Beispiel #1
0
int main(int argc, char* argv[])
{
  // Instantiate a class with global functions.
  

  // 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());

  // Turn off adaptive time stepping if R-K method is not embedded.
  if (bt.is_embedded() == false && ADAPTIVE_TIME_STEP_ON == true) {
    warn("R-K method not embedded, turning off adaptive time stepping.");
    ADAPTIVE_TIME_STEP_ON = false;
  }

  // Load the mesh.
  Mesh mesh, basemesh;
  MeshReaderH2D mloader;
  mloader.load("square.mesh", &basemesh);
  mesh.copy(&basemesh);

  // Initial mesh refinements.
  for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();

  // Convert initial condition into a Solution<std::complex<double> >.
  CustomInitialCondition psi_time_prev(&mesh);

  // Initialize the weak formulation.
  double current_time = 0;

  CustomWeakFormGPRK wf(h, m, g, omega);

  // Initialize boundary conditions.
  DefaultEssentialBCConst<std::complex<double> > bc_essential("Bdy", 0.0);
  EssentialBCs<std::complex<double> > bcs(&bc_essential);

  // Create an H1 space with default shapeset.
  H1Space<std::complex<double> > space(&mesh, &bcs, P_INIT);
  int ndof = space.get_num_dofs();
  info("ndof = %d", ndof);
 
  // Initialize the FE problem.
  DiscreteProblem<std::complex<double> > dp(&wf, &space);

  // Create a refinement selector.
  H1ProjBasedSelector<std::complex<double> > selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);

  // Visualize initial condition.
  char title[100];

  ScalarView sview_real("Initial condition - real part", new WinGeom(0, 0, 600, 500));
  ScalarView sview_imag("Initial condition - imaginary part", new WinGeom(610, 0, 600, 500));

  sview_real.show_mesh(false);
  sview_imag.show_mesh(false);
  sview_real.fix_scale_width(50);
  sview_imag.fix_scale_width(50);
  OrderView ord_view("Initial mesh", new WinGeom(445, 0, 440, 350));
  ord_view.fix_scale_width(50);
  ScalarView time_error_view("Temporal error", new WinGeom(0, 400, 440, 350));
  time_error_view.fix_scale_width(50);
  time_error_view.fix_scale_width(60);
  ScalarView space_error_view("Spatial error", new WinGeom(445, 400, 440, 350));
  space_error_view.fix_scale_width(50);
  RealFilter real(&psi_time_prev);
  ImagFilter imag(&psi_time_prev);
  sview_real.show(&real);
  sview_imag.show(&imag);
  ord_view.show(&space);

  // Graph for time step history.
  SimpleGraph time_step_graph;
  if (ADAPTIVE_TIME_STEP_ON) info("Time step history will be saved to file time_step_history.dat.");
  
  // Time stepping:
  int num_time_steps = (int)(T_FINAL/time_step + 0.5);
  for(int ts = 1; ts <= num_time_steps; ts++)
  // Time stepping loop.
  double current_time = 0.0; int ts = 1;
  do 
  {
    info("Begin time step %d.", ts);
    // Periodic global derefinement.
    if (ts > 1 && ts % UNREF_FREQ == 0) 
    {
      info("Global mesh derefinement.");
      switch (UNREF_METHOD) {
        case 1: mesh.copy(&basemesh);
                space.set_uniform_order(P_INIT);
                break;
        case 2: mesh.unrefine_all_elements();
                space.set_uniform_order(P_INIT);
                break;
        case 3: mesh.unrefine_all_elements();
                //space.adjust_element_order(-1, P_INIT);
                space.adjust_element_order(-1, -1, P_INIT, P_INIT);
                break;
        default: error("Wrong global derefinement method.");
      }

      ndof = Space<std::complex<double> >::get_num_dofs(&space);
    }
    info("ndof: %d", ndof);

    // Spatial adaptivity loop. Note: psi_time_prev must not be 
    // changed during spatial adaptivity. 
    Solution<std::complex<double> > ref_sln;
    Solution<std::complex<double> >* time_error_fn;
    if (bt.is_embedded() == true) time_error_fn = new Solution<std::complex<double> >(&mesh);
    else time_error_fn = NULL;
    bool done = false; int as = 1;
    double err_est;
    do {
      // Construct globally refined reference mesh and setup reference space.
      Space<std::complex<double> >* ref_space = Space<std::complex<double> >::construct_refined_space(&space);

      // Initialize discrete problem on reference mesh.
      DiscreteProblem<std::complex<double> >* ref_dp = new DiscreteProblem<std::complex<double> >(&wf, ref_space);
      
      RungeKutta<std::complex<double> > runge_kutta(ref_dp, &bt, matrix_solver_type);

      // Runge-Kutta step on the fine mesh.
      info("Runge-Kutta time step on fine mesh (t = %g s, time step = %g s, stages: %d).", 
         current_time, time_step, bt.get_size());
      bool verbose = true;

      try
      {
        runge_kutta.rk_time_step_newton(current_time, time_step, &psi_time_prev, 
                                    &ref_sln, time_error_fn, false, false, verbose, 
                                    NEWTON_TOL_FINE, NEWTON_MAX_ITER);
      }
      catch(Exceptions::Exception& e)
      {
        e.printMsg();
        error("Runge-Kutta time step failed");
      }

      /* If ADAPTIVE_TIME_STEP_ON == true, estimate temporal error. 
         If too large or too small, then adjust it and restart the time step. */

      double rel_err_time = 0;
      if (bt.is_embedded() == true) {
        info("Calculating temporal error estimate.");

        // Show temporal error.
        char title[100];
        sprintf(title, "Temporal error est, spatial adaptivity step %d", as);     
        time_error_view.set_title(title);
        time_error_view.show_mesh(false);
        RealFilter abs_time(time_error_fn);
        AbsFilter abs_tef(&abs_time);
        time_error_view.show(&abs_tef, HERMES_EPS_HIGH);

        rel_err_time = Global<std::complex<double> >::calc_norm(time_error_fn, HERMES_H1_NORM) / 
                       Global<std::complex<double> >::calc_norm(&ref_sln, HERMES_H1_NORM) * 100;
        if (ADAPTIVE_TIME_STEP_ON == false) info("rel_err_time: %g%%", rel_err_time);
      }

      if (ADAPTIVE_TIME_STEP_ON) {
        if (rel_err_time > TIME_ERR_TOL_UPPER) {
          info("rel_err_time %g%% is above upper limit %g%%", rel_err_time, TIME_ERR_TOL_UPPER);
          info("Decreasing time step from %g to %g s and restarting time step.", 
               time_step, time_step * TIME_STEP_DEC_RATIO);
          time_step *= TIME_STEP_DEC_RATIO;
          delete ref_space;
          delete ref_dp;
          continue;
        }
        else if (rel_err_time < TIME_ERR_TOL_LOWER) {
          info("rel_err_time = %g%% is below lower limit %g%%", rel_err_time, TIME_ERR_TOL_LOWER);
          info("Increasing time step from %g to %g s.", time_step, time_step * TIME_STEP_INC_RATIO);
          time_step *= TIME_STEP_INC_RATIO;
          delete ref_space;
          delete ref_dp;
          continue;
        }
        else {
          info("rel_err_time = %g%% is in acceptable interval (%g%%, %g%%)", 
            rel_err_time, TIME_ERR_TOL_LOWER, TIME_ERR_TOL_UPPER);
        }

        // Add entry to time step history graph.
        time_step_graph.add_values(current_time, time_step);
        time_step_graph.save("time_step_history.dat");
      }

      /* Estimate spatial errors and perform mesh refinement */

      info("Spatial adaptivity step %d.", as);

      // Project the fine mesh solution onto the coarse mesh.
      Solution<std::complex<double> > sln;
      info("Projecting fine mesh solution on coarse mesh for error estimation.");
      OGProjection<std::complex<double> >::project_global(&space, &ref_sln, &sln, matrix_solver_type); 

      // Show spatial error.
      sprintf(title, "Spatial error est, spatial adaptivity step %d", as);  
      DiffFilter<std::complex<double> >* space_error_fn = new DiffFilter<std::complex<double> >(Hermes::vector<MeshFunction<std::complex<double> >*>(&ref_sln, &sln));   
      space_error_view.set_title(title);
      space_error_view.show_mesh(false);
      RealFilter abs_space(space_error_fn);
      AbsFilter abs_sef(&abs_space);
      space_error_view.show(&abs_sef);

      // Calculate element errors and spatial error estimate.
      info("Calculating spatial error estimate.");
      Adapt<std::complex<double> >* adaptivity = new Adapt<std::complex<double> >(&space);
      double err_rel_space = adaptivity->calc_err_est(&sln, &ref_sln) * 100;

      // Report results.
      info("ndof: %d, ref_ndof: %d, err_rel_space: %g%%", 
           Space<std::complex<double> >::get_num_dofs(&space), Space<std::complex<double> >::get_num_dofs(ref_space), err_rel_space);

      // If err_est too large, adapt the mesh.
      if (err_rel_space < SPACE_ERR_TOL) done = true;
      else 
      {
        info("Adapting the coarse mesh.");
        done = adaptivity->adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);

        if (Space<std::complex<double> >::get_num_dofs(&space) >= NDOF_STOP) 
          done = true;
        else
          // Increase the counter of performed adaptivity steps.
          as++;
      }
      
      // Clean up.
      delete adaptivity;
      delete ref_space;
      delete ref_dp;
      delete space_error_fn;
    }
    while (done == false);

    // Clean up.
    if (time_error_fn != NULL) delete time_error_fn;

    // Visualize the solution and mesh.
    char title[100];
    sprintf(title, "Solution - real part, Time %3.2f s", current_time);
    sview_real.set_title(title);
    sprintf(title, "Solution - imaginary part, Time %3.2f s", current_time);
    sview_imag.set_title(title);
    RealFilter real(&ref_sln);
    ImagFilter imag(&ref_sln);
    sview_real.show(&real);
    sview_imag.show(&imag);
    sprintf(title, "Mesh, time %g s", current_time);
    ord_view.set_title(title);
    ord_view.show(&space);

    // Copy last reference solution into psi_time_prev.
    psi_time_prev.copy(&ref_sln);

    // Increase current time and counter of time steps.
    current_time += time_step;
    ts++;
  }
  while (current_time < T_FINAL);

  // Wait for all views to be closed.
  View::wait();
  return 0;
}
Beispiel #2
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()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage explicit R-K method.", bt.get_size());
  if (bt.is_diagonally_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage diagonally implicit R-K method.", bt.get_size());
  if (bt.is_fully_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage fully implicit R-K method.", bt.get_size());

  // Turn off adaptive time stepping if R-K method is not embedded.
  if (bt.is_embedded() == false && ADAPTIVE_TIME_STEP_ON == true) {
    Hermes::Mixins::Loggable::Static::warn("R-K method not embedded, turning off adaptive time stepping.");
    ADAPTIVE_TIME_STEP_ON = false;
  }

  // Load the mesh.
  MeshSharedPtr mesh(new Mesh), basemesh(new Mesh);
  MeshReaderH2D mloader;
  mloader.load("square.mesh", basemesh);
  mesh->copy(basemesh);

  // Initial mesh refinements.
  for(int i = 0; i < INIT_REF_NUM; i++) mesh->refine_all_elements();

  // Convert initial condition into a Solution<complex>.
  MeshFunctionSharedPtr<complex> psi_time_prev(new CustomInitialCondition(mesh));

  // Initialize the weak formulation.
  double current_time = 0;

  // Initialize weak formulation.
  CustomWeakFormGPRK wf(h, m, g, omega);

  // Initialize boundary conditions.
  DefaultEssentialBCConst<complex> bc_essential("Bdy", 0.0);
  EssentialBCs<complex> bcs(&bc_essential);

  // Create an H1 space with default shapeset.
  SpaceSharedPtr<complex> space(new H1Space<complex> (mesh, &bcs, P_INIT));
  int ndof = space->get_num_dofs();
  Hermes::Mixins::Loggable::Static::info("ndof = %d", ndof);

  // Initialize the FE problem.
  DiscreteProblem<complex> dp(&wf, space);

  // Create a refinement selector.
  H1ProjBasedSelector<complex> selector(CAND_LIST);

  // Visualize initial condition.
  char title[100];

  ScalarView sview_real("Initial condition - real part", new WinGeom(0, 0, 600, 500));
  ScalarView sview_imag("Initial condition - imaginary part", new WinGeom(610, 0, 600, 500));

  sview_real.show_mesh(false);
  sview_imag.show_mesh(false);
  sview_real.fix_scale_width(50);
  sview_imag.fix_scale_width(50);
  OrderView ord_view("Initial mesh", new WinGeom(445, 0, 440, 350));
  ord_view.fix_scale_width(50);
  ScalarView time_error_view("Temporal error", new WinGeom(0, 400, 440, 350));
  time_error_view.fix_scale_width(50);
  time_error_view.fix_scale_width(60);
  ScalarView space_error_view("Spatial error", new WinGeom(445, 400, 440, 350));
  space_error_view.fix_scale_width(50);
  MeshFunctionSharedPtr<double> real(new RealFilter(psi_time_prev));

  MeshFunctionSharedPtr<double> imag(new ImagFilter(psi_time_prev));

  sview_real.show(real);
  sview_imag.show(imag);
  ord_view.show(space);

  // Graph for time step history.
  SimpleGraph time_step_graph;
  if (ADAPTIVE_TIME_STEP_ON) Hermes::Mixins::Loggable::Static::info("Time step history will be saved to file time_step_history.dat.");

  // Time stepping:
  int num_time_steps = (int)(T_FINAL/time_step + 0.5);
  for(int ts = 1; ts <= num_time_steps; ts++)
    // Time stepping loop.
      double current_time = 0.0; int ts = 1;
  do 
  {
    Hermes::Mixins::Loggable::Static::info("Begin time step %d.", ts);
    // Periodic global derefinement.
    if (ts > 1 && ts % UNREF_FREQ == 0) 
    {
      Hermes::Mixins::Loggable::Static::info("Global mesh derefinement.");
      switch (UNREF_METHOD) {
      case 1: mesh->copy(basemesh);
        space->set_uniform_order(P_INIT);
        break;
      case 2: space->unrefine_all_mesh_elements();
        space->set_uniform_order(P_INIT);
        break;
      case 3: space->unrefine_all_mesh_elements();
        space->adjust_element_order(-1, -1, P_INIT, P_INIT);
        break;
      default: throw Hermes::Exceptions::Exception("Wrong global derefinement method.");
      }

      ndof = Space<complex>::get_num_dofs(space);
    }
    Hermes::Mixins::Loggable::Static::info("ndof: %d", ndof);

    // Spatial adaptivity loop. Note: psi_time_prev must not be 
    // changed during spatial adaptivity. 
    MeshFunctionSharedPtr<complex> ref_sln(new Solution<complex>());
    MeshFunctionSharedPtr<complex> time_error_fn(new Solution<complex>);
    bool done = false;
    int as = 1;
    double err_est;
    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();

      // Initialize discrete problem on reference mesh.
      DiscreteProblem<complex>* ref_dp = new DiscreteProblem<complex>(&wf, ref_space);

      RungeKutta<complex> runge_kutta(&wf, ref_space, &bt);

      // Runge-Kutta step on the fine mesh->
      Hermes::Mixins::Loggable::Static::info("Runge-Kutta time step on fine mesh (t = %g s, time step = %g s, stages: %d).", 
        current_time, time_step, bt.get_size());
      bool verbose = true;

      try
      {
        runge_kutta.set_time(current_time);
        runge_kutta.set_time_step(time_step);
        runge_kutta.set_max_allowed_iterations(NEWTON_MAX_ITER);
        runge_kutta.set_tolerance(NEWTON_TOL_FINE);
        runge_kutta.rk_time_step_newton(psi_time_prev, ref_sln, time_error_fn);
      }
      catch(Exceptions::Exception& e)
      {
        e.print_msg();
        throw Hermes::Exceptions::Exception("Runge-Kutta time step failed");
      }

      /* If ADAPTIVE_TIME_STEP_ON == true, estimate temporal error. 
      If too large or too small, then adjust it and restart the time step. */

      double rel_err_time = 0;
      if (bt.is_embedded() == true) {
        Hermes::Mixins::Loggable::Static::info("Calculating temporal error estimate.");

        // Show temporal error.
        char title[100];
        sprintf(title, "Temporal error est, spatial adaptivity step %d", as);     
        time_error_view.set_title(title);
        time_error_view.show_mesh(false);
        MeshFunctionSharedPtr<double> abs_time(new RealFilter(time_error_fn));

        MeshFunctionSharedPtr<double> abs_tef(new AbsFilter(abs_time));

        time_error_view.show(abs_tef);

        rel_err_time = Global<complex>::calc_norm(time_error_fn.get(), HERMES_H1_NORM) / 
          Global<complex>::calc_norm(ref_sln.get(), HERMES_H1_NORM) * 100;
        if (ADAPTIVE_TIME_STEP_ON == false) Hermes::Mixins::Loggable::Static::info("rel_err_time: %g%%", rel_err_time);
      }

      if (ADAPTIVE_TIME_STEP_ON) {
        if (rel_err_time > TIME_ERR_TOL_UPPER) {
          Hermes::Mixins::Loggable::Static::info("rel_err_time %g%% is above upper limit %g%%", rel_err_time, TIME_ERR_TOL_UPPER);
          Hermes::Mixins::Loggable::Static::info("Decreasing time step from %g to %g s and restarting time step.", 
            time_step, time_step * TIME_STEP_DEC_RATIO);
          time_step *= TIME_STEP_DEC_RATIO;

          delete ref_dp;
          continue;
        }
        else if (rel_err_time < TIME_ERR_TOL_LOWER) {
          Hermes::Mixins::Loggable::Static::info("rel_err_time = %g%% is below lower limit %g%%", rel_err_time, TIME_ERR_TOL_LOWER);
          Hermes::Mixins::Loggable::Static::info("Increasing time step from %g to %g s.", time_step, time_step * TIME_STEP_INC_RATIO);
          time_step *= TIME_STEP_INC_RATIO;

          delete ref_dp;
          continue;
        }
        else {
          Hermes::Mixins::Loggable::Static::info("rel_err_time = %g%% is in acceptable interval (%g%%, %g%%)", 
            rel_err_time, TIME_ERR_TOL_LOWER, TIME_ERR_TOL_UPPER);
        }

        // Add entry to time step history graph.
        time_step_graph.add_values(current_time, time_step);
        time_step_graph.save("time_step_history.dat");
      }

      /* Estimate spatial errors and perform mesh refinement */

      Hermes::Mixins::Loggable::Static::info("Spatial adaptivity step %d.", as);

      // Project the fine mesh solution onto the coarse mesh.
      MeshFunctionSharedPtr<complex> sln(new Solution<complex>);
      Hermes::Mixins::Loggable::Static::info("Projecting fine mesh solution on coarse mesh for error estimation.");
      OGProjection<complex> ogProjection; ogProjection.project_global(space, ref_sln, sln); 

      // Show spatial error.
      sprintf(title, "Spatial error est, spatial adaptivity step %d", as);  
      MeshFunctionSharedPtr<complex> space_error_fn(new DiffFilter<complex>(Hermes::vector<MeshFunctionSharedPtr<complex> >(ref_sln, sln)));

      space_error_view.set_title(title);
      space_error_view.show_mesh(false);

      MeshFunctionSharedPtr<double> abs_space(new RealFilter(space_error_fn));
      MeshFunctionSharedPtr<double> abs_sef(new AbsFilter(abs_space));

      space_error_view.show(abs_sef);

      // Calculate element errors and spatial error estimate.
      Hermes::Mixins::Loggable::Static::info("Calculating spatial error estimate.");
      Adapt<complex> adaptivity(space);
      double err_rel_space = errorCalculator.get_total_error_squared() * 100;

      // Report results.
      Hermes::Mixins::Loggable::Static::info("ndof: %d, ref_ndof: %d, err_rel_space: %g%%", 
        Space<complex>::get_num_dofs(space), Space<complex>::get_num_dofs(ref_space), err_rel_space);

      // If err_est too large, adapt the mesh.
      if (err_rel_space < SPACE_ERR_TOL) done = true;
      else 
      {
        Hermes::Mixins::Loggable::Static::info("Adapting the coarse mesh.");
        done = adaptivity.adapt(&selector);

        // Increase the counter of performed adaptivity steps.
        as++;
      }

      // Clean up.
      
      delete ref_dp;
    }
    while (done == false);

    // Visualize the solution and mesh->
    char title[100];
    sprintf(title, "Solution - real part, Time %3.2f s", current_time);
    sview_real.set_title(title);
    sprintf(title, "Solution - imaginary part, Time %3.2f s", current_time);
    sview_imag.set_title(title);
    MeshFunctionSharedPtr<double> real(new RealFilter(ref_sln));
    MeshFunctionSharedPtr<double> imag(new ImagFilter(ref_sln));
    sview_real.show(real);
    sview_imag.show(imag);
    sprintf(title, "Mesh, time %g s", current_time);
    ord_view.set_title(title);
    ord_view.show(space);

    // Copy last reference solution into psi_time_prev.
    psi_time_prev->copy(ref_sln);

    // Increase current time and counter of time steps.
    current_time += time_step;
    ts++;
  }
  while (current_time < T_FINAL);

  // Wait for all views to be closed.
  View::wait();
  return 0;
}