int main(int argc, char* argv[])
{
// Choose a Butcher's table or define your own.
ButcherTable bt(butcher_table_type);
// Initialize the time.
double current_time = 0;
// mesh->
MeshSharedPtr mesh(new Mesh);
// Init mesh->
MeshReaderH2D mloader;
mloader.load("cathedral.mesh", mesh);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++)
mesh->refine_all_elements();
mesh->refine_towards_boundary("Boundary_air", INIT_REF_NUM_BDY);
mesh->refine_towards_boundary("Boundary_ground", INIT_REF_NUM_BDY);
// Initialize boundary conditions.
Hermes::Hermes2D::DefaultEssentialBCConst<double> bc_essential("Boundary_ground", TEMP_INIT);
Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);
// space->
SpaceSharedPtr<double> space(new H1Space<double>(mesh, &bcs, P_INIT));
// Solution pointer.
MeshFunctionSharedPtr<double> sln_time_prev(new ConstantSolution<double>(mesh, TEMP_INIT));
MeshFunctionSharedPtr<double> sln_time_new(new Solution<double>(mesh));
WeakFormSharedPtr<double> wf(new CustomWeakFormHeatRK("Boundary_air", ALPHA, LAMBDA, HEATCAP, RHO, ¤t_time, TEMP_INIT, T_FINAL));
// Initialize views.
Hermes::Hermes2D::Views::ScalarView Tview("Temperature", new Hermes::Hermes2D::Views::WinGeom(0, 0, 450, 600));
Tview.set_min_max_range(0, 20);
Tview.fix_scale_width(30);
// Initialize Runge-Kutta time stepping.
RungeKutta<double> runge_kutta(wf, space, &bt);
runge_kutta.set_tolerance(NEWTON_TOL);
runge_kutta.set_verbose_output(true);
runge_kutta.set_time_step(time_step);
// Iteration number.
int iteration = 0;
// Time stepping loop:
do
{
// Perform one Runge-Kutta time step according to the selected Butcher's table.
try
{
runge_kutta.set_time(current_time);
runge_kutta.rk_time_step_newton(sln_time_prev, sln_time_new);
}
catch (Exceptions::Exception& e)
{
e.print_msg();
}
// Show the new_ time level solution.
char title[100];
sprintf(title, "Time %3.2f s", current_time);
Tview.set_title(title);
Tview.show(sln_time_new);
// Copy solution for the new_ time step.
sln_time_prev->copy(sln_time_new);
// Increase current time and time step counter.
current_time += time_step;
iteration++;
} while (current_time < T_FINAL);
// Wait for the view to be closed.
Hermes::Hermes2D::Views::View::wait();
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("cathedral.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary("Boundary air", INIT_REF_NUM_BDY);
mesh.refine_towards_boundary("Boundary ground", INIT_REF_NUM_BDY);
// Previous time level solution (initialized by the external temperature).
Solution tsln(&mesh, TEMP_INIT);
// Initialize the weak formulation.
double current_time = 0;
CustomWeakFormHeatRK1 wf("Boundary air", ALPHA, LAMBDA, HEATCAP, RHO, time_step,
¤t_time, TEMP_INIT, T_FINAL, &tsln);
// Initialize boundary conditions.
DefaultEssentialBCConst bc_essential("Boundary ground", TEMP_INIT);
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);
solver->set_factorization_scheme(HERMES_REUSE_FACTORIZATION_COMPLETELY);
// Initial coefficient vector for the Newton's method.
scalar* coeff_vec = new scalar[ndof];
memset(coeff_vec, 0, ndof*sizeof(scalar));
// Initialize views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 450, 600));
Tview.set_min_max_range(0,20);
Tview.fix_scale_width(30);
// Time stepping:
int ts = 1;
bool jacobian_changed = true;
do
{
info("---- Time step %d, time %3.5f s", ts, current_time);
// Perform Newton's iteration.
if (!hermes2d.solve_newton(coeff_vec, &dp, solver, matrix, rhs,
jacobian_changed)) error("Newton's iteration failed.");
jacobian_changed = false;
// Translate the resulting coefficient vector into the Solution sln.
Solution::vector_to_solution(coeff_vec, &space, &tsln);
// Visualize the solution.
char title[100];
sprintf(title, "Time %3.2f s", current_time);
Tview.set_title(title);
Tview.show(&tsln);
// Increase current time and time step counter.
current_time += time_step;
ts++;
}
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("cathedral.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_AIR, INIT_REF_NUM_BDY);
mesh.refine_towards_boundary(BDY_GROUND, INIT_REF_NUM_BDY);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(Hermes::vector<std::string>(BDY_GROUND));
bc_types.add_bc_newton(BDY_AIR);
// Enter Dirichlet boundary values.
BCValues bc_values;
bc_values.add_const(BDY_GROUND, TEMP_INIT);
// Initialize an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Previous time level solution (initialized by the external temperature).
Solution u_prev_time(&mesh, TEMP_INIT);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(stac_jacobian_vol));
wf.add_vector_form(callback(stac_residual_vol));
wf.add_matrix_form_surf(callback(stac_jacobian_surf), BDY_AIR);
wf.add_vector_form_surf(callback(stac_residual_surf), BDY_AIR);
// Project the initial condition on the FE space to obtain initial solution coefficient vector.
info("Projecting initial condition to translate initial condition into a vector.");
scalar* coeff_vec = new scalar[ndof];
OGProjection::project_global(&space, &u_prev_time, coeff_vec, matrix_solver);
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem dp(&wf, &space, is_linear);
// Initialize views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 450, 600));
Tview.set_min_max_range(0,20);
Tview.fix_scale_width(30);
// Time stepping loop:
double current_time = 0.0; int ts = 1;
do
{
// Perform one Runge-Kutta time step according to the selected Butcher's table.
info("Runge-Kutta time step (t = %g, tau = %g, stages: %d).",
current_time, time_step, bt.get_size());
bool verbose = true;
bool is_linear = true;
if (!rk_time_step(current_time, time_step, &bt, coeff_vec, &dp, matrix_solver,
verbose, is_linear)) {
error("Runge-Kutta time step failed, try to decrease time step size.");
}
// Convert coeff_vec into a new time level solution.
Solution::vector_to_solution(coeff_vec, &space, &u_prev_time);
// Update time.
current_time += time_step;
// Show the new time level solution.
char title[100];
sprintf(title, "Time %3.2f, exterior temperature %3.5f", current_time, temp_ext(current_time));
Tview.set_title(title);
Tview.show(&u_prev_time);
// Increase counter of time steps.
ts++;
}
while (current_time < T_FINAL);
// Cleanup.
delete [] coeff_vec;
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("cathedral.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(bdy_air, INIT_REF_NUM_BDY);
// Initialize an H1 space with default shepeset.
H1Space space(&mesh, bc_types, essential_bc_values, P_INIT);
int ndof = get_num_dofs(&space);
info("ndof = %d.", ndof);
// Set initial condition.
Solution tsln;
tsln.set_const(&mesh, T_INIT);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, double>, bilinear_form<Ord, Ord>);
wf.add_matrix_form_surf(bilinear_form_surf<double, double>, bilinear_form_surf<Ord, Ord>, bdy_air);
wf.add_vector_form(linear_form<double, double>, linear_form<Ord, Ord>, H2D_ANY, &tsln);
wf.add_vector_form_surf(linear_form_surf<double, double>, linear_form_surf<Ord, Ord>, bdy_air);
// Initialize the linear problem.
LinearProblem lp(&wf, &space);
// Initialize matrix solver.
Matrix* mat; Vector* rhs; CommonSolver* solver;
init_matrix_solver(matrix_solver, ndof, mat, rhs, solver);
// Initialize views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 450, 600));
char title[100];
sprintf(title, "Time %3.5f, exterior temperature %3.5f", TIME, temp_ext(TIME));
Tview.set_min_max_range(0,20);
Tview.set_title(title);
Tview.fix_scale_width(3);
// Time stepping:
int nsteps = (int)(FINAL_TIME/TAU + 0.5);
bool rhsonly = false;
for(int ts = 1; ts <= nsteps; ts++)
{
info("---- Time step %d, time %3.5f, ext_temp %g", ts, TIME, temp_ext(TIME));
// Assemble stiffness matrix and rhs.
lp.assemble(mat, rhs, rhsonly);
rhsonly = true;
// Solve the matrix problem.
if (!solver->solve(mat, rhs)) error ("Matrix solver failed.\n");
// Update tsln.
tsln.set_fe_solution(&space, rhs);
// Update the time variable.
TIME += TAU;
// Visualize the solution.
sprintf(title, "Time %3.2f, exterior temperature %3.5f", TIME, temp_ext(TIME));
Tview.set_title(title);
Tview.show(&tsln);
}
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// load and refine mesh
Mesh mesh;
mesh.load("cathedral.mesh");
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(2, 5);
// set up shapeset
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// set up spaces
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// set initial condition
Solution tsln;
tsln.set_const(&mesh, T_INIT);
// weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, bilinear_form<double, double>, bilinear_form<Ord, Ord>);
wf.add_biform_surf(0, 0, bilinear_form_surf<double, double>, bilinear_form_surf<Ord, Ord>, marker_air);
wf.add_liform(0, linear_form<double, double>, linear_form<Ord, Ord>, ANY, 1, &tsln);
wf.add_liform_surf(0, linear_form_surf<double, double>, linear_form_surf<Ord, Ord>, marker_air);
// matrix solver
UmfpackSolver umfpack;
// linear system
LinSystem ls(&wf, &umfpack);
ls.set_spaces(1, &space);
ls.set_pss(1, &pss);
// visualisation
ScalarView Tview("Temperature", 0, 0, 450, 600);
char title[100];
sprintf(title, "Time %3.5f, exterior temperature %3.5f", TIME, temp_ext(TIME));
Tview.set_min_max_range(0,20);
Tview.set_title(title);
Tview.fix_scale_width(3);
// time stepping
int nsteps = (int)(FINAL_TIME/TAU + 0.5);
bool rhsonly = false;
for(int n = 1; n <= nsteps; n++)
{
info("\n---- Time %3.5f, time step %d, ext_temp %g ----------", TIME, n, temp_ext(TIME));
// assemble and solve
ls.assemble(rhsonly);
rhsonly = true;
ls.solve(1, &tsln);
// shifting the time variable
TIME += TAU;
// visualization of solution
sprintf(title, "Time %3.2f, exterior temperature %3.5f", TIME, temp_ext(TIME));
Tview.set_title(title);
Tview.show(&tsln);
//Tview.wait_for_keypress();
}
// Note: a separate example shows how to create videos
// wait for keyboard or mouse input
View::wait("Waiting for keyboard or mouse input.");
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("cathedral.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_AIR, INIT_REF_NUM_BDY);
mesh.refine_towards_boundary(BDY_GROUND, INIT_REF_NUM_BDY);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(Hermes::vector<std::string>(BDY_GROUND));
bc_types.add_bc_newton(BDY_AIR);
// Enter Dirichlet boundary values.
BCValues bc_values;
bc_values.add_const(BDY_GROUND, TEMP_INIT);
// Initialize an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Previous time level solution (initialized by the external temperature).
Solution tsln(&mesh, TEMP_INIT);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(bilinear_form));
wf.add_matrix_form_surf(callback(bilinear_form_surf), BDY_AIR);
wf.add_vector_form(callback(linear_form), HERMES_ANY, &tsln);
wf.add_vector_form_surf(callback(linear_form_surf), BDY_AIR);
// 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);
solver->set_factorization_scheme(HERMES_REUSE_FACTORIZATION_COMPLETELY);
// Initialize views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 450, 600));
Tview.set_min_max_range(0,20);
Tview.fix_scale_width(30);
// Time stepping:
int ts = 1; bool rhs_only = false;
do
{
info("---- Time step %d, time %3.5f s, ext_temp %g C", ts, current_time, temp_ext(current_time));
// First time assemble both the stiffness matrix and right-hand side vector,
// then just the right-hand side vector.
if (rhs_only == false) info("Assembling the stiffness matrix and right-hand side vector.");
else info("Assembling the right-hand side vector (only).");
dp.assemble(matrix, rhs, rhs_only);
rhs_only = true;
// 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, &tsln);
else error ("Matrix solver failed.\n");
// Visualize the solution.
char title[100];
sprintf(title, "Time %3.2f s, exterior temperature %3.5f C", current_time, temp_ext(current_time));
Tview.set_title(title);
Tview.show(&tsln);
// Increase current time and time step counter.
current_time += time_step;
ts++;
}
while (current_time < T_FINAL);
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
#ifdef WITH_PARALUTION
HermesCommonApi.set_integral_param_value(matrixSolverType, SOLVER_PARALUTION_AMG);
// Load the mesh.
MeshSharedPtr mesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("domain.mesh", mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh->refine_all_elements();
mesh->refine_towards_boundary("Boundary air", INIT_REF_NUM_BDY);
mesh->refine_towards_boundary("Boundary ground", INIT_REF_NUM_BDY);
// Previous time level solution (initialized by the external temperature).
MeshFunctionSharedPtr<double> tsln(new ConstantSolution<double> (mesh, TEMP_INIT));
// Initialize the weak formulation.
double current_time = 0;
CustomWeakFormHeatRK1 wf("Boundary air", ALPHA, LAMBDA, HEATCAP, RHO, time_step,
¤t_time, TEMP_INIT, T_FINAL, tsln);
// Initialize boundary conditions.
DefaultEssentialBCConst<double> bc_essential("Boundary ground", TEMP_INIT);
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 Newton solver.
NewtonSolver<double> newton(&wf, space);
#ifdef SHOW_OUTPUT
newton.set_verbose_output(true);
#else
newton.set_verbose_output(false);
#endif
newton.set_jacobian_constant();
newton.get_linear_matrix_solver()->as_AMGSolver()->set_smoother(Solvers::GMRES, Preconditioners::ILU);
newton.get_linear_matrix_solver()->as_LoopSolver()->set_tolerance(1e-1, RelativeTolerance);
#ifdef SHOW_OUTPUT
// Initialize views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 450, 600));
Tview.set_min_max_range(0,20);
Tview.fix_scale_width(30);
#endif
// Time stepping:
int ts = 1;
do
{
Hermes::Mixins::Loggable::Static::info("---- Time step %d, time %3.5f s", ts, current_time);
newton.solve();
// Translate the resulting coefficient vector into the Solution sln.
Solution<double>::vector_to_solution(newton.get_sln_vector(), space, tsln);
#ifdef SHOW_OUTPUT
// Visualize the solution.
char title[100];
sprintf(title, "Time %3.2f s", current_time);
Tview.set_title(title);
Tview.show(tsln);
#endif
// Increase current time and time step counter.
current_time += time_step;
ts++;
}
while (current_time < T_FINAL);
// Wait for the view to be closed.
#ifdef SHOW_OUTPUT
View::wait();
#endif
return 0;
#endif
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("cathedral.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_AIR, INIT_REF_NUM_BDY);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(BDY_GROUND);
bc_types.add_bc_newton(BDY_AIR);
// Enter Dirichlet boundary values.
BCValues bc_values;
bc_values.add_const(BDY_GROUND, T_INIT);
// Initialize an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Initialize the solution.
Solution tsln;
// Set the initial condition.
tsln.set_const(&mesh, T_INIT);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, double>, bilinear_form<Ord, Ord>);
wf.add_matrix_form_surf(bilinear_form_surf<double, double>, bilinear_form_surf<Ord, Ord>, BDY_AIR);
wf.add_vector_form(linear_form<double, double>, linear_form<Ord, Ord>, HERMES_ANY, &tsln);
wf.add_vector_form_surf(linear_form_surf<double, double>, linear_form_surf<Ord, Ord>, BDY_AIR);
// 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 views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 450, 600));
char title[100];
sprintf(title, "Time %3.5f, exterior temperature %3.5f", TIME, temp_ext(TIME));
Tview.set_min_max_range(0,20);
Tview.set_title(title);
Tview.fix_scale_width(3);
// Time stepping:
int nsteps = (int)(FINAL_TIME/TAU + 0.5);
bool rhs_only = false;
for(int ts = 1; ts <= nsteps; ts++)
{
info("---- Time step %d, time %3.5f, ext_temp %g", ts, TIME, temp_ext(TIME));
// First time assemble both the stiffness matrix and right-hand side vector,
// then just the right-hand side vector.
if (rhs_only == false) info("Assembling the stiffness matrix and right-hand side vector.");
else info("Assembling the right-hand side vector (only).");
dp.assemble(matrix, rhs, rhs_only);
rhs_only = true;
// 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, &tsln);
else
error ("Matrix solver failed.\n");
// Update the time variable.
TIME += TAU;
// Visualize the solution.
sprintf(title, "Time %3.2f, exterior temperature %3.5f", TIME, temp_ext(TIME));
Tview.set_title(title);
Tview.show(&tsln);
}
// Wait for the view to be closed.
View::wait();
// Clean up.
delete solver;
delete matrix;
delete rhs;
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("wall.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_BOTTOM, INIT_REF_NUM_BDY);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_neumann(Hermes::vector<int>(BDY_RIGHT, BDY_LEFT));
bc_types.add_bc_newton(Hermes::vector<int>(BDY_BOTTOM, BDY_TOP));
// Initialize an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, NULL, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Previous and next time level solutions.
Solution* sln_time_prev = new Solution(&mesh, TEMP_INIT);
Solution* sln_time_new = new Solution(&mesh);
Solution* time_error_fn = new Solution(&mesh, 0.0);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(stac_jacobian_vol, stac_jacobian_vol_ord, HERMES_NONSYM, HERMES_ANY, sln_time_prev);
wf.add_vector_form(stac_residual_vol, stac_residual_vol_ord, HERMES_ANY, sln_time_prev);
wf.add_matrix_form_surf(stac_jacobian_bottom, stac_jacobian_bottom_ord, BDY_BOTTOM, sln_time_prev);
wf.add_vector_form_surf(stac_residual_bottom, stac_residual_bottom_ord, BDY_BOTTOM, sln_time_prev);
wf.add_matrix_form_surf(stac_jacobian_top, stac_jacobian_top_ord, BDY_TOP, sln_time_prev);
wf.add_vector_form_surf(stac_residual_top, stac_residual_top_ord, BDY_TOP, sln_time_prev);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
// Initialize views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 1500, 400));
Tview.fix_scale_width(40);
ScalarView eview("Temporal error", new WinGeom(0, 450, 1500, 400));
eview.fix_scale_width(40);
// Graph for time step history.
SimpleGraph time_step_graph;
info("Time step history will be saved to file time_step_history.dat.");
// 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, tau = %g s, stages: %d).",
current_time, time_step, bt.get_size());
bool verbose = true;
bool is_linear = true;
if (!rk_time_step(current_time, time_step, &bt, sln_time_prev, sln_time_new, time_error_fn, &dp, matrix_solver,
verbose, is_linear)) {
error("Runge-Kutta time step failed, try to decrease time step size.");
}
// Plot error function.
char title[100];
sprintf(title, "Temporal error, t = %g", current_time);
eview.set_title(title);
AbsFilter abs_tef(time_error_fn);
eview.show(&abs_tef, HERMES_EPS_VERYHIGH);
// Calculate relative time stepping error and decide whether the
// time step can be accepted. If not, then the time step size is
// reduced and the entire time step repeated. If yes, then another
// check is run, and if the relative error is very low, time step
// is increased.
double rel_err_time = calc_norm(time_error_fn, HERMES_H1_NORM) / calc_norm(sln_time_new, HERMES_H1_NORM) * 100;
info("rel_err_time = %g%%", rel_err_time);
if (rel_err_time > TIME_TOL_UPPER) {
info("rel_err_time above upper limit %g%% -> decreasing time step from %g to %g and restarting time step.",
TIME_TOL_UPPER, time_step, time_step * TIME_STEP_DEC_RATIO);
time_step *= TIME_STEP_DEC_RATIO;
continue;
}
if (rel_err_time < TIME_TOL_LOWER) {
info("rel_err_time = below lower limit %g%% -> increasing time step from %g to %g",
TIME_TOL_UPPER, time_step, time_step * TIME_STEP_INC_RATIO);
time_step *= TIME_STEP_INC_RATIO;
}
// Add entry to the timestep graph.
time_step_graph.add_values(current_time, time_step);
time_step_graph.save("time_step_history.dat");
// Update time.
current_time += time_step;
// Show the new time level solution.
sprintf(title, "Time %3.2f s", current_time);
Tview.set_title(title);
Tview.show(sln_time_new);
// Copy solution for the new time step.
sln_time_prev->copy(sln_time_new);
// Increase counter of time steps.
ts++;
}
while (current_time < T_FINAL);
// Cleanup.
delete sln_time_prev;
delete sln_time_new;
delete time_error_fn;
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("cathedral.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(bdy_air, INIT_REF_NUM_BDY);
// Initialize an H1 space with default shepeset.
H1Space space(&mesh, bc_types, essential_bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Initialize the solution.
Solution tsln;
// Set the initial condition.
tsln.set_const(&mesh, T_INIT);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, double>, bilinear_form<Ord, Ord>);
wf.add_matrix_form_surf(bilinear_form_surf<double, double>, bilinear_form_surf<Ord, Ord>, bdy_air);
wf.add_vector_form(linear_form<double, double>, linear_form<Ord, Ord>, HERMES_ANY, &tsln);
wf.add_vector_form_surf(linear_form_surf<double, double>, linear_form_surf<Ord, Ord>, bdy_air);
// 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 views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 450, 600));
char title[100];
sprintf(title, "Time %3.5f, exterior temperature %3.5f", TIME, temp_ext(TIME));
Tview.set_min_max_range(0,20);
Tview.set_title(title);
Tview.fix_scale_width(3);
// Time stepping:
int nsteps = (int)(FINAL_TIME/TAU + 0.5);
bool rhs_only = false;
for(int ts = 1; ts <= nsteps; ts++)
{
info("---- Time step %d, time %3.5f, ext_temp %g", ts, TIME, temp_ext(TIME));
// First time assemble both the stiffness matrix and right-hand side vector,
// then just the right-hand side vector.
if (rhs_only == false) info("Assembling the stiffness matrix and right-hand side vector.");
else info("Assembling the right-hand side vector (only).");
dp.assemble(matrix, rhs, rhs_only);
rhs_only = true;
// 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, &tsln);
else
error ("Matrix solver failed.\n");
if (ts % OUTPUT_FREQUENCY == 0) {
Linearizer lin;
int item = H2D_FN_VAL_0;
double eps = HERMES_EPS_NORMAL;
double max_abs = -1.0;
MeshFunction* xdisp = NULL;
MeshFunction* ydisp = NULL;
double dmult = 1.0;
lin.process_solution(&tsln, item, eps, max_abs, xdisp, ydisp, dmult);
char* filename = new char[100];
sprintf(filename, "tsln_%d.lin", ts);
// Save Linearizer data.
lin.save_data(filename);
info("Linearizer data saved to file %s.", filename);
// Save complete Solution.
sprintf(filename, "tsln_%d.dat", ts);
bool compress = false; // Gzip compression not used as it only works on Linux.
tsln.save(filename, compress);
info("Complete Solution saved to file %s.", filename);
}
// Update the time variable.
TIME += TAU;
}
info("Let's assume that the remote computation has finished and you fetched the *.lin files.");
info("Visualizing Linearizer data from file tsln_40.lin.");
// First use ScalarView to read and show the Linearizer data.
WinGeom* win_geom_1 = new WinGeom(0, 0, 450, 600);
ScalarView sview_1("Saved Linearizer data", win_geom_1);
sview_1.lin.load_data("tsln_40.lin");
sview_1.set_min_max_range(0,20);
sview_1.fix_scale_width(3);
sview_1.show_linearizer_data();
info("Visualizing Solution from file tsln_60.dat.");
Solution sln_from_file;
sln_from_file.load("tsln_60.dat");
WinGeom* win_geom_2 = new WinGeom(460, 0, 450, 600);
ScalarView sview_2("Saved Solution data", win_geom_2);
sview_2.set_min_max_range(0,20);
sview_2.fix_scale_width(3);
sview_2.show(&sln_from_file);
info("Visualizing Mesh and Orders extracted from the Solution.");
int p_init = 1;
// The NULLs are for bc_types() and essential_bc_values().
H1Space space_from_file(sln_from_file.get_mesh(), NULL, NULL, p_init);
space_from_file.set_element_orders(sln_from_file.get_element_orders());
WinGeom* win_geom_3 = new WinGeom(920, 0, 450, 600);
OrderView oview("Saved Solution -> Space", win_geom_3);
oview.show(&space_from_file);
// Clean up.
delete solver;
delete matrix;
delete rhs;
// 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;
MeshReaderH2D mloader;
mloader.load("wall.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_RIGHT, 2);
mesh.refine_towards_boundary(BDY_FIRE, INIT_REF_NUM_BDY);
// Initialize essential boundary conditions (none).
EssentialBCs<double> bcs;
// Initialize 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);
// Previous and next time level solutions.
ConstantSolution<double> sln_time_prev(&mesh, TEMP_INIT);
ZeroSolution sln_time_new(&mesh);
ConstantSolution<double> time_error_fn(&mesh, 0.0);
// Initialize the weak formulation.
double current_time = 0;
CustomWeakFormHeatRK wf(BDY_FIRE, BDY_AIR, ALPHA_FIRE, ALPHA_AIR,
RHO, HEATCAP, TEMP_EXT_AIR, TEMP_INIT, ¤t_time);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, &space);
// Initialize views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 1500, 400));
Tview.fix_scale_width(40);
ScalarView eview("Temporal error", new WinGeom(0, 450, 1500, 400));
eview.fix_scale_width(40);
// Graph for time step history.
SimpleGraph time_step_graph;
info("Time step history will be saved to file time_step_history.dat.");
// Initialize Runge-Kutta time stepping.
RungeKutta<double> runge_kutta(&dp, &bt, matrix_solver_type);
// Time stepping loop:
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, tau = %g s, stages: %d).",
current_time, time_step, bt.get_size());
bool jacobian_changed = false;
bool verbose = true;
try
{
runge_kutta.rk_time_step_newton(current_time, time_step, &sln_time_prev, &sln_time_new,
&time_error_fn, !jacobian_changed, false, verbose);
}
catch(Exceptions::Exception& e)
{
e.printMsg();
error("Runge-Kutta time step failed");
}
// Plot error function.
char title[100];
sprintf(title, "Temporal error, t = %g", current_time);
eview.set_title(title);
AbsFilter abs_tef(&time_error_fn);
eview.show(&abs_tef, HERMES_EPS_VERYHIGH);
// Calculate relative time stepping error and decide whether the
// time step can be accepted. If not, then the time step size is
// reduced and the entire time step repeated. If yes, then another
// check is run, and if the relative error is very low, time step
// is increased.
double rel_err_time = Global<double>::calc_norm(&time_error_fn, HERMES_H1_NORM)
/ Global<double>::calc_norm(&sln_time_new, HERMES_H1_NORM) * 100;
info("rel_err_time = %g%%", rel_err_time);
if (rel_err_time > TIME_TOL_UPPER) {
info("rel_err_time above upper limit %g%% -> decreasing time step from %g to %g and restarting time step.",
TIME_TOL_UPPER, time_step, time_step * TIME_STEP_DEC_RATIO);
time_step *= TIME_STEP_DEC_RATIO;
continue;
}
if (rel_err_time < TIME_TOL_LOWER) {
info("rel_err_time = below lower limit %g%% -> increasing time step from %g to %g",
TIME_TOL_UPPER, time_step, time_step * TIME_STEP_INC_RATIO);
time_step *= TIME_STEP_INC_RATIO;
}
// Add entry to the timestep graph.
time_step_graph.add_values(current_time, time_step);
time_step_graph.save("time_step_history.dat");
// Update time.
current_time += time_step;
// Show the new time level solution.
sprintf(title, "Time %3.2f s", current_time);
Tview.set_title(title);
Tview.show(&sln_time_new);
// Copy solution for the new time step.
sln_time_prev.copy(&sln_time_new);
// Increase counter of time steps.
ts++;
}
while (current_time < T_FINAL);
// Wait for the view to be closed.
View::wait();
return 0;
}
