EssentialBCs<double> bcs_whole_domain(&bc_essential_whole_domain);
DefaultEssentialBCConst<double> bc_essential_bottom_left_corner(Hermes::vector<std::string>("Bottom Left", "Horizontal Left"), 0.0);
EssentialBCs<double> bcs_bottom_left_corner(&bc_essential_bottom_left_corner);
DefaultEssentialBCConst<double> bc_essential_complement(Hermes::vector<std::string>("Bottom Right", "Top Right", "Top Left", "Horizontal Left", "Vertical Bottom"), 0.0);
EssentialBCs<double> bcs_complement(&bc_essential_complement);
// Create H1 spaces with default shapeset.
H1Space<double> space_whole_domain(&mesh_whole_domain, &bcs_whole_domain, P_INIT);
int ndof_whole_domain = space_whole_domain.get_num_dofs();
H1Space<double> space_bottom_left_corner(&mesh_bottom_left_corner, &bcs_bottom_left_corner, P_INIT);
int ndof_bottom_left_corner = space_bottom_left_corner.get_num_dofs();
H1Space<double> space_complement(&mesh_complement, &bcs_complement, P_INIT);
int ndof_complement = space_complement.get_num_dofs();
if(ndof_whole_domain == 225 && ndof_bottom_left_corner == 56 && ndof_complement == 161)
{
info("Success!");
return TEST_SUCCESS;
}
else
{
info("Failure!");
return TEST_FAILURE;
}
return 0;
}
void CalculationContinuity<Scalar>::Record::load_mesh(Mesh* mesh)
{
MeshReaderH2DXML reader;
std::stringstream filename;
filename << CalculationContinuity<Scalar>::mesh_file_name << 0 << '_' << (std::string)"t = " << this->time << (std::string)"n = " << this->number << (std::string)".h2d";
try
{
reader.load(filename.str().c_str(), mesh);
}
catch(Hermes::Exceptions::MeshLoadFailureException& e)
{
throw IOCalculationContinuityException(CalculationContinuityException::meshes, IOCalculationContinuityException::input, filename.str().c_str(), e.what());
}
}
int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr mesh_whole_domain(new Mesh), mesh_bottom_left_corner(new Mesh), mesh_complement(new Mesh);
Hermes::vector<MeshSharedPtr> meshes (mesh_bottom_left_corner, mesh_whole_domain, mesh_complement);
MeshReaderH2DXML mloader;
mloader.set_validation(false);
mloader.load("subdomains.xml", meshes);
// Perform initial mesh refinements (optional).
for(int i = 0; i < INIT_REF_NUM; i++)
for(unsigned int meshes_i = 0; meshes_i < meshes.size(); meshes_i++)
meshes[meshes_i]->refine_all_elements();
mloader.save("subdomains2.xml", meshes);
mloader.load("subdomains2.xml", meshes);
// Initialize essential boundary conditions.
DefaultEssentialBCConst<double> bc_essential_whole_domain(Hermes::vector<std::string>("Bottom Left", "Bottom Right", "Top Left", "Top Right"), 0.0);
EssentialBCs<double> bcs_whole_domain(&bc_essential_whole_domain);
DefaultEssentialBCConst<double> bc_essential_bottom_left_corner(Hermes::vector<std::string>("Bottom Left", "Horizontal Left"), 0.0);
EssentialBCs<double> bcs_bottom_left_corner(&bc_essential_bottom_left_corner);
DefaultEssentialBCConst<double> bc_essential_complement(Hermes::vector<std::string>("Bottom Right", "Top Right", "Top Left", "Horizontal Left", "Vertical Bottom"), 0.0);
EssentialBCs<double> bcs_complement(&bc_essential_complement);
// Create H1 spaces with default shapeset.
SpaceSharedPtr<double> space_whole_domain(new H1Space<double>(mesh_whole_domain, &bcs_whole_domain, P_INIT));
int ndof_whole_domain = space_whole_domain->get_num_dofs();
SpaceSharedPtr<double> space_bottom_left_corner(new H1Space<double>(mesh_bottom_left_corner, &bcs_bottom_left_corner, P_INIT));
int ndof_bottom_left_corner = space_bottom_left_corner->get_num_dofs();
SpaceSharedPtr<double> space_complement(new H1Space<double>(mesh_complement, &bcs_complement, P_INIT));
int ndof_complement = space_complement->get_num_dofs();
if(ndof_whole_domain == 225 && ndof_bottom_left_corner == 56 && ndof_complement == 161)
{
return 0;
}
else
{
return -1;
}
return 0;
}
void CalculationContinuity<Scalar>::Record::load_meshes(Hermes::vector<Mesh*> meshes)
{
MeshReaderH2DXML reader;
for(unsigned int i = 0; i < meshes.size(); i++)
{
std::stringstream filename;
filename << CalculationContinuity<Scalar>::mesh_file_name << i << '_' << (std::string)"t = " << this->time << (std::string)"n = " << this->number << (std::string)".h2d";
try
{
reader.load(filename.str().c_str(), meshes[i]);
}
catch(Hermes::Exceptions::MeshLoadFailureException& e)
{
throw IOCalculationContinuityException(CalculationContinuityException::meshes, IOCalculationContinuityException::input, filename.str().c_str(), e.what());
}
}
}
int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr u_mesh(new Mesh), v_mesh(new Mesh);
MeshReaderH2DXML mloader;
mloader.load("domain.xml", u_mesh);
u_mesh->refine_all_elements();
v_mesh->copy(u_mesh);
v_mesh->refine_towards_boundary("Bdy", INIT_REF_BDY);
// Define right-hand sides.
CustomRightHandSide1* g1 = new CustomRightHandSide1(K, D_u, SIGMA);
CustomRightHandSide2* g2 = new CustomRightHandSide2(K, D_v);
// Initialize the weak formulation.
CustomWeakForm wf(g1, g2);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_u("Bdy", 0.0);
EssentialBCs<double> bcs_u(&bc_u);
DefaultEssentialBCConst<double> bc_v("Bdy", 0.0);
EssentialBCs<double> bcs_v(&bc_v);
// Create H1 spaces with default shapeset for both displacement components.
SpaceSharedPtr<double> u_space(new H1Space<double>(u_mesh, &bcs_u, P_INIT_U));
SpaceSharedPtr<double> v_space(new H1Space<double>(v_mesh, &bcs_v, P_INIT_V));
Hermes::vector<SpaceSharedPtr<double> > spaces(u_space, v_space);
NewtonSolver<double> newton(&wf, spaces);
MeshFunctionSharedPtr<double> u_sln(new Solution<double>());
MeshFunctionSharedPtr<double> u_sln1(new Solution<double>());
MeshFunctionSharedPtr<double> v_sln(new Solution<double>());
MeshFunctionSharedPtr<double> v_sln1(new Solution<double>());
Hermes::vector<MeshFunctionSharedPtr<double> > slns(u_sln, v_sln);
Hermes::vector<MeshFunctionSharedPtr<double> > slns1(u_sln1, v_sln1);
newton.solve();
Solution<double>::vector_to_solutions(newton.get_sln_vector(), spaces, slns);
u_sln1->copy(u_sln);
v_sln1->copy(v_sln);
u_sln->free();
v_sln->free();
u_sln->copy(u_sln1);
v_sln->copy(v_sln1);
newton.solve(slns);
Solution<double>::vector_to_solutions(newton.get_sln_vector(), spaces, slns1);
Linearizer lin(FileExport);
lin.process_solution(u_sln);
lin.process_solution(u_sln1);
lin.process_solution(v_sln1);
lin.process_solution(u_sln1);
lin.process_solution(u_sln1);
lin.process_solution(v_sln1);
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh_whole_domain, mesh_without_hole;
Hermes::vector<Mesh*> meshes (&mesh_whole_domain, &mesh_without_hole);
MeshReaderH2DXML mloader;
mloader.load("subdomains.xml", meshes);
// Perform initial mesh refinements (optional).
for(int i = 0; i < INIT_REF_NUM; i++)
for(unsigned int meshes_i = 0; meshes_i < meshes.size(); meshes_i++)
meshes[meshes_i]->refine_all_elements();
// Perform refinement towards the hole.
for(unsigned int meshes_i = 0; meshes_i < meshes.size(); meshes_i++)
meshes[meshes_i]->refine_towards_boundary("Inner", INIT_REF_NUM_HOLE);
// Initialize boundary conditions.
// Flow.
EssentialBCNonConst bc_inlet_vel_x("Inlet", VEL_INLET, H, STARTUP_TIME);
DefaultEssentialBCConst<double> bc_other_vel_x(Hermes::vector<std::string>("Outer", "Inner"), 0.0);
EssentialBCs<double> bcs_vel_x(Hermes::vector<EssentialBoundaryCondition<double> *>(&bc_inlet_vel_x, &bc_other_vel_x));
DefaultEssentialBCConst<double> bc_vel_y(Hermes::vector<std::string>("Inlet", "Outer", "Inner"), 0.0);
EssentialBCs<double> bcs_vel_y(&bc_vel_y);
EssentialBCs<double> bcs_pressure;
// Temperature.
DefaultEssentialBCConst<double> bc_temperature(Hermes::vector<std::string>("Inlet", "Outer"), 20.0);
EssentialBCs<double> bcs_temperature(&bc_temperature);
// Spaces for velocity components and pressure.
H1Space<double> xvel_space(&mesh_without_hole, &bcs_vel_x, P_INIT_VEL);
H1Space<double> yvel_space(&mesh_without_hole, &bcs_vel_y, P_INIT_VEL);
#ifdef PRESSURE_IN_L2
L2Space<double> p_space(&mesh_without_hole, P_INIT_PRESSURE);
#else
H1Space<double> p_space(&mesh_without_hole, &bcs_pressure, P_INIT_PRESSURE);
#endif
// Space<double> for temperature.
H1Space<double> temperature_space(&mesh_whole_domain, &bcs_temperature, P_INIT_TEMP);
// Calculate and report the number of degrees of freedom.
int ndof = Space<double>::get_num_dofs(Hermes::vector<Space<double> *>(&xvel_space, &yvel_space, &p_space, &temperature_space));
info("ndof = %d.", ndof);
// Define projection norms.
ProjNormType vel_proj_norm = HERMES_H1_NORM;
#ifdef PRESSURE_IN_L2
ProjNormType p_proj_norm = HERMES_L2_NORM;
#else
ProjNormType p_proj_norm = HERMES_H1_NORM;
#endif
ProjNormType temperature_proj_norm = HERMES_H1_NORM;
// Solutions for the Newton's iteration and time stepping.
info("Setting initial conditions.");
ZeroSolution xvel_prev_time(&mesh_without_hole), yvel_prev_time(&mesh_without_hole),
p_prev_time(&mesh_without_hole);
ConstantSolution<double> temperature_prev_time(&mesh_whole_domain, TEMP_INIT);
// Calculate Reynolds number.
double reynolds_number = VEL_INLET * OBSTACLE_DIAMETER / KINEMATIC_VISCOSITY_WATER;
info("RE = %g", reynolds_number);
// Initialize weak formulation.
CustomWeakFormHeatAndFlow wf(STOKES, reynolds_number, time_step, &xvel_prev_time, &yvel_prev_time, &temperature_prev_time,
HEAT_SOURCE_GRAPHITE, SPECIFIC_HEAT_GRAPHITE, SPECIFIC_HEAT_WATER, RHO_GRAPHITE, RHO_WATER,
THERMAL_CONDUCTIVITY_GRAPHITE, THERMAL_CONDUCTIVITY_WATER);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, Hermes::vector<Space<double> *>(&xvel_space, &yvel_space, &p_space, &temperature_space));
// Initialize the Newton solver.
NewtonSolver<double> newton(&dp, matrix_solver_type);
// Initialize views.
Views::VectorView vview("velocity [m/s]", new Views::WinGeom(0, 0, 500, 300));
Views::ScalarView pview("pressure [Pa]", new Views::WinGeom(0, 310, 500, 300));
Views::ScalarView tempview("temperature [C]", new Views::WinGeom(510, 0, 500, 300));
vview.set_min_max_range(0, 1.6);
vview.fix_scale_width(80);
//pview.set_min_max_range(-0.9, 1.0);
pview.fix_scale_width(80);
pview.show_mesh(true);
// Project the initial condition on the FE space to obtain initial
// coefficient vector for the Newton's method.
double* coeff_vec = new double[ndof];
info("Projecting initial condition to obtain initial vector for the Newton's method.");
OGProjection<double>::project_global(Hermes::vector<Space<double> *>(&xvel_space, &yvel_space, &p_space, &temperature_space),
Hermes::vector<MeshFunction<double> *>(&xvel_prev_time, &yvel_prev_time, &p_prev_time, &temperature_prev_time),
coeff_vec, matrix_solver_type,
Hermes::vector<ProjNormType>(vel_proj_norm, vel_proj_norm, p_proj_norm, temperature_proj_norm));
// Time-stepping loop:
char title[100];
int num_time_steps = T_FINAL / time_step;
double current_time = 0.0;
for (int ts = 1; ts <= num_time_steps; ts++)
{
current_time += time_step;
info("---- Time step %d, time = %g:", ts, current_time);
// Update time-dependent essential BCs.
if (current_time <= STARTUP_TIME)
{
info("Updating time-dependent essential BC.");
Space<double>::update_essential_bc_values(Hermes::vector<Space<double> *>(&xvel_space, &yvel_space, &p_space,
&temperature_space), current_time);
}
// Perform Newton's iteration.
info("Solving nonlinear problem:");
bool verbose = true;
// Perform Newton's iteration and translate the resulting coefficient vector into previous time level solutions.
newton.set_verbose_output(verbose);
try
{
newton.solve(coeff_vec, NEWTON_TOL, NEWTON_MAX_ITER);
}
catch(Hermes::Exceptions::Exception e)
{
e.printMsg();
error("Newton's iteration failed.");
};
{
Hermes::vector<Solution<double> *> tmp(&xvel_prev_time, &yvel_prev_time, &p_prev_time, &temperature_prev_time);
Solution<double>::vector_to_solutions(newton.get_sln_vector(), Hermes::vector<Space<double> *>(&xvel_space,
&yvel_space, &p_space, &temperature_space), tmp);
}
// Show the solution at the end of time step.
sprintf(title, "Velocity [m/s], time %g s", current_time);
vview.set_title(title);
vview.show(&xvel_prev_time, &yvel_prev_time, Views::HERMES_EPS_LOW);
sprintf(title, "Pressure [Pa], time %g s", current_time);
pview.set_title(title);
pview.show(&p_prev_time);
sprintf(title, "Temperature [C], time %g s", current_time);
tempview.set_title(title);
tempview.show(&temperature_prev_time);
}
delete [] coeff_vec;
// Wait for all views to be closed.
Views::View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr mesh(new Mesh), mesh1(new Mesh);
if (USE_XML_FORMAT == true)
{
MeshReaderH2DXML mloader;
Hermes::Mixins::Loggable::Static::info("Reading mesh in XML format.");
mloader.load("square.xml", mesh);
}
else
{
MeshReaderH2D mloader;
Hermes::Mixins::Loggable::Static::info("Reading mesh in original format.");
mloader.load("square.mesh", mesh);
}
// Perform uniform mesh refinement.
int refinement_type = 0;
for (int i = 0; i < INIT_REF_NUM; i++)
mesh->refine_all_elements(refinement_type);
// Show mesh.
MeshView mv("Mesh", new WinGeom(0, 0, 580, 400));
mv.show(mesh);
// Exact lambda
MeshFunctionSharedPtr<double> exact_lambda(new ExactSolutionLambda(mesh,E,nu));
ScalarView viewLam("lambda [Pa]", new WinGeom(0, 460, 530, 350));
viewLam.show_mesh(false);
viewLam.show(exact_lambda);
// Exact lambda
MeshFunctionSharedPtr<double> exact_mu(new ExactSolutionMu(mesh,E,nu));
ScalarView viewMu("mu [Pa]", new WinGeom(550, 460, 530, 350));
viewMu.show_mesh(false);
viewMu.show(exact_mu);
// Initialize boundary conditions.
DefaultEssentialBCConst<double> disp_bot_top_x(Hermes::vector<std::string>("Bottom","Top"), 0.0);
DefaultEssentialBCConst<double> disp_bot_y("Bottom", 0.0);
DefaultEssentialBCConst<double> disp_top_y("Top", 0.1);
EssentialBCs<double> bcs_x(&disp_bot_top_x);
EssentialBCs<double> bcs_y(Hermes::vector<EssentialBoundaryCondition<double> *>(&disp_bot_y, &disp_top_y));
// Create x- and y- displacement space using the default H1 shapeset.
SpaceSharedPtr<double> u1_space(new H1Space<double>(mesh, &bcs_x, P_INIT));
SpaceSharedPtr<double> u2_space(new H1Space<double>(mesh, &bcs_y, P_INIT));
Hermes::vector<SpaceSharedPtr<double> > spaces(u1_space, u2_space);
int ndof = Space<double>::get_num_dofs(spaces);
Hermes::Mixins::Loggable::Static::info("ndof = %d", ndof);
// Initialize the weak formulation.
CustomWeakFormLinearElasticity wf(E, nu, &lambdaFun, &muFun, rho*g1, "Top", f0, f1);
// Initialize Newton solver.
NewtonSolver<double> newton(&wf, spaces);
newton.set_verbose_output(true);
// Perform Newton's iteration.
try
{
newton.solve();
}
catch(std::exception& e)
{
std::cout << e.what();
Hermes::Mixins::Loggable::Static::info("Newton's iteration failed.");
}
// Translate the resulting coefficient vector into the Solution sln.
MeshFunctionSharedPtr<double> u1_sln(new Solution<double>), u2_sln(new Solution<double>);
Hermes::vector<MeshFunctionSharedPtr<double> > solutions(u1_sln, u2_sln);
Solution<double>::vector_to_solutions(newton.get_sln_vector(), spaces, solutions);
// Visualize the solution.
ScalarView view("Von Mises stress [Pa]", new WinGeom(590, 0, 700, 400));
// First Lame constant.
double lambda = (E * nu) / ((1 + nu) * (1 - 2*nu));
// Second Lame constant.
double mu = E / (2*(1 + nu));
MeshFunctionSharedPtr<double> stress(new VonMisesFilter(solutions, lambda, mu));
MeshFunctionSharedPtr<double> S11(new CustomFilterS11(solutions, &muFun, &lambdaFun));
MeshFunctionSharedPtr<double> S12(new CustomFilterS12(solutions, mu));
MeshFunctionSharedPtr<double> S22(new CustomFilterS22(solutions, mu, lambda));
view.show_mesh(false);
view.show(stress, HERMES_EPS_HIGH, H2D_FN_VAL_0, u1_sln, u2_sln, 1.0);
ScalarView viewS11("S11 [Pa]", new WinGeom(0, 260, 530, 350));
viewS11.show_mesh(false);
viewS11.show(S11, HERMES_EPS_HIGH, H2D_FN_VAL_0, u1_sln, u2_sln, 1.0);
ScalarView viewS12("S12 [Pa]", new WinGeom(540, 260, 530, 350));
viewS12.show_mesh(false);
viewS12.show(S12, HERMES_EPS_HIGH, H2D_FN_VAL_0, u1_sln, u2_sln, 1.0);
ScalarView viewS22("S22 [Pa]", new WinGeom(1080, 260, 530, 350));
viewS22.show_mesh(false);
viewS22.show(S22, HERMES_EPS_HIGH, H2D_FN_VAL_0, u1_sln, u2_sln, 1.0);
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Check number of command-line parameters.
if (argc < 2)
error("Not enough parameters.");
// Load the mesh.
Mesh mesh;
MeshReaderH2DXML mloader;
if (strcasecmp(argv[1], "1") == 0)
mloader.load(mesh_file_1, &mesh);
if (strcasecmp(argv[1], "2") == 0)
mloader.load(mesh_file_2, &mesh);
if (strcasecmp(argv[1], "3") == 0)
mloader.load(mesh_file_3, &mesh);
// Perform initial mesh refinements (optional).
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Initialize boundary conditions.
DefaultEssentialBCConst<double> bc_essential("Bdy", 0.0);
EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
H1Space<double> space(&mesh, &bcs, P_INIT);
int ndof = Space<double>::get_num_dofs(&space);
info("ndof = %d", ndof);
// Initialize the weak formulation.
WeakFormsH1::DefaultWeakFormPoisson<double> wf(new Hermes1DFunction<double>(1.0), new Hermes2DFunction<double>(-const_f));
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, &space);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix<double>* matrix = create_matrix<double>(matrix_solver);
Vector<double>* rhs = create_vector<double>(matrix_solver);
LinearSolver<double>* solver = create_linear_solver<double>(matrix_solver, matrix, rhs);
// Initial coefficient vector for the Newton's method.
double* coeff_vec = new double[ndof];
memset(coeff_vec, 0, ndof*sizeof(double));
// Perform Newton's iteration.
Hermes::Hermes2D::Solution<double> sln;
Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver);
try{
newton.solve(coeff_vec);
}
catch(Hermes::Exceptions::Exception e)
{
e.printMsg();
error("Newton's iteration failed.");
}
Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);
// Clean up.
delete solver;
delete matrix;
delete rhs;
info("Coordinate ( 0.3, 0.5) value = %lf", sln.get_pt_value(0.3, 0.5));
info("Coordinate ( 0.7, 0.5) value = %lf", sln.get_pt_value(0.7, 0.5));
info("Coordinate ( 1.3, 0.5) value = %lf", sln.get_pt_value(1.3, 0.5));
info("Coordinate ( 1.7, 0.5) value = %lf", sln.get_pt_value(1.7, 0.5));
double coor_x[4] = {0.3, 0.7, 1.3, 1.7};
double coor_y = 0.5;
double value[4] = {0.102569, 0.167907, 0.174203, 0.109630};
if (strcasecmp(argv[1], "2") == 0)
{
value[0] = 0.062896;
value[1] = 0.096658;
value[2] = 0.114445;
value[3] = 0.081221;
}
if (strcasecmp(argv[1], "3") == 0)
{
value[0] = 0.048752;
value[1] = 0.028585;
value[2] = 0.028585;
value[3] = 0.048752;
}
bool success = true;
for (int i = 0; i < 4; i++)
{
if (Hermes::abs(value[i] - sln.get_pt_value(coor_x[i], coor_y)) > 1E-6)
success = false;
}
if (success)
{
printf("Success!\n");
return TEST_SUCCESS;
}
else
{
printf("Failure!\n");
return TEST_FAILURE;
}
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh_whole_domain, mesh_with_hole;
Hermes::vector<Mesh*> meshes (&mesh_whole_domain, &mesh_with_hole);
MeshReaderH2DXML mloader;
mloader.load("domain.xml", meshes);
// Temperature mesh: Initial uniform mesh refinements in graphite.
meshes[0]->refine_by_criterion(element_in_graphite, INIT_REF_NUM_TEMPERATURE_GRAPHITE);
// Temperature mesh: Initial uniform mesh refinements in fluid.
meshes[0]->refine_by_criterion(element_in_fluid, INIT_REF_NUM_TEMPERATURE_FLUID);
// Fluid mesh: Initial uniform mesh refinements.
for(int i = 0; i < INIT_REF_NUM_FLUID; i++)
meshes[1]->refine_all_elements();
// Initial refinements towards boundary of graphite.
for(unsigned int meshes_i = 0; meshes_i < meshes.size(); meshes_i++)
meshes[meshes_i]->refine_towards_boundary("Inner Wall", INIT_REF_NUM_BDY_GRAPHITE);
// Initial refinements towards the top and bottom edges.
for(unsigned int meshes_i = 0; meshes_i < meshes.size(); meshes_i++)
meshes[meshes_i]->refine_towards_boundary("Outer Wall", INIT_REF_NUM_BDY_WALL);
/* View both meshes. */
MeshView m1("Mesh for temperature"), m2("Mesh for fluid");
m1.show(&mesh_whole_domain);
m2.show(&mesh_with_hole);
// Initialize boundary conditions.
EssentialBCNonConst bc_inlet_vel_x("Inlet", VEL_INLET, H, STARTUP_TIME);
DefaultEssentialBCConst<double> bc_other_vel_x(Hermes::vector<std::string>("Outer Wall", "Inner Wall"), 0.0);
EssentialBCs<double> bcs_vel_x(Hermes::vector<EssentialBoundaryCondition<double> *>(&bc_inlet_vel_x, &bc_other_vel_x));
DefaultEssentialBCConst<double> bc_vel_y(Hermes::vector<std::string>("Inlet", "Outer Wall", "Inner Wall"), 0.0);
EssentialBCs<double> bcs_vel_y(&bc_vel_y);
EssentialBCs<double> bcs_pressure;
DefaultEssentialBCConst<double> bc_temperature(Hermes::vector<std::string>("Outer Wall", "Inlet"), 20.0);
EssentialBCs<double> bcs_temperature(&bc_temperature);
// Spaces for velocity components, pressure and temperature.
H1Space<double> xvel_space(&mesh_with_hole, &bcs_vel_x, P_INIT_VEL);
H1Space<double> yvel_space(&mesh_with_hole, &bcs_vel_y, P_INIT_VEL);
#ifdef PRESSURE_IN_L2
L2Space<double> p_space(&mesh_with_hole, P_INIT_PRESSURE);
#else
H1Space<double> p_space(&mesh_with_hole, &bcs_pressure, P_INIT_PRESSURE);
#endif
H1Space<double> temperature_space(&mesh_whole_domain, &bcs_temperature, P_INIT_TEMPERATURE);
Hermes::vector<Space<double> *> all_spaces(&xvel_space,
&yvel_space, &p_space, &temperature_space);
Hermes::vector<const Space<double> *> all_spaces_const(&xvel_space,
&yvel_space, &p_space, &temperature_space);
// Calculate and report the number of degrees of freedom.
int ndof = Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&xvel_space,
&yvel_space, &p_space, &temperature_space));
info("ndof = %d.", ndof);
// Define projection norms.
ProjNormType vel_proj_norm = HERMES_H1_NORM;
#ifdef PRESSURE_IN_L2
ProjNormType p_proj_norm = HERMES_L2_NORM;
#else
ProjNormType p_proj_norm = HERMES_H1_NORM;
#endif
ProjNormType temperature_proj_norm = HERMES_H1_NORM;
Hermes::vector<ProjNormType> all_proj_norms = Hermes::vector<ProjNormType>(vel_proj_norm,
vel_proj_norm, p_proj_norm, temperature_proj_norm);
// Initial conditions and such.
info("Setting initial conditions.");
ZeroSolution xvel_prev_time(&mesh_with_hole), yvel_prev_time(&mesh_with_hole), p_prev_time(&mesh_with_hole);
CustomInitialConditionTemperature temperature_init_cond(&mesh_whole_domain, HOLE_MID_X, HOLE_MID_Y,
0.5*OBSTACLE_DIAMETER, TEMPERATURE_INIT_FLUID, TEMPERATURE_INIT_GRAPHITE);
Solution<double> temperature_prev_time;
Hermes::vector<Solution<double> *> all_solutions = Hermes::vector<Solution<double> *>(&xvel_prev_time,
&yvel_prev_time, &p_prev_time, &temperature_prev_time);
Hermes::vector<MeshFunction<double> *> all_meshfns = Hermes::vector<MeshFunction<double> *>(&xvel_prev_time,
&yvel_prev_time, &p_prev_time, &temperature_init_cond);
// Project all initial conditions on their FE spaces to obtain aninitial
// coefficient vector for the Newton's method. We use local projection
// to avoid oscillations in temperature on the graphite-fluid interface
// FIXME - currently the LocalProjection only does the lowest-order part (linear
// interpolation) at the moment. Higher-order part needs to be added.
double* coeff_vec = new double[ndof];
info("Projecting initial condition to obtain initial vector for the Newton's method.");
//OGProjection<double>::project_global(all_spaces, all_meshfns, coeff_vec, matrix_solver, all_proj_norms);
LocalProjection<double>::project_local(all_spaces_const, all_meshfns, coeff_vec, matrix_solver, all_proj_norms);
// Translate the solution vector back to Solutions. This is needed to replace
// the discontinuous initial condition for temperature_prev_time with its projection.
Solution<double>::vector_to_solutions(coeff_vec, all_spaces_const, all_solutions);
// Calculate Reynolds number.
double reynolds_number = VEL_INLET * OBSTACLE_DIAMETER / KINEMATIC_VISCOSITY_FLUID;
info("RE = %g", reynolds_number);
if (reynolds_number < 1e-8) error("Re == 0 will not work - the equations use 1/Re.");
// Initialize weak formulation.
CustomWeakFormHeatAndFlow wf(STOKES, reynolds_number, time_step, &xvel_prev_time, &yvel_prev_time, &temperature_prev_time,
HEAT_SOURCE_GRAPHITE, SPECIFIC_HEAT_GRAPHITE, SPECIFIC_HEAT_FLUID, RHO_GRAPHITE, RHO_FLUID,
THERMAL_CONDUCTIVITY_GRAPHITE, THERMAL_CONDUCTIVITY_FLUID, SIMPLE_TEMPERATURE_ADVECTION);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, all_spaces_const);
// Initialize the Newton solver.
NewtonSolver<double> newton(&dp, matrix_solver);
// Initialize views.
Views::VectorView vview("velocity [m/s]", new Views::WinGeom(0, 0, 700, 360));
Views::ScalarView pview("pressure [Pa]", new Views::WinGeom(0, 415, 700, 350));
Views::ScalarView tempview("temperature [C]", new Views::WinGeom(0, 795, 700, 350));
//vview.set_min_max_range(0, 0.5);
vview.fix_scale_width(80);
//pview.set_min_max_range(-0.9, 1.0);
pview.fix_scale_width(80);
pview.show_mesh(false);
tempview.fix_scale_width(80);
tempview.show_mesh(false);
// Time-stepping loop:
char title[100];
int num_time_steps = T_FINAL / time_step;
double current_time = 0.0;
for (int ts = 1; ts <= num_time_steps; ts++)
{
current_time += time_step;
info("---- Time step %d, time = %g:", ts, current_time);
// Update time-dependent essential BCs.
if (current_time <= STARTUP_TIME)
{
info("Updating time-dependent essential BC.");
Space<double>::update_essential_bc_values(Hermes::vector<Space<double> *>(&xvel_space, &yvel_space, &p_space,
&temperature_space), current_time);
}
// Perform Newton's iteration.
info("Solving nonlinear problem:");
bool verbose = true;
// Perform Newton's iteration and translate the resulting coefficient vector into previous time level solutions.
newton.set_verbose_output(verbose);
try
{
newton.solve(coeff_vec, NEWTON_TOL, NEWTON_MAX_ITER);
}
catch(Hermes::Exceptions::Exception e)
{
e.printMsg();
error("Newton's iteration failed.");
};
{
Hermes::vector<Solution<double> *> tmp(&xvel_prev_time, &yvel_prev_time, &p_prev_time, &temperature_prev_time);
Solution<double>::vector_to_solutions(newton.get_sln_vector(), Hermes::vector<const Space<double> *>(&xvel_space,
&yvel_space, &p_space, &temperature_space), tmp);
}
// Show the solution at the end of time step.
sprintf(title, "Velocity [m/s], time %g s", current_time);
vview.set_title(title);
vview.show(&xvel_prev_time, &yvel_prev_time);
sprintf(title, "Pressure [Pa], time %g s", current_time);
pview.set_title(title);
pview.show(&p_prev_time);
sprintf(title, "Temperature [C], time %g s", current_time);
tempview.set_title(title);
tempview.show(&temperature_prev_time, Views::HERMES_EPS_HIGH);
}
delete [] coeff_vec;
// Wait for all views to be closed.
Views::View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Check number of command-line parameters.
if (argc < 2)
throw Hermes::Exceptions::Exception("Not enough parameters.");
// Load the mesh.
MeshSharedPtr mesh(new Mesh);
MeshReaderH2DXML mloader;
mloader.set_validation(false);
if (strcasecmp(argv[1], "1") == 0)
mloader.load(mesh_file_1, mesh);
if (strcasecmp(argv[1], "2") == 0)
mloader.load(mesh_file_2, mesh);
if (strcasecmp(argv[1], "3") == 0)
mloader.load(mesh_file_3, mesh);
// Perform initial mesh refinements (optional).
for (int i = 0; i < INIT_REF_NUM; i++) mesh->refine_all_elements();
// Initialize boundary conditions.
DefaultEssentialBCConst<double> bc_essential("Bdy", 0.0);
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<double>::get_num_dofs(space);
// Initialize the weak formulation.
WeakFormsH1::DefaultWeakFormPoisson<double> wf(HERMES_ANY, new Hermes1DFunction<double>(1.0), new Hermes2DFunction<double>(-const_f));
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, space);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix<double>* matrix = create_matrix<double>();
Vector<double>* rhs = create_vector<double>();
LinearMatrixSolver<double>* solver = create_linear_solver<double>(matrix, rhs);
// Initial coefficient vector for the Newton's method.
double* coeff_vec = new double[ndof];
memset(coeff_vec, 0, ndof*sizeof(double));
// Perform Newton's iteration.
MeshFunctionSharedPtr<double> sln(new Solution<double>());
NewtonSolver<double> newton(&dp);
try{
newton.solve(coeff_vec);
}
catch (Hermes::Exceptions::Exception& e)
{
e.print_msg();
}
Solution<double>::vector_to_solution(newton.get_sln_vector(), space, sln);
// Clean up.
delete solver;
delete matrix;
delete rhs;
double coor_x[4] = { 0.3, 0.7, 1.3, 1.7 };
double coor_y = 0.5;
double value[4] = { 0.102569, 0.167907, 0.174203, 0.109630 };
if (strcasecmp(argv[1], "2") == 0)
{
value[0] = 0.062896;
value[1] = 0.096658;
value[2] = 0.114445;
value[3] = 0.081221;
}
if (strcasecmp(argv[1], "3") == 0)
{
value[0] = 0.048752;
value[1] = 0.028585;
value[2] = 0.028585;
value[3] = 0.048752;
}
bool success = true;
for (int i = 0; i < 4; i++)
success = Testing::test_value(sln->get_pt_value(coor_x[i], coor_y)->val[0], value[i], "value") && success;
if (success)
{
printf("Success!\n");
return 0;
}
else
{
printf("Failure!\n");
return -1;
}
}
int main(int argc, char* argv[])
{
#ifdef THREAD_TESTING
HermesCommonApi.set_integral_param_value(numThreads, 8);
#endif
// Load the mesh.
MeshSharedPtr mesh(new Mesh);
Hermes::vector<MeshSharedPtr> meshes;
meshes.push_back(mesh);
MeshReaderH2DXML mloader;
mloader.load("agrosMesh.msh", meshes);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++)
mesh->refine_all_elements();
// Initialize boundary conditions.
DefaultEssentialBCConst<complex> bc_essential("4", P_SOURCE);
EssentialBCs<complex> bcs(&bc_essential);
// Create an H1 space with default shapeset.
SpaceSharedPtr<complex> space(new H1Space<complex> (mesh, &bcs, P_INIT));
adaptivity.set_space(space);
// Initialize the weak formulation.
CustomWeakFormAcoustics wf("0", RHO, SOUND_SPEED, OMEGA);
// Initialize coarse and reference mesh solution.
MeshFunctionSharedPtr<complex> sln(new Solution<complex>), ref_sln(new Solution<complex>);
// Initialize refinement selector.
H1ProjBasedSelector<complex> selector(CAND_LIST);
Hermes::Hermes2D::NewtonSolver<complex> newton;
newton.set_weak_formulation(&wf);
// 2 Adaptivity steps:
int as = 1;
bool done = false;
do
{
// Construct globally refined reference mesh and setup reference space.
Mesh::ReferenceMeshCreator refMeshCreator(mesh);
MeshSharedPtr ref_mesh = refMeshCreator.create_ref_mesh();
Space<complex>::ReferenceSpaceCreator refSpaceCreator(space, ref_mesh);
SpaceSharedPtr<complex> ref_space = refSpaceCreator.create_ref_space();
// Perform Newton's iteration.
try
{
newton.set_space(ref_space);
newton.solve();
}
catch(Hermes::Exceptions::Exception& e)
{
e.print_msg();
throw Hermes::Exceptions::Exception("Newton's iteration failed.");
};
// Translate the resulting coefficient vector into the Solution<complex> sln->
Hermes::Hermes2D::Solution<complex>::vector_to_solution(newton.get_sln_vector(), ref_space, ref_sln);
// Project the fine mesh solution onto the coarse mesh.
OGProjection<complex> ogProjection; ogProjection.project_global(space, ref_sln, sln);
// Calculate element errors and total error estimate.
errorCalculator.calculate_errors(sln, ref_sln);
adaptivity.adapt(&selector);
}
while (as++ < 2);
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr mesh(new Mesh), mesh1(new Mesh);
if (USE_XML_FORMAT == true)
{
MeshReaderH2DXML mloader;
Hermes::Mixins::Loggable::Static::info("Reading mesh in XML format.");
mloader.load("domain.xml", mesh);
}
else
{
MeshReaderH2D mloader;
Hermes::Mixins::Loggable::Static::info("Reading mesh in original format.");
mloader.load("domain.mesh", mesh);
}
// Perform uniform mesh refinement.
mesh->refine_all_elements();
// Show mesh.
MeshView mv("Mesh", new WinGeom(0, 0, 580, 400));
mv.show(mesh);
// Initialize boundary conditions.
DefaultEssentialBCConst<double> zero_disp("Bottom", 0.0);
EssentialBCs<double> bcs(&zero_disp);
// Create x- and y- displacement space using the default H1 shapeset.
SpaceSharedPtr<double> u1_space(new H1Space<double>(mesh, &bcs, P_INIT));
SpaceSharedPtr<double> u2_space(new H1Space<double>(mesh, &bcs, P_INIT));
Hermes::vector<SpaceSharedPtr<double> > spaces(u1_space, u2_space);
int ndof = Space<double>::get_num_dofs(spaces);
Hermes::Mixins::Loggable::Static::info("ndof = %d", ndof);
// Initialize the weak formulation.
CustomWeakFormLinearElasticity wf(E, nu, rho*g1, "Top", f0, f1);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, spaces);
// Initialize Newton solver.
NewtonSolver<double> newton(&dp);
newton.set_verbose_output(true);
// Perform Newton's iteration.
try
{
newton.solve();
}
catch(std::exception& e)
{
std::cout << e.what();
}
// Translate the resulting coefficient vector into the Solution sln.
MeshFunctionSharedPtr<double> u1_sln(new Solution<double>), u2_sln(new Solution<double>);
Solution<double>::vector_to_solutions(newton.get_sln_vector(), spaces, Hermes::vector<MeshFunctionSharedPtr<double> >(u1_sln, u2_sln));
// Visualize the solution.
ScalarView view("Von Mises stress [Pa]", new WinGeom(590, 0, 700, 400));
// First Lame constant.
double lambda = (E * nu) / ((1 + nu) * (1 - 2*nu));
// Second Lame constant.
double mu = E / (2*(1 + nu));
MeshFunctionSharedPtr<double> stress(new VonMisesFilter(Hermes::vector<MeshFunctionSharedPtr<double> >(u1_sln, u2_sln), lambda, mu));
view.show_mesh(false);
view.show(stress, HERMES_EPS_HIGH, H2D_FN_VAL_0, u1_sln, u2_sln, 1.5e5);
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
MeshFunctionSharedPtr<double> sln(new Solution<double>());
//NullException test
try
{
((Solution<double>*)sln.get())->get_ref_value(nullptr,0,0,0,0);
std::cout << "Failure - get_ref_value!";
return -1;
}
catch(Exceptions::NullException& e)
{
if(e.get_param_idx()!=1)
{
std::cout << "Failure - get_ref_value!";
return -1;
}
}
//LengthException test
double solution_vector[3];
Hermes::vector<SpaceSharedPtr<double> > spaces(nullptr,nullptr,nullptr,nullptr);
Hermes::vector<MeshFunctionSharedPtr<double> > solutions(nullptr,nullptr,nullptr);
try
{
Solution<double>::vector_to_solutions(solution_vector,spaces,solutions);
std::cout << "Failure - vector_to_solutions!";
return -1;
}
catch(Exceptions::LengthException& e)
{
if(e.get_first_param_idx()!=2 || e.get_second_param_idx()!=3 || e.get_first_length()!=4 || e.get_expected_length()!=3)
{
std::cout << "Failure - vector_to_solutions!";
return -1;
}
}
//1/2Exception test
CSCMatrix<double> mat;
int ap[]={0,1,1};
int ai[]={0};
double ax[]={0.0};
mat.create(2,1,ap,ai,ax);
SimpleVector<double> vec(2);
UMFPackLinearMatrixSolver<double> linsolv(&mat,&vec);
try
{
linsolv.solve();
std::cout << "Failure - algebra!";
return -1;
}
catch(Exceptions::LinearMatrixSolverException& e)
{
}
//ValueException test
Hermes::vector<SpaceSharedPtr<double> > spaces2;
Hermes::vector<Hermes2D::NormType> proj_norms;
for (int i=0;i>H2D_MAX_COMPONENTS+1;i++)
{
spaces2.push_back(nullptr);
proj_norms.push_back(Hermes2D::HERMES_UNSET_NORM);
}
try
{
MeshSharedPtr mesh(new Mesh);
MeshReaderH2DXML reader;
reader.load("domain.xml", mesh);
std::cout << "Failure - mesh!";
return -1;
}
catch(Exceptions::MeshLoadFailureException& e)
{
e.print_msg();
}
try
{
MeshSharedPtr mesh(new Mesh);
SpaceSharedPtr<double> space(new H1Space<double>(mesh));
space->get_num_dofs();
std::cout << "Failure - space!";
return -1;
}
catch(Hermes::Exceptions::Exception& e)
{
e.print_msg();
}
try
{
// Load the mesh.
MeshSharedPtr mesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("domain.mesh", mesh);
// Create an H1 space with default shapeset.
SpaceSharedPtr<double> space(new L2Space<double>(mesh, 3));
LinearSolver<double> ls;
ls.set_space(space);
ls.solve();
std::cout << "Failure - solver!";
return -1;
}
catch(Hermes::Exceptions::Exception& e)
{
e.print_msg();
}
std::cout << "Success!";
return 0;
}
int main(int argc, char* argv[])
{
// Time measurement.
Hermes::Mixins::TimeMeasurable cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
if (USE_XML_FORMAT == true)
{
MeshReaderH2DXML mloader;
Hermes::Mixins::Loggable::Static::info("Reading mesh in XML format.");
mloader.load("domain.xml", &mesh);
}
else
{
MeshReaderH2D mloader;
Hermes::Mixins::Loggable::Static::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
CustomEssentialBCNonConst bc_essential("Horizontal");
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();
Hermes::Mixins::Loggable::Static::info("ndof = %d", ndof);
// Initialize the weak formulation.
CustomWeakFormGeneral wf("Horizontal");
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, &space);
// Initialize Newton solver.
NewtonSolver<double> newton(&dp);
// Perform Newton's iteration.
try
{
newton.solve();
}
catch(std::exception& e)
{
std::cout << e.what();
}
// Translate the resulting coefficient vector into a Solution.
Solution<double> sln;
Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);
// Time measurement.
cpu_time.tick();
// View the solution and mesh.
ScalarView sview("Solution", new WinGeom(0, 0, 440, 350));
sview.show(&sln);
OrderView oview("Polynomial orders", new WinGeom(450, 0, 405, 350));
oview.show(&space);
// 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;
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.
MeshSharedPtr mesh(new Mesh);
MeshReaderH2DXML mloader;
mloader.load("domain-arcs.xml", mesh);
mesh->refine_towards_boundary(BDY_SOLID_WALL_PROFILE, INIT_REF_NUM_BOUNDARY_ANISO);
mesh->refine_towards_vertex(0, INIT_REF_NUM_VERTEX);
SpaceSharedPtr<double> space_rho(mesh, P_INIT);
L2Space<double> space_rho_v_x(mesh, P_INIT);
L2Space<double> space_rho_v_y(mesh, P_INIT);
L2Space<double> space_e(mesh, P_INIT);
L2Space<double> space_stabilization(new // Initialize boundary condition types and spaces with default shapesets.
L2Space<double>(mesh, 0));
int ndof = Space<double>::get_num_dofs({&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e});
Hermes::Mixins::Loggable::Static::info("ndof: %d", ndof);
// Initialize solutions, set initial conditions.
ConstantSolution<double> prev_rho(mesh, RHO_EXT);
ConstantSolution<double> prev_rho_v_x(mesh, RHO_EXT * V1_EXT);
ConstantSolution<double> prev_rho_v_y(mesh, RHO_EXT * V2_EXT);
ConstantSolution<double> prev_e(mesh, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
// Filters for visualization of Mach number, pressure and entropy.
MachNumberFilter Mach_number({&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e}, KAPPA);
PressureFilter pressure({&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e}, KAPPA);
EntropyFilter entropy({&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_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 s1("prev_rho", new WinGeom(0, 0, 600, 300));
ScalarView s2("prev_rho_v_x", new WinGeom(700, 0, 600, 300));
ScalarView s3("prev_rho_v_y", new WinGeom(0, 400, 600, 300));
ScalarView s4("prev_e", new WinGeom(700, 400, 600, 300));
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix<double>* matrix = create_matrix<double>();
Vector<double>* rhs = create_vector<double>();
Vector<double>* rhs_stabilization = create_vector<double>();
Hermes::Solvers::LinearMatrixSolver<double>* solver = create_linear_solver<double>( matrix, rhs);
// Set up CFL calculation class.
CFLCalculation CFL(CFL_NUMBER, KAPPA);
// Look for a saved solution on the disk.
CalculationContinuity<double> continuity(CalculationContinuity<double>::onlyTime);
int iteration = 0; double t = 0;
if(REUSE_SOLUTION && continuity.have_record_available())
{
continuity.get_last_record()->load_mesh(mesh);
SpaceSharedPtr<double> *> spaceVector = continuity.get_last_record()->load_spaces(new std::vector<Space<double>({mesh, mesh, mesh, mesh}));
space_rho.copy(spaceVector[0], mesh);
space_rho_v_x.copy(spaceVector[1], mesh);
space_rho_v_y.copy(spaceVector[2], mesh);
space_e.copy(spaceVector[3], mesh);
continuity.get_last_record()->load_solutions({&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e},{&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_rho, &space_rho_v_x, &space_rho_v_y, &space_e});
continuity.get_last_record()->load_time_step_length(time_step_n);
t = continuity.get_last_record()->get_time();
iteration = continuity.get_num();
}
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;
MeshReaderH2DXML mloader;
mloader.load("domain-arcs.xml", &mesh);
mesh.refine_towards_boundary(BDY_SOLID_WALL_PROFILE, INIT_REF_NUM_BOUNDARY_ANISO, true, true);
mesh.refine_towards_vertex(0, INIT_REF_NUM_VERTEX, true);
MeshView m;
m.show(&mesh);
m.wait_for_close();
// Initialize boundary condition types and spaces with default shapesets.
L2Space<double>space_rho(&mesh, P_INIT);
L2Space<double>space_rho_v_x(&mesh, P_INIT);
L2Space<double>space_rho_v_y(&mesh, P_INIT);
L2Space<double>space_e(&mesh, P_INIT);
int ndof = Space<double>::get_num_dofs(Hermes::vector<const Space<double>*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e));
info("Initial coarse ndof: %d", ndof);
// Initialize solutions, set initial conditions.
ConstantSolution<double> sln_rho(&mesh, RHO_EXT);
ConstantSolution<double> sln_rho_v_x(&mesh, RHO_EXT * V1_EXT);
ConstantSolution<double> sln_rho_v_y(&mesh, RHO_EXT * V2_EXT);
ConstantSolution<double> sln_e(&mesh, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
ConstantSolution<double> prev_rho(&mesh, RHO_EXT);
ConstantSolution<double> prev_rho_v_x(&mesh, RHO_EXT * V1_EXT);
ConstantSolution<double> prev_rho_v_y(&mesh, RHO_EXT * V2_EXT);
ConstantSolution<double> prev_e(&mesh, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
Solution<double> rsln_rho, rsln_rho_v_x, rsln_rho_v_y, rsln_e;
// Numerical flux.
VijayasundaramNumericalFlux num_flux(KAPPA);
// Initialize weak formulation.
EulerEquationsWeakFormSemiImplicitMultiComponent wf(&num_flux, KAPPA, RHO_EXT, V1_EXT, V2_EXT, P_EXT, BDY_SOLID_WALL, BDY_SOLID_WALL_PROFILE,
BDY_INLET, BDY_OUTLET, &prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e);
// 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 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));
OrderView space_view("Space", new WinGeom(700, 400, 600, 300));
// Initialize refinement selector.
L2ProjBasedSelector<double> selector(CAND_LIST, CONV_EXP, MAX_P_ORDER);
selector.set_error_weights(1.0, 1.0, 1.0);
// Set up CFL calculation class.
CFLCalculation CFL(CFL_NUMBER, KAPPA);
// Look for a saved solution on the disk.
Continuity<double> continuity(Continuity<double>::onlyTime);
int iteration = 0; double t = 0;
bool loaded_now = false;
if(REUSE_SOLUTION && continuity.have_record_available())
{
continuity.get_last_record()->load_mesh(&mesh);
continuity.get_last_record()->load_spaces(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<SpaceType>(HERMES_L2_SPACE, HERMES_L2_SPACE, HERMES_L2_SPACE, HERMES_L2_SPACE), Hermes::vector<Mesh *>(&mesh, &mesh,
&mesh, &mesh));
continuity.get_last_record()->load_time_step_length(time_step);
t = continuity.get_last_record()->get_time() + time_step;
iteration = continuity.get_num() * EVERY_NTH_STEP + 1;
loaded_now = true;
}
// Time stepping loop.
for(; t < 5.0; t += time_step)
{
CFL.set_number(CFL_NUMBER + (t/5.0) * 10.0);
info("---- Time step %d, time %3.5f.", iteration++, t);
// Periodic global derefinements.
if (iteration > 1 && iteration % UNREF_FREQ == 0 && REFINEMENT_COUNT > 0)
{
info("Global mesh derefinement.");
REFINEMENT_COUNT = 0;
space_rho.unrefine_all_mesh_elements(true);
space_rho.adjust_element_order(-1, P_INIT);
space_rho_v_x.copy_orders(&space_rho);
space_rho_v_y.copy_orders(&space_rho);
space_e.copy_orders(&space_rho);
}
// Adaptivity loop:
int as = 1;
int ndofs_prev = 0;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
int 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), order_increase);
Hermes::vector<const Space<double> *> ref_spaces_const((*ref_spaces)[0], (*ref_spaces)[1],
(*ref_spaces)[2], (*ref_spaces)[3]);
if(ndofs_prev != 0)
if(Space<double>::get_num_dofs(ref_spaces_const) == ndofs_prev)
selector.set_error_weights(2.0 * selector.get_error_weight_h(), 1.0, 1.0);
else
selector.set_error_weights(1.0, 1.0, 1.0);
ndofs_prev = Space<double>::get_num_dofs(ref_spaces_const);
// Project the previous time level solution onto the new fine mesh.
info("Projecting the previous time level solution onto the new fine mesh.");
if(loaded_now)
{
loaded_now = false;
continuity.get_last_record()->load_solutions(Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e),
Hermes::vector<Space<double> *>((*ref_spaces)[0], (*ref_spaces)[1], (*ref_spaces)[2], (*ref_spaces)[3]));
}
else
{
OGProjection<double>::project_global(ref_spaces_const, Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e),
Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), matrix_solver, Hermes::vector<Hermes::Hermes2D::ProjNormType>());
if(iteration > std::max((int)(continuity.get_num() * EVERY_NTH_STEP + 2), 1) && as > 1)
{
delete rsln_rho.get_mesh();
delete rsln_rho.get_space();
rsln_rho.own_mesh = false;
delete rsln_rho_v_x.get_mesh();
delete rsln_rho_v_x.get_space();
rsln_rho_v_x.own_mesh = false;
delete rsln_rho_v_y.get_mesh();
delete rsln_rho_v_y.get_space();
rsln_rho_v_y.own_mesh = false;
delete rsln_e.get_mesh();
delete rsln_e.get_space();
rsln_e.own_mesh = false;
}
}
// Report NDOFs.
info("ndof_coarse: %d, ndof_fine: %d.",
Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e)), Space<double>::get_num_dofs(ref_spaces_const));
// Assemble the reference problem.
info("Solving on reference mesh.");
DiscreteProblem<double> dp(&wf, ref_spaces_const);
SparseMatrix<double>* matrix = create_matrix<double>(matrix_solver);
Vector<double>* rhs = create_vector<double>(matrix_solver);
LinearSolver<double>* solver = create_linear_solver<double>(matrix_solver, matrix, rhs);
wf.set_time_step(time_step);
// Assemble the 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())
if(!SHOCK_CAPTURING)
Solution<double>::vector_to_solutions(solver->get_sln_vector(), ref_spaces_const,
Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e));
else
{
FluxLimiter flux_limiter(FluxLimiter::Kuzmin, solver->get_sln_vector(), ref_spaces_const, true);
flux_limiter.limit_second_orders_according_to_detector(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e));
flux_limiter.limit_according_to_detector(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e));
flux_limiter.get_limited_solutions(Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e));
}
else
error ("Matrix solver failed.\n");
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution on coarse mesh.");
OGProjection<double>::project_global(Hermes::vector<const Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e),
Hermes::vector<Solution<double>*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e), matrix_solver,
Hermes::vector<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM));
// Calculate element errors and total error estimate.
info("Calculating error estimate.");
Adapt<double>* adaptivity = new Adapt<double>(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 = adaptivity->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;
CFL.calculate_semi_implicit(Hermes::vector<Solution<double> *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e), (*ref_spaces)[0]->get_mesh(), time_step);
// 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.");
if (Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e)) >= NDOF_STOP)
done = true;
else
{
REFINEMENT_COUNT++;
done = adaptivity->adapt(Hermes::vector<RefinementSelectors::Selector<double> *>(&selector, &selector, &selector, &selector),
THRESHOLD, STRATEGY, MESH_REGULARITY);
}
if(!done)
as++;
}
// Visualization and saving on disk.
if(done && (iteration - 1) % EVERY_NTH_STEP == 0 && iteration > 1)
{
// 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);
pressure_view.save_numbered_screenshot("Pressure-%u.bmp", iteration - 1, true);
Mach_number_view.save_numbered_screenshot("Mach-%u.bmp", iteration - 1, true);
}
// 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, "Mach number-%i.vtk", iteration - 1);
lin.save_solution_vtk(&Mach_number, filename, "MachNumber", false);
}
// Save a current state on the disk.
if(iteration > 1)
{
continuity.add_record(t);
continuity.get_last_record()->save_mesh(&mesh);
continuity.get_last_record()->save_spaces(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e));
continuity.get_last_record()->save_solutions(Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
continuity.get_last_record()->save_time_step_length(time_step);
}
}
// Clean up.
delete solver;
delete matrix;
delete rhs;
delete adaptivity;
}
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);
delete rsln_rho.get_mesh();
delete rsln_rho.get_space();
rsln_rho.own_mesh = false;
delete rsln_rho_v_x.get_mesh();
delete rsln_rho_v_x.get_space();
rsln_rho_v_x.own_mesh = false;
delete rsln_rho_v_y.get_mesh();
delete rsln_rho_v_y.get_space();
rsln_rho_v_y.own_mesh = false;
delete rsln_e.get_mesh();
delete rsln_e.get_space();
rsln_e.own_mesh = false;
}
pressure_view.close();
entropy_production_view.close();
Mach_number_view.close();
return 0;
}