int main(int argc, char* argv[])
{
// Choose a Butcher's table or define your own.
ButcherTable bt(butcher_table_type);
if (bt.is_explicit()) info("Using a %d-stage explicit R-K method.", bt.get_size());
if (bt.is_diagonally_implicit()) info("Using a %d-stage diagonally implicit R-K method.", bt.get_size());
if (bt.is_fully_implicit()) info("Using a %d-stage fully implicit R-K method.", bt.get_size());
// Load the mesh.
Mesh mesh;
MeshReaderH2D mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinemets.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Initialize solutions.
CustomInitialConditionWave E_sln(&mesh);
ZeroSolutionVector F_sln(&mesh);
Hermes::vector<Solution<double>*> slns(&E_sln, &F_sln);
// Initialize the weak formulation.
CustomWeakFormWave wf(C_SQUARED);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_essential("Perfect conductor", 0.0);
EssentialBCs<double> bcs(&bc_essential);
// Create x- and y- displacement space using the default H1 shapeset.
HcurlSpace<double> E_space(&mesh, &bcs, P_INIT);
HcurlSpace<double> F_space(&mesh, &bcs, P_INIT);
Hermes::vector<Space<double> *> spaces = Hermes::vector<Space<double> *>(&E_space, &F_space);
info("ndof = %d.", Space<double>::get_num_dofs(spaces));
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, spaces);
// Initialize views.
ScalarView E1_view("Solution E1", new WinGeom(0, 0, 400, 350));
E1_view.fix_scale_width(50);
ScalarView E2_view("Solution E2", new WinGeom(410, 0, 400, 350));
E2_view.fix_scale_width(50);
// Initialize Runge-Kutta time stepping.
RungeKutta<double> runge_kutta(&dp, &bt, matrix_solver_type);
// Time stepping loop.
double current_time = 0;
int ts = 1;
do
{
// Perform one Runge-Kutta time step according to the selected Butcher's table.
info("Runge-Kutta time step (t = %g s, time_step = %g s, stages: %d).",
current_time, time_step, bt.get_size());
bool verbose = true;
bool jacobian_changed = true;
try
{
runge_kutta.rk_time_step_newton(current_time, time_step, slns, slns, jacobian_changed, verbose);
}
catch(Exceptions::Exception& e)
{
e.printMsg();
error("Runge-Kutta time step failed");
}
// Visualize the solutions.
char title[100];
sprintf(title, "E1, t = %g", current_time);
E1_view.set_title(title);
E1_view.show(&E_sln, HERMES_EPS_NORMAL, H2D_FN_VAL_0);
sprintf(title, "E2, t = %g", current_time);
E2_view.set_title(title);
E2_view.show(&E_sln, HERMES_EPS_NORMAL, H2D_FN_VAL_1);
// Update time.
current_time += time_step;
} while (current_time < T_FINAL);
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
MeshReaderH2D mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinemets.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Initialize solutions.
CustomInitialConditionWave E_sln(&mesh);
ZeroSolutionVector F_sln(&mesh);
Hermes::vector<Solution<double>*> slns(&E_sln, &F_sln);
// Initialize the weak formulation.
CustomWeakFormWave wf(time_step, C_SQUARED, &E_sln, &F_sln);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_essential("Perfect conductor", 0.0);
EssentialBCs<double> bcs(&bc_essential);
// Create x- and y- displacement space using the default H1 shapeset.
HcurlSpace<double> E_space(&mesh, &bcs, P_INIT);
HcurlSpace<double> F_space(&mesh, &bcs, P_INIT);
Hermes::vector<Space<double> *> spaces = Hermes::vector<Space<double> *>(&E_space, &F_space);
info("ndof = %d.", Space<double>::get_num_dofs(spaces));
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, spaces);
// 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);
solver->set_factorization_scheme(HERMES_REUSE_FACTORIZATION_COMPLETELY);
// Initialize views.
ScalarView E1_view("Solution E1", new WinGeom(0, 0, 400, 350));
E1_view.fix_scale_width(50);
ScalarView E2_view("Solution E2", new WinGeom(410, 0, 400, 350));
E2_view.fix_scale_width(50);
// Time stepping loop.
double current_time = 0; int ts = 1;
do
{
// Perform one implicit Euler time step.
info("Implicit Euler time step (t = %g s, time_step = %g s).", current_time, time_step);
// First time assemble both the stiffness matrix and right-hand side vector,
// then just the right-hand side vector.
if (ts == 1) {
info("Assembling the stiffness matrix and right-hand side vector.");
dp.assemble(matrix, rhs);
static char file_name[1024];
sprintf(file_name, "matrix.m");
FILE *f = fopen(file_name, "w");
matrix->dump(f, "A");
fclose(f);
}
else {
info("Assembling the right-hand side vector (only).");
dp.assemble(rhs);
}
// Solve the linear system and if successful, obtain the solution.
info("Solving the matrix problem.");
if(solver->solve()) Solution<double>::vector_to_solutions(solver->get_sln_vector(), spaces, slns);
else error ("Matrix solver failed.\n");
// Visualize the solutions.
char title[100];
sprintf(title, "E1, t = %g", current_time);
E1_view.set_title(title);
E1_view.show(&E_sln, HERMES_EPS_NORMAL, H2D_FN_VAL_0);
sprintf(title, "E2, t = %g", current_time);
E2_view.set_title(title);
E2_view.show(&E_sln, HERMES_EPS_NORMAL, H2D_FN_VAL_1);
// Update time.
current_time += time_step;
} while (current_time < T_FINAL);
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Choose a Butcher's table or define your own.
ButcherTable bt(butcher_table_type);
if (bt.is_explicit()) info("Using a %d-stage explicit R-K method.", bt.get_size());
if (bt.is_diagonally_implicit()) info("Using a %d-stage diagonally implicit R-K method.", bt.get_size());
if (bt.is_fully_implicit()) info("Using a %d-stage fully implicit R-K method.", bt.get_size());
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("../domain.mesh", &mesh);
// Perform initial mesh refinemets.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Initialize solutions.
CustomInitialConditionWave E_sln(&mesh);
Solution F_sln(&mesh, 0.0, 0.0);
Hermes::vector<Solution*> slns(&E_sln, &F_sln);
// Initialize the weak formulation.
CustomWeakFormWave wf(C_SQUARED);
// Initialize boundary conditions
DefaultEssentialBCConst bc_essential(BDY, 0.0);
EssentialBCs bcs(&bc_essential);
// Create x- and y- displacement space using the default H1 shapeset.
HcurlSpace E_space(&mesh, &bcs, P_INIT);
HcurlSpace F_space(&mesh, &bcs, P_INIT);
Hermes::vector<Space *> spaces = Hermes::vector<Space *>(&E_space, &F_space);
info("ndof = %d.", Space::get_num_dofs(spaces));
// Initialize the FE problem.
DiscreteProblem dp(&wf, spaces);
// Initialize Runge-Kutta time stepping.
RungeKutta runge_kutta(&dp, &bt, matrix_solver);
// Time stepping loop.
double current_time = 0; int ts = 1;
do
{
// Perform one Runge-Kutta time step according to the selected Butcher's table.
info("Runge-Kutta time step (t = %g s, time_step = %g s, stages: %d).",
current_time, time_step, bt.get_size());
bool verbose = true;
bool jacobian_changed = true;
if (!runge_kutta.rk_time_step(current_time, time_step, slns, slns, jacobian_changed, verbose))
error("Runge-Kutta time step failed, try to decrease time step size.");
// Update time.
current_time += time_step;
} while (current_time < T_FINAL);
double coord_x[4] = {0.3, 0.6, 0.9, 1.4};
double coord_y[4] = {0, 0.3, 0.5, 0.7};
info("Coordinate (0.3, 0.0) value = %lf", F_sln.get_pt_value(coord_x[0], coord_y[0]));
info("Coordinate (0.6, 0.3) value = %lf", F_sln.get_pt_value(coord_x[1], coord_y[1]));
info("Coordinate (0.9, 0.5) value = %lf", F_sln.get_pt_value(coord_x[2], coord_y[2]));
info("Coordinate (1.4, 0.7) value = %lf", F_sln.get_pt_value(coord_x[3], coord_y[3]));
double t_value[4] = {-0.144673, -0.264077, -0.336536, -0.368983};
bool success = true;
for (int i = 0; i < 4; i++)
{
if (fabs(t_value[i] - F_sln.get_pt_value(coord_x[i], coord_y[i])) > 1E-6) success = false;
}
if (success) {
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}
int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr mesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("domain.mesh", mesh);
// Perform initial mesh refinemets.
for (int i = 0; i < INIT_REF_NUM; i++) mesh->refine_all_elements();
// Initialize solutions.
MeshFunctionSharedPtr<double> E_sln(new CustomInitialConditionWave(mesh));
MeshFunctionSharedPtr<double> F_sln(new ZeroSolutionVector<double>(mesh));
Hermes::vector<MeshFunctionSharedPtr<double> > slns(E_sln, F_sln);
// Initialize the weak formulation.
CustomWeakFormWaveIE wf(time_step, C_SQUARED, E_sln, F_sln);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_essential("Perfect conductor", 0.0);
EssentialBCs<double> bcs(&bc_essential);
SpaceSharedPtr<double> E_space(new HcurlSpace<double>(mesh, &bcs, P_INIT));
SpaceSharedPtr<double> F_space(new HcurlSpace<double>(mesh, &bcs, P_INIT));
Hermes::vector<SpaceSharedPtr<double> > spaces = Hermes::vector<SpaceSharedPtr<double> >(E_space, F_space);
int ndof = HcurlSpace<double>::get_num_dofs(spaces);
Hermes::Mixins::Loggable::Static::info("ndof = %d.", ndof);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, spaces);
// Project the initial condition on the FE space to obtain initial
// coefficient vector for the Newton's method.
// NOTE: If you want to start from the zero vector, just define
// coeff_vec to be a vector of ndof zeros (no projection is needed).
Hermes::Mixins::Loggable::Static::info("Projecting to obtain initial vector for the Newton's method.");
double* coeff_vec = new double[ndof];
OGProjection<double> ogProjection; ogProjection.project_global(spaces, slns, coeff_vec);
// Initialize Newton solver.
NewtonSolver<double> newton(&dp);
// Initialize views.
ScalarView E1_view("Solution E1", new WinGeom(0, 0, 400, 350));
E1_view.fix_scale_width(50);
ScalarView E2_view("Solution E2", new WinGeom(410, 0, 400, 350));
E2_view.fix_scale_width(50);
ScalarView F1_view("Solution F1", new WinGeom(0, 410, 400, 350));
F1_view.fix_scale_width(50);
ScalarView F2_view("Solution F2", new WinGeom(410, 410, 400, 350));
F2_view.fix_scale_width(50);
// Time stepping loop.
double current_time = 0; int ts = 1;
do
{
// Perform one implicit Euler time step.
Hermes::Mixins::Loggable::Static::info("Implicit Euler time step (t = %g s, time_step = %g s).", current_time, time_step);
// Perform Newton's iteration.
try
{
newton.set_max_allowed_iterations(NEWTON_MAX_ITER);
newton.set_tolerance(NEWTON_TOL, Hermes::Solvers::ResidualNormAbsolute);
newton.solve(coeff_vec);
}
catch(Hermes::Exceptions::Exception e)
{
e.print_msg();
throw Hermes::Exceptions::Exception("Newton's iteration failed.");
}
// Translate the resulting coefficient vector into Solutions.
Solution<double>::vector_to_solutions(newton.get_sln_vector(), spaces, slns);
// Visualize the solutions.
char title[100];
sprintf(title, "E1, t = %g", current_time + time_step);
E1_view.set_title(title);
E1_view.show(E_sln, H2D_FN_VAL_0);
sprintf(title, "E2, t = %g", current_time + time_step);
E2_view.set_title(title);
E2_view.show(E_sln, H2D_FN_VAL_1);
sprintf(title, "F1, t = %g", current_time + time_step);
F1_view.set_title(title);
F1_view.show(F_sln, H2D_FN_VAL_0);
sprintf(title, "F2, t = %g", current_time + time_step);
F2_view.set_title(title);
F2_view.show(F_sln, H2D_FN_VAL_1);
//View::wait();
// Update time.
current_time += time_step;
} while (current_time < T_FINAL);
// Wait for the view to be closed.
View::wait();
return 0;
}
