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[])
{
// 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;
}
