Exemple #1
0
int main(int argc, char* argv[])
{
  // Load the mesh.
  Hermes::Hermes2D::Mesh mesh;
  Hermes::Hermes2D::MeshReaderH2DXML mloader;
  mloader.load("domain.xml", &mesh);

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

  // This is here basically to show off that we can save a mesh with refinements and load it back again.
  mloader.save("domain2.xml", &mesh);
  mloader.load("domain2.xml", &mesh);

  // Initialize the weak formulation.
  CustomWeakFormPoisson wf(new Hermes::Hermes1DFunction<double>(LAMBDA_AL), "Aluminum", 
    new Hermes::Hermes1DFunction<double>(LAMBDA_CU), "Copper", new Hermes::Hermes2DFunction<double>(-VOLUME_HEAT_SRC));

  // Initialize essential boundary conditions.
  Hermes::Hermes2D::DefaultEssentialBCConst<double> bc_essential(Hermes::vector<std::string>("Bottom", "Inner", "Outer", "Left"),
    FIXED_BDY_TEMP);
  Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);

  // Create an H1 space with default shapeset.
  Hermes::Hermes2D::H1Space<double> space(&mesh, &bcs, P_INIT);
  int ndof = space.get_num_dofs();
  info("ndof = %d", ndof);

  // Initialize the FE problem.
  Hermes::Hermes2D::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));

  // Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
  Hermes::Hermes2D::Solution<double> sln;
  Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
  try
  {
    newton.solve_keep_jacobian(coeff_vec, 1e-3, 10);
  }
  catch(Hermes::Exceptions::Exception e)
  {
    e.printMsg();
    Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);

    // VTK output.
    if (VTK_VISUALIZATION)
    {
      // Output solution in VTK format.
      Hermes::Hermes2D::Views::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.
      Hermes::Hermes2D::Views::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)
    {
      Hermes::Hermes2D::Views::ScalarView view("Solution", new Hermes::Hermes2D::Views::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::Hermes2D::Views::HERMES_EPS_HIGH);
      Hermes::Hermes2D::Views::View::wait();
    }

    // Clean up.
    delete [] coeff_vec;
  }

  Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);

  // VTK output.
  if (VTK_VISUALIZATION)
  {
    // Output solution in VTK format.
    Hermes::Hermes2D::Views::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.
    Hermes::Hermes2D::Views::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)
  {
    Hermes::Hermes2D::Views::ScalarView view("Solution", new Hermes::Hermes2D::Views::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::Hermes2D::Views::HERMES_EPS_HIGH);
    Hermes::Hermes2D::Views::View::wait();
  }

  // Clean up.
  delete [] coeff_vec;

  return 0;
}
Exemple #2
0
int main(int argc, char* argv[])
{
  // Load the mesh.
  Hermes::Hermes2D::Mesh mesh;
  Hermes::Hermes2D::MeshReaderH2DXML mloader;
  mloader.load("../domain.xml", &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 Hermes::Hermes1DFunction<double>(LAMBDA_AL), "Copper",
    new Hermes::Hermes1DFunction<double>(LAMBDA_CU), new Hermes::Hermes2DFunction<double>(-VOLUME_HEAT_SRC));

  // Initialize essential boundary conditions.
  Hermes::Hermes2D::DefaultEssentialBCConst<double> bc_essential(Hermes::vector<std::string>("Bottom", "Inner", "Outer", "Left"),
    FIXED_BDY_TEMP);
  Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);

  // Create an H1 space with default shapeset.
  Hermes::Hermes2D::H1Space<double> space(&mesh, &bcs, P_INIT);
  int ndof = space.get_num_dofs();
  info("ndof = %d", ndof);

  // Initialize the FE problem.
  Hermes::Hermes2D::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));

  // Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
  Hermes::Hermes2D::Solution<double> sln;
  Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
  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);

  // Actual test. The values of 'sum' depend on the
  // current shapeset. If you change the shapeset,
  // you need to correct these numbers.
  double sum = 0;
  for (int i = 0; i < ndof; i++)
    sum += newton.get_sln_vector()[i];
  printf("coefficient sum = %g\n", sum);

  // Clean up.
  delete [] coeff_vec;

  bool success = true;
  if (std::abs(sum + 0.357318) > 1e-4) success = false;

  if (success == true)
  {
    printf("Success!\n");
    return TEST_SUCCESS;
  }
  else
  {
    printf("Failure!\n");
    return TEST_FAILURE;
  }
}
Exemple #3
0
int main(int argc, char* argv[])
{
  // Load the mesh.
  Hermes::Hermes2D::Mesh mesh;
  Hermes::Hermes2D::MeshReaderH2D mloader;
  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.
  CustomWeakFormPoissonNewton wf("Aluminum", new Hermes::Hermes1DFunction<double>(LAMBDA_AL), 
    "Copper", new Hermes::Hermes1DFunction<double>(LAMBDA_CU), 
    new Hermes::Hermes2DFunction<double>(-VOLUME_HEAT_SRC),
    "Outer", ALPHA, T_EXTERIOR);

  // Initialize boundary conditions.
  CustomDirichletCondition bc_essential(Hermes::vector<std::string>("Bottom", "Inner", "Left"),
    BDY_A_PARAM, BDY_B_PARAM, BDY_C_PARAM);
  Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);

  // Create an H1 space with default shapeset.
  Hermes::Hermes2D::H1Space<double> space(&mesh, &bcs, P_INIT);

  // Testing n_dof and correctness of solution vector
  // for p_init = 1, 2, ..., 10
  bool success = true;
  for (int p_init = 1; p_init <= 10; p_init++) 
  {
    info("********* p_init = %d *********\n", p_init);
    space.set_uniform_order(p_init);
    int ndof = space.get_num_dofs();
    info("ndof = %d", ndof);

    // Initialize the FE problem.
    Hermes::Hermes2D::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));

    // Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
    Hermes::Hermes2D::Solution<double> sln;
    Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
    if (!newton.solve(coeff_vec)) 
      error("Newton's iteration failed.");
    else
      Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);

    double sum = 0;
    for (int i=0; i < ndof; i++) sum += coeff_vec[i];
    printf("coefficient sum = %g\n", sum);

    // Actual test. The values of 'sum' depend on the
    // current shapeset. If you change the shapeset,
    // you need to correct these numbers.
    if (p_init == 1 && fabs(sum - 61.8227) > 1e-1) success = false;
    if (p_init == 2 && fabs(sum - 60.8105) > 1e-1) success = false;
    if (p_init == 3 && fabs(sum - 61.5511) > 1e-1) success = false;
    if (p_init == 4 && fabs(sum - 60.8191) > 1e-1) success = false;
    if (p_init == 5 && fabs(sum - 61.5304) > 1e-1) success = false;
    if (p_init == 6 && fabs(sum - 60.8064) > 1e-1) success = false;
    if (p_init == 7 && fabs(sum - 61.5323) > 1e-1) success = false;
    if (p_init == 8 && fabs(sum - 60.7863) > 1e-1) success = false;
    if (p_init == 9 && fabs(sum - 61.5408) > 1e-1) success = false;
    if (p_init == 10 && fabs(sum - 60.7637) > 1e-1) success = false;

    // Clean up.
    delete [] coeff_vec;
  }

  if (success == 1) {
    printf("Success!\n");
    return TEST_SUCCESS;
  }
  else {
    printf("Failure!\n");
    return TEST_FAILURE;
  }
}
int main(int argc, char* argv[])
{
    // Load the mesh.
    Hermes::Hermes2D::Mesh mesh;
    Hermes::Hermes2D::H2DReader mloader;
    mloader.load("domain.mesh", &mesh);

    // Perform initial mesh refinements (optional).
    int refinement_type = 2;            // Split elements vertically.
    for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(refinement_type);

    // Show the mesh.
    Hermes::Hermes2D::Views::MeshView mview("Mesh", new Hermes::Hermes2D::Views::WinGeom(0, 0, 900, 250));
    if (HERMES_VISUALIZATION) {
        mview.show(&mesh);
        //mview.wait();
    }

    // Initialize the weak formulation.
    CustomWeakFormPoisson wf("Al", new Hermes::Hermes1DFunction<double>(LAMBDA_AL), "Cu",
                             new Hermes::Hermes1DFunction<double>(LAMBDA_CU), new Hermes::Hermes2DFunction<double>(-VOLUME_HEAT_SRC));

    // Initialize essential boundary conditions.
    Hermes::Hermes2D::DefaultEssentialBCConst<double> bc_essential(Hermes::vector<std::string>("Left", "Right"),
            FIXED_BDY_TEMP);
    Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);

    // Create an H1 space with default shapeset.
    Hermes::Hermes2D::H1Space<double> space(&mesh, &bcs, P_INIT);
    int ndof = space.get_num_dofs();
    info("ndof = %d", ndof);

    // Initialize the FE problem.
    Hermes::Hermes2D::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));

    // Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
    Hermes::Hermes2D::Solution<double> sln;
    Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
    if (!newton.solve(coeff_vec))
        error("Newton's iteration failed.");
    else
        Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);

    // Get info about time spent during assembling in its respective parts.
    dp.get_all_profiling_output(std::cout);

    // VTK output.
    if (VTK_VISUALIZATION)
    {
        // Output solution in VTK format.
        Hermes::Hermes2D::Views::Linearizer<double> 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.
        Hermes::Hermes2D::Views::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)
    {
        Hermes::Hermes2D::Views::ScalarView<double> view("Solution", new Hermes::Hermes2D::Views::WinGeom(0, 300, 900, 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::Hermes2D::Views::HERMES_EPS_HIGH);
        Hermes::Hermes2D::Views::View::wait();
    }

    // Clean up.
    delete [] coeff_vec;

    return 0;
}
Exemple #5
0
int main(int argc, char* argv[])
{
  // Load the mesh.
  Hermes::Hermes2D::Mesh mesh;
  Hermes::Hermes2D::MeshReaderH2D mloader;
  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.
  CustomWeakFormPoissonNewton wf("Aluminum", new Hermes::Hermes1DFunction<double>(LAMBDA_AL), 
    "Copper", new Hermes::Hermes1DFunction<double>(LAMBDA_CU), 
    new Hermes::Hermes2DFunction<double>(-VOLUME_HEAT_SRC),
    "Outer", ALPHA, T_EXTERIOR);

  // Initialize boundary conditions.
  CustomDirichletCondition bc_essential(Hermes::vector<std::string>("Bottom", "Inner", "Left"),
    BDY_A_PARAM, BDY_B_PARAM, BDY_C_PARAM);
  Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);

  // Create an H1 space with default shapeset.
  Hermes::Hermes2D::H1Space<double> space(&mesh, &bcs, P_INIT);
  int ndof = space.get_num_dofs();
  info("ndof = %d", ndof);

  // Initialize the FE problem.
  Hermes::Hermes2D::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 the Newton solver.
  Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);

  // Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
  Hermes::Hermes2D::Solution<double> sln;
  if (!newton.solve(coeff_vec)) 
    error("Newton's iteration failed.");
  else
    Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);

  // VTK output.
  if (VTK_VISUALIZATION) {
    // Output solution in VTK format.
    Hermes::Hermes2D::Views::Linearizer lin(&sln);
    bool mode_3D = true;
    lin.save_solution_vtk("sln.vtk", "Temperature", mode_3D);
    info("Solution in VTK format saved to file %s.", "sln.vtk");

    // Output mesh and element orders in VTK format.
    Hermes::Hermes2D::Views::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) {
    Hermes::Hermes2D::Views::ScalarView view("Solution", new Hermes::Hermes2D::Views::WinGeom(0, 0, 440, 350));
    view.show(&sln, Hermes::Hermes2D::Views::HERMES_EPS_VERYHIGH);
    Hermes::Hermes2D::Views::View::wait();
  }

  // Clean up.
  delete [] coeff_vec;

  return 0;
}