C++ Adapt类代码示例

int main(int argc, char* argv[])
{
  // Load the mesh.
  Mesh mesh;
  H2DReader mloader;
  mloader.load("square.mesh", &mesh);

  // Perform initial mesh refinements.
  for(int i = 0; i < INIT_GLOB_REF_NUM; i++) mesh.refine_all_elements();
  mesh.refine_towards_boundary(1, INIT_BDY_REF_NUM);

  // Create an H1 space with default shapeset.
  H1Space space(&mesh, bc_types, essential_bc_values, P_INIT);

  // Initialize the weak formulation.
  WeakForm wf;
  wf.add_matrix_form(callback(jac), HERMES_UNSYM, HERMES_ANY);
  wf.add_vector_form(callback(res), HERMES_ANY);

  // Initialize the FE problem.
  bool is_linear = false;
  DiscreteProblem dp_coarse(&wf, &space, is_linear);

  // Set up the solver, matrix, and rhs for the coarse mesh according to the solver selection.
  SparseMatrix* matrix_coarse = create_matrix(matrix_solver);
  Vector* rhs_coarse = create_vector(matrix_solver);
  Solver* solver_coarse = create_linear_solver(matrix_solver, matrix_coarse, rhs_coarse);

  // Create a selector which will select optimal candidate.
  H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);

  // Initialize coarse and reference mesh solution.
  Solution sln, ref_sln;

  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();

  // DOF and CPU convergence graphs.
  SimpleGraph graph_dof_est, graph_cpu_est;

  // Project the initial condition on the FE space to obtain initial 
  // coefficient vector for the Newton's method.
  info("Projecting initial condition to obtain initial vector on the coarse mesh.");
  scalar* coeff_vec_coarse = new scalar[Space::get_num_dofs(&space)] ;
  Solution* init_sln = new Solution(&mesh, init_cond);
  OGProjection::project_global(&space, init_sln, coeff_vec_coarse, matrix_solver); 
  delete init_sln;

  // Newton's loop on the coarse mesh. This is needed to obtain a good 
  // starting point for the Newton's method on the reference mesh.
  info("Solving on coarse mesh:");
  bool verbose = true;
  if (!solve_newton(coeff_vec_coarse, &dp_coarse, solver_coarse, matrix_coarse, rhs_coarse, 
      NEWTON_TOL_COARSE, NEWTON_MAX_ITER, verbose)) error("Newton's iteration failed.");

  // Translate the resulting coefficient vector into the Solution sln.
  Solution::vector_to_solution(coeff_vec_coarse, &space, &sln);

  // Cleanup after the Newton loop on the coarse mesh.
  delete matrix_coarse;
  delete rhs_coarse;
  delete solver_coarse;
  delete [] coeff_vec_coarse;

  // Adaptivity loop:
  int as = 1; 
  bool done = false;
  do
  {
    info("---- Adaptivity step %d:", as);

    // Construct globally refined reference mesh and setup reference space.
    Space* ref_space = construct_refined_space(&space);

    // Initialize discrete problem on the reference mesh.
    DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space, is_linear);

    // Initialize matrix solver.
    SparseMatrix* matrix = create_matrix(matrix_solver);
    Vector* rhs = create_vector(matrix_solver);
    Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);

    // Calculate initial coefficient vector on the reference mesh.
    scalar* coeff_vec = new scalar[Space::get_num_dofs(ref_space)];
    if (as == 1) 
    {
      // In the first step, project the coarse mesh solution.
      info("Projecting coarse mesh solution to obtain initial vector on new fine mesh.");
      OGProjection::project_global(ref_space, &sln, coeff_vec, matrix_solver);
    }
    else 
    {
      // In all other steps, project the previous fine mesh solution.
      info("Projecting previous fine mesh solution to obtain initial vector on new fine mesh.");
      OGProjection::project_global(ref_space, &ref_sln, coeff_vec, matrix_solver);
    }

    // Now we can deallocate the previous fine mesh.
    if(as > 1) delete ref_sln.get_mesh();
//.........这里部分代码省略.........

int main(int argc, char* argv[])
{
  // Instantiate a class with global functions.
  Hermes2D hermes2d;

  // Load the mesh.
  Mesh mesh;
  H2DReader mloader;
  mloader.load("domain.mesh", &mesh);

  // Perform initial mesh refinement.
  for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
  //mesh.refine_towards_vertex(3, 5);

  // Define exact solution.
  CustomExactSolution exact_sln(&mesh);

  // Initialize the weak formulation.
  DefaultWeakFormLaplace wf;

  // Initialize boundary conditions
  DefaultEssentialBCNonConst bc_essential("Bdy", &exact_sln);
  EssentialBCs bcs(&bc_essential);

  // Create an H1 space with default shapeset.
  H1Space space(&mesh, &bcs, P_INIT);

  // Initialize refinement selector.
  H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);

  // Initialize views.
  ScalarView sview("Solution", new WinGeom(0, 0, 440, 350));
  sview.show_mesh(false);
  OrderView  oview("Polynomial orders", new WinGeom(450, 0, 410, 350));

  // DOF and CPU convergence graphs.
  SimpleGraph graph_dof, graph_cpu, graph_dof_exact, graph_cpu_exact;

  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();

  // Adaptivity loop:
  int as = 1; bool done = false;
  do
  {
    info("---- Adaptivity step %d:", as);

    // Construct globally refined reference mesh and setup reference space.
    Space* ref_space = Space::construct_refined_space(&space);
    int ndof_ref = Space::get_num_dofs(ref_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);

    // Initialize reference problem.
    info("Solving on reference mesh.");
    DiscreteProblem dp(&wf, ref_space);

    // Time measurement.
    cpu_time.tick();

    // Initial coefficient vector for the Newton's method.  
    scalar* coeff_vec = new scalar[ndof_ref];
    memset(coeff_vec, 0, ndof_ref * sizeof(scalar));

    // Perform Newton's iteration.
    if (!hermes2d.solve_newton(coeff_vec, &dp, solver, matrix, rhs)) error("Newton's iteration failed.");

    // Translate the resulting coefficient vector into the Solution sln.
    Solution ref_sln;
    Solution::vector_to_solution(coeff_vec, ref_space, &ref_sln);

    // Project the fine mesh solution onto the coarse mesh.
    Solution sln;
    info("Projecting reference solution on coarse mesh.");
    OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);

    // View the coarse mesh solution and polynomial orders.
    sview.show(&sln);
    oview.show(&space);

    // Calculate element errors and total error estimate.
    info("Calculating error estimate and exact error.");
    Adapt* adaptivity = new Adapt(&space);
    double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln) * 100;

    // Calculate exact error.
    double err_exact_rel = hermes2d.calc_rel_error(&sln, &exact_sln, HERMES_H1_NORM) * 100;
   
    // Report results.
    info("ndof_coarse: %d, ndof_fine: %d", Space::get_num_dofs(&space), Space::get_num_dofs(ref_space));
    info("err_est_rel: %g%%, err_exact_rel: %g%%", err_est_rel, err_exact_rel);

    // Time measurement.
    cpu_time.tick();

    // Add entry to DOF and CPU convergence graphs.
//.........这里部分代码省略.........

int main(int argc, char* argv[])
{
  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();
 
  // Load the mesh.
  Mesh mesh;
  H2DReader mloader;
  mloader.load("domain.mesh", &mesh);

  // Perform initial mesh refinements.
  mesh.refine_all_elements();

  // Initialize boundary conditions.
  CustomEssentialBCNonConst bc_essential(BDY_HORIZONTAL);
  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 weak formulation.
  CustomWeakFormGeneral wf;

  // Initialize coarse and reference mesh solution.
  Solution sln, ref_sln;

  // Initialize refinement selector. 
  H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);

  // Initialize views.
  ScalarView sview("Solution", new WinGeom(0, 0, 440, 350));
  sview.show_mesh(false);
  OrderView  oview("Polynomial orders", new WinGeom(450, 0, 400, 350));
  
  // DOF and CPU convergence graphs initialization.
  SimpleGraph graph_dof, graph_cpu;

  // Adaptivity loop:
  int as = 1; 
  bool done = false;
  do
  {
    info("---- Adaptivity step %d:", as);

    // Construct globally refined reference mesh and setup reference space.
    Space* ref_space = Space::construct_refined_space(&space);
  
    // Initialize matrix solver.
    SparseMatrix* matrix = create_matrix(matrix_solver);
    Vector* rhs = create_vector(matrix_solver);
    Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);

    // Assemble reference problem.
    info("Solving on reference mesh.");
    bool is_linear = true;
    DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space, is_linear);
    dp->assemble(matrix, rhs);

    // Time measurement.
    cpu_time.tick();
    
    // Solve the linear system of the reference problem. If successful, obtain the solution.
    if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), ref_space, &ref_sln);
    else error ("Matrix solver failed.\n");
  
    // Time measurement.
    cpu_time.tick();

    // Project the fine mesh solution onto the coarse mesh.
    info("Projecting reference solution on coarse mesh.");
    OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver); 
   
    // View the coarse mesh solution and polynomial orders.
    sview.show(&sln);
    oview.show(&space);

    // Calculate element errors and total error estimate.
    info("Calculating error estimate."); 
    Adapt* adaptivity = new Adapt(&space);
    double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln) * 100;

    // Report results.
    info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%", 
      Space::get_num_dofs(&space), Space::get_num_dofs(ref_space), err_est_rel);

    // Time measurement.
    cpu_time.tick();

    // Add entry to DOF and CPU convergence graphs.
    graph_dof.add_values(Space::get_num_dofs(&space), err_est_rel);
    graph_dof.save("conv_dof_est.dat");
    graph_cpu.add_values(cpu_time.accumulated(), err_est_rel);
    graph_cpu.save("conv_cpu_est.dat");

    // If err_est_rel too large, adapt the mesh.
    if (err_est_rel < ERR_STOP) done = true;
    else 
//.........这里部分代码省略.........

int main(int argc, char* argv[])
{
  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();

  // Load the mesh.
  Mesh mesh;
  MeshReaderH2D mloader;
  mloader.load("square.mesh", &mesh);
  
  // Create an H1 space with default shapeset.
  H1Space<double> space(&mesh, P_INIT);

  // Initialize the weak formulation.
  WeakForm<double> wf_dummy;

  // Initialize coarse and reference mesh solution.
  Solution<double> sln;
  ExactSolutionCustom* ref_sln = NULL;

  // Initialize refinement selector.
  H1ProjBasedSelector<double> selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);

  // Initialize views.
  ScalarView sview("Scalar potential Phi", new WinGeom(0, 0, 610, 300));
  sview.fix_scale_width(40);
  sview.show_mesh(false);
  OrderView  oview("Mesh", new WinGeom(620, 0, 600, 300));

  // DOF and CPU convergence graphs.
  SimpleGraph graph_dof, graph_cpu;

  // Adapt<double>ivity loop:
  int as = 1; bool done = false;
  do
  {
    info("---- Adapt<double>ivity step %d:", as);

    // Construct globally refined reference mesh and setup reference space.
    Space<double>* ref_space = Space<double>::construct_refined_space(&space);

    // Assign the function f() to the fine mesh.
    info("Assigning f() to the fine mesh.");
    if(ref_sln != NULL) delete ref_sln;
    ref_sln = new ExactSolutionCustom(ref_space->get_mesh());

    // Time measurement.
    cpu_time.tick();
    
    // Project the fine mesh solution onto the coarse mesh.
    info("Projecting reference solution on coarse mesh.");
    OGProjection<double>::project_global(&space, ref_sln, &sln, matrix_solver); 
   
    // View the coarse mesh solution and polynomial orders.
    sview.show(&sln);
    oview.show(&space);

    // Calculate element errors and total error estimate.
    info("Calculating exact error."); 
    Adapt<double>* adaptivity = new Adapt<double>(&space);
    // Note: the error estimate is now equal to the exact error.
    double err_exact_rel = adaptivity->calc_err_est(&sln, ref_sln) * 100;

    // Report results.
    info("ndof_coarse: %d, ndof_fine: %d, err_exact_rel: %g%%", 
      Space<double>::get_num_dofs(&space), Space<double>::get_num_dofs(ref_space), err_exact_rel);

    // Time measurement.
    cpu_time.tick();

    // Add entry to DOF and CPU convergence graphs.
    graph_dof.add_values(Space<double>::get_num_dofs(&space), err_exact_rel);
    graph_dof.save("conv_dof.dat");
    graph_cpu.add_values(cpu_time.accumulated(), err_exact_rel);
    graph_cpu.save("conv_cpu.dat");

    // If err_exact_rel too large, adapt the mesh.
    if (err_exact_rel < ERR_STOP) done = true;
    else 
    {
      info("Adapting coarse mesh.");
      done = adaptivity->adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);
      
      // Increase the counter of performed adaptivity steps.
      if (done == false)  as++;
    }
    if (Space<double>::get_num_dofs(&space) >= NDOF_STOP) done = true;

    // Clean up.
    delete adaptivity;
    if (done == false)
      delete ref_space->get_mesh();
    delete ref_space;
  }
  while (done == false);
  
  verbose("Total running time: %g s", cpu_time.accumulated());

  // Show the reference solution - the final result.
//.........这里部分代码省略.........

//.........这里部分代码省略.........
    space = new L2Space(&mesh, P_INIT);
    selector = new L2ProjBasedSelector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
    norm = HERMES_L2_NORM;
    // Disable weighting of refinement candidates.
    selector->set_error_weights(1, 1, 1);
    
    wf = new CustomWeakFormDiscontinuousGalerkin(bcs, EPSILON);
  }
  
  // Initialize coarse and reference mesh solution.
  Solution sln, ref_sln;
  
  // Set exact solution.
  CustomExactSolution exact(&mesh, EPSILON);
  
  // DOF and CPU convergence graphs initialization.
  SimpleGraph graph_dof, graph_cpu, graph_dof_exact, graph_cpu_exact;
  
  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();

  // Setup data structures for solving the discrete algebraic problem.
  SparseMatrix* matrix = create_matrix(matrix_solver);
  Vector* rhs = create_vector(matrix_solver);
  Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
  
  // Adaptivity loop:
  int as = 1; 
  bool done = false;
  Space* actual_sln_space;
  do
  {
    info("---- Adaptivity step %d:", as);

    if (STRATEGY == -1)
      actual_sln_space = space;
    else
      // Construct globally refined reference mesh and setup reference space.
      actual_sln_space = Space::construct_refined_space(space, ORDER_INCREASE);

    int ndof_fine = Space::get_num_dofs(actual_sln_space);
    int ndof_coarse = Space::get_num_dofs(space);
    
    // Solve the linear system. If successful, obtain the solution.
    info("Solving on the refined mesh (%d NDOF).", ndof_fine);
    
    DiscreteProblem dp(wf, actual_sln_space);
    
    // Initial coefficient vector for the Newton's method.  
    scalar* coeff_vec = new scalar[ndof_fine];
    memset(coeff_vec, 0, ndof_fine * sizeof(scalar));
    
    // Perform Newton's iteration.
    if (!hermes2d.solve_newton(coeff_vec, &dp, solver, matrix, rhs)) 
      error("Newton's iteration failed.");
    Solution::vector_to_solution(solver->get_solution(), actual_sln_space, &ref_sln);
    
    // Calculate exact error.
    double err_exact_rel = hermes2d.calc_rel_error(&ref_sln, &exact, norm) * 100;
    info("ndof_fine: %d, err_exact_rel: %g%%", ndof_fine, err_exact_rel);

    if (STRATEGY == -1) done = true;  // Do not adapt.
    else
    {  
      Adapt* adaptivity = new Adapt(space, norm);

int main(int argc, char* argv[])
{
  // Instantiate a class with global functions.
  Hermes2D hermes2d;

  // Load the mesh.
  Mesh u_mesh, v_mesh;
  H2DReader mloader;
  mloader.load("../square.mesh", &u_mesh);
  if (MULTI == false) u_mesh.refine_towards_boundary("Outer", INIT_REF_BDY);

  // Create initial mesh (master mesh).
  v_mesh.copy(&u_mesh);

  // Initial mesh refinements in the v_mesh towards the boundary.
  if (MULTI == true) v_mesh.refine_towards_boundary("Outer", INIT_REF_BDY);

  // Set exact solutions.
  ExactSolutionFitzHughNagumo1 exact_u(&u_mesh);
  ExactSolutionFitzHughNagumo2 exact_v(&v_mesh, K);

  // Define right-hand sides.
  CustomRightHandSide1 rhs_1(K, D_u, SIGMA);
  CustomRightHandSide2 rhs_2(K, D_v);

  // Initialize the weak formulation.
  WeakFormFitzHughNagumo wf(&rhs_1, &rhs_2);
  
  // Initialize boundary conditions
  DefaultEssentialBCConst bc_u("Outer", 0.0);
  EssentialBCs bcs_u(&bc_u);
  DefaultEssentialBCConst bc_v("Outer", 0.0);
  EssentialBCs bcs_v(&bc_v);

  // Create H1 spaces with default shapeset for both displacement components.
  H1Space u_space(&u_mesh, &bcs_u, P_INIT_U);
  H1Space v_space(MULTI ? &v_mesh : &u_mesh, &bcs_v, P_INIT_V);

  // Initialize coarse and reference mesh solutions.
  Solution u_sln, v_sln, u_ref_sln, v_ref_sln;

  // Initialize refinement selector.
  H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);

  // DOF and CPU convergence graphs.
  SimpleGraph graph_dof_est, graph_cpu_est, 
              graph_dof_exact, graph_cpu_exact;

  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();

  // Adaptivity loop:
  int as = 1; 
  bool done = false;
  do
  {
    info("---- Adaptivity step %d:", as);

    // Construct globally refined reference mesh and setup reference space.
    Hermes::vector<Space *>* ref_spaces = 
      Space::construct_refined_spaces(Hermes::vector<Space *>(&u_space, &v_space));
    int ndof_ref = Space::get_num_dofs(Hermes::vector<Space *>(&u_space, &v_space));

    // Initialize matrix solver.
    SparseMatrix* matrix = create_matrix(matrix_solver);
    Vector* rhs = create_vector(matrix_solver);
    Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);

    // Initialize reference problem.
    info("Solving on reference mesh.");
    DiscreteProblem* dp = new DiscreteProblem(&wf, *ref_spaces);
    dp->assemble(matrix, rhs);

    // Time measurement.
    cpu_time.tick();
    
    // Initial coefficient vector for the Newton's method.  
    scalar* coeff_vec = new scalar[ndof_ref];
    memset(coeff_vec, 0, ndof_ref * sizeof(scalar));

    // Perform Newton's iteration.
    if (!hermes2d.solve_newton(coeff_vec, dp, solver, matrix, rhs)) error("Newton's iteration failed.");

    // Translate the resulting coefficient vector into the Solution sln.
    Solution::vector_to_solutions(coeff_vec, *ref_spaces, Hermes::vector<Solution *>(&u_ref_sln, &v_ref_sln));

    // Project the fine mesh solution onto the coarse mesh.
    info("Projecting reference solution on coarse mesh.");
    OGProjection::project_global(Hermes::vector<Space *>(&u_space, &v_space), Hermes::vector<Solution *>(&u_ref_sln, &v_ref_sln), 
                   Hermes::vector<Solution *>(&u_sln, &v_sln), matrix_solver); 
   
    // Calculate element errors.
    info("Calculating error estimate and exact error."); 
    Adapt* adaptivity = new Adapt(Hermes::vector<Space *>(&u_space, &v_space));
    
    // Calculate error estimate for each solution component and the total error estimate.
    Hermes::vector<double> err_est_rel;
    double err_est_rel_total = adaptivity->calc_err_est(Hermes::vector<Solution *>(&u_sln, &v_sln), 
                               Hermes::vector<Solution *>(&u_ref_sln, &v_ref_sln), &err_est_rel) * 100;
//.........这里部分代码省略.........

//.........这里部分代码省略.........
     
      // Calculate initial coefficient vector for Newton on the fine mesh.
      if (as == 1 && ts == 1) {
        info("Projecting coarse mesh solution to obtain initial vector on new fine mesh.");
        OGProjection::project_global(ref_space, &sln, coeff_vec, matrix_solver);
      }
      else {
        info("Projecting previous fine mesh solution to obtain initial vector on new fine mesh.");
        OGProjection::project_global(ref_space, &ref_sln, coeff_vec, matrix_solver);
        delete ref_sln.get_mesh();
      }

      // Initialize the FE problem.
      bool is_linear = false;
      DiscreteProblem dp(&wf, ref_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);

      // Perform Newton's iteration.
      info("Solving on fine mesh.");
      if (!solve_newton(coeff_vec, &dp, solver, matrix, rhs, 
          NEWTON_TOL_FINE, NEWTON_MAX_ITER, verbose)) error("Newton's iteration failed.");

      // Translate the resulting coefficient vector into the actual solutions. 
      Solution::vector_to_solutions(coeff_vec, ref_space, &ref_sln);

      // Project the fine mesh solution on the coarse mesh.
      info("Projecting fine mesh solution on coarse mesh for error calculation.");
      OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);

      // Calculate element errors.
      info("Calculating error estimate and exact error."); 
      Adapt* adaptivity = new Adapt(&space);
      
      // Calculate error estimate wrt. fine mesh solution.
      double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln) * 100;

      // Calculate error wrt. exact solution.
      ExactSolution exact(&mesh, exact_sol);
      bool solutions_for_adapt = false;
      double err_exact_rel = adaptivity->calc_err_exact(&sln, &exact, solutions_for_adapt) * 100;

      // Report results.
      info("ndof_coarse: %d, ndof_fine: %d", 
	    Space::get_num_dofs(&space), Space::get_num_dofs(ref_space));
      info("space_err_est_rel: %g%%, space_err_exact_rel: %g%%", 
	    err_est_rel, err_exact_rel);

      // Add entries to convergence graphs.
      graph_time_err_est.add_values(ts*TAU, err_est_rel);
      graph_time_err_est.save("time_error_est.dat");
      graph_time_err_exact.add_values(ts*TAU, err_exact_rel);
      graph_time_err_exact.save("time_error_exact.dat");
      graph_time_dof.add_values(ts*TAU, Space::get_num_dofs(&space));
      graph_time_dof.save("time_dof.dat");
      graph_time_cpu.add_values(ts*TAU, cpu_time.accumulated());
      graph_time_cpu.save("time_cpu.dat");

      // If space_err_est too large, adapt the mesh.
      if (err_est_rel < ERR_STOP) done = true;
      else {
        info("Adapting coarse mesh.");
        done = adaptivity->adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);
        if (Space::get_num_dofs(&space) >= NDOF_STOP) 
          done = true;
        else
          as++;
      }

      // Cleanup.
      delete [] coeff_vec;
      delete solver;
      delete matrix;
      delete rhs;
      delete adaptivity;
      delete ref_space;
    }
    while (!done);

    // Copy new time level solution into sln_prev_time.
    sln_prev_time.copy(&ref_sln);
  }

  delete ref_sln.get_mesh();
  
  int ndof_allowed = 35;
  printf("ndof actual = %d\n", ndof);
  printf("ndof allowed = %d\n", ndof_allowed);
  if (ndof <= ndof_allowed) {      // ndofs was 33 at the time this test was created
    printf("Success!\n");
    return ERR_SUCCESS;
  }
  else {
    printf("Failure!\n");
    return ERR_FAILURE;
  }
}

//.........这里部分代码省略.........
      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, -1, P_INIT, P_INIT);
                break;
      }

      ndof_coarse = Space<double>::get_num_dofs(&space);
    }

    // Spatial adaptivity loop. Note: sln_time_prev must not be changed 
    // during spatial adaptivity. 
    bool done = false; int as = 1;
    double err_est;
    do {
      Hermes::Mixins::Loggable::Static::info("Time step %d, adaptivity step %d:", ts, as);

      // Construct globally refined reference mesh and setup reference space.
      Space<double>* ref_space = Space<double>::construct_refined_space(&space);
      int ndof_ref = Space<double>::get_num_dofs(ref_space);

      // Perform one Runge-Kutta time step according to the selected Butcher's table.
      try
      {
        runge_kutta.set_space(ref_space);
        runge_kutta.set_verbose_output(true);
        runge_kutta.setTime(current_time);
        runge_kutta.setTimeStep(time_step);
        runge_kutta.rk_time_step_newton(&sln_time_prev, &sln_time_new);
      }
      catch(Exceptions::Exception& e)
      {
        std::cout << e.what();
        
      }

      // Project the fine mesh solution onto the coarse mesh.
      Solution<double> sln_coarse;
      Hermes::Mixins::Loggable::Static::info("Projecting fine mesh solution on coarse mesh for error estimation.");
      OGProjection<double> ogProjection; ogProjection.project_global(&space, &sln_time_new, &sln_coarse); 

      // Calculate element errors and total error estimate.
      Hermes::Mixins::Loggable::Static::info("Calculating error estimate.");
      Adapt<double>* adaptivity = new Adapt<double>(&space);
      double err_est_rel_total = adaptivity->calc_err_est(&sln_coarse, &sln_time_new) * 100;

      // Report results.
      Hermes::Mixins::Loggable::Static::info("ndof_coarse: %d, ndof_ref: %d, err_est_rel: %g%%", 
           Space<double>::get_num_dofs(&space), Space<double>::get_num_dofs(ref_space), err_est_rel_total);

      // If err_est too large, adapt the mesh.
      if (err_est_rel_total < ERR_STOP) done = true;
      else 
      {
        Hermes::Mixins::Loggable::Static::info("Adapting the coarse mesh.");
        done = adaptivity->adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);

        if (Space<double>::get_num_dofs(&space) >= NDOF_STOP) 
          done = true;
        else
          // Increase the counter of performed adaptivity steps.
          as++;
      }
      
      // Visualize the solution and mesh.
      char title[100];
      sprintf(title, "Solution<double>, time %g", current_time);
      view.set_title(title);
      view.show_mesh(false);
      view.show(&sln_time_new);
      sprintf(title, "Mesh, time %g", current_time);
      ordview.set_title(title);
      ordview.show(&space);

      // Clean up.
      delete adaptivity;
      if(!done) {
        delete ref_space;
        delete sln_time_new.get_mesh();
      }
    }
    while (done == false);

    sln_time_prev.copy(&sln_time_new);

    // 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;
}

//.........这里部分代码省略.........
      delete solver_coarse;
      delete [] coeff_vec_coarse;
    }

    // Adaptivity loop. Note: sln_prev_time must not be changed during spatial adaptivity. 
    bool done = false; int as = 1;
    double err_est;
    do {
      info("Time step %d, adaptivity step %d:", ts, as);

      // Construct globally refined reference mesh and setup reference space.
      Space* ref_space = construct_refined_space(&space);

      // Initialize matrix solver.
      SparseMatrix* matrix = create_matrix(matrix_solver);
      Vector* rhs = create_vector(matrix_solver);
      Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
      scalar* coeff_vec = new scalar[Space::get_num_dofs(ref_space)];

      // Initialize discrete problem on reference mesh.
      DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space, is_linear);

      // Calculate initial coefficient vector for Newton on the fine mesh.
      if (ts == 1 && as == 1) {
        info("Projecting coarse mesh solution to obtain coefficient vector on fine mesh.");
        OGProjection::project_global(ref_space, &sln, coeff_vec, matrix_solver);
      }
      else {
        info("Projecting last fine mesh solution to obtain coefficient vector on new fine mesh.");
        OGProjection::project_global(ref_space, &ref_sln, coeff_vec, matrix_solver);
      }

      // Now we can deallocate the previous fine mesh.
      if(as > 1) delete ref_sln.get_mesh();

      // Newton's loop on the fine mesh.
      info("Solving on fine mesh:");
      bool verbose = true;
      if (!solve_newton(coeff_vec, dp, solver, matrix, rhs, 
	  	        NEWTON_TOL_FINE, NEWTON_MAX_ITER, verbose)) error("Newton's iteration failed.");

      // Store the result in ref_sln.
      Solution::vector_to_solution(coeff_vec, ref_space, &ref_sln);

      // Project the fine mesh solution onto the coarse mesh.
      info("Projecting fine mesh solution on coarse mesh for error estimation.");
      OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver); 

      // Calculate element errors and total error estimate.
      info("Calculating error estimate.");
      Adapt* adaptivity = new Adapt(&space);
      double err_est_rel_total = adaptivity->calc_err_est(&sln, &ref_sln) * 100;

      // Report results.
      info("ndof: %d, ref_ndof: %d, err_est_rel: %g%%", 
           Space::get_num_dofs(&space), Space::get_num_dofs(ref_space), err_est_rel_total);

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

        if (Space::get_num_dofs(&space) >= NDOF_STOP) 
          done = true;
        else
          // Increase the counter of performed adaptivity steps.
          as++;
      }
      
      // Clean up.
      delete solver;
      delete matrix;
      delete rhs;
      delete adaptivity;
      delete ref_space;
      delete dp;
      delete [] coeff_vec;
    }
    while (done == false);

    // Visualize the solution and mesh.
    char title[100];
    sprintf(title, "Solution, time %g", ts*TAU);
    view.set_title(title);
    view.show_mesh(false);
    view.show(&sln);
    sprintf(title, "Mesh, time %g", ts*TAU);
    ordview.set_title(title);
    ordview.show(&space);

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

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

int main(int argc, char **args) 
{
  // Test variable.
  int success_test = 1;

  if (argc < 2) error("Not enough parameters.");

  // Load the mesh.
	Mesh mesh;
  H3DReader mloader;
  if (!mloader.load(args[1], &mesh)) error("Loading mesh file '%s'.", args[1]);

	// Initialize the space.
	int mx = 2;
	Ord3 order(mx, mx, mx);
	H1Space space(&mesh, bc_types, NULL, order);
#if defined LIN_DIRICHLET || defined NLN_DIRICHLET
	space.set_essential_bc_values(essential_bc_values);
#endif
	// Initialize the weak formulation.
	WeakForm wf;
	wf.add_vector_form(form_0<double, scalar>, form_0<Ord, Ord>);
#if defined LIN_NEUMANN || defined LIN_NEWTON
	wf.add_vector_form_surf(form_0_surf<double, scalar>, form_0_surf<Ord, Ord>);
#endif
#if defined LIN_DIRICHLET || defined NLN_DIRICHLET
	// preconditioner
	wf.add_matrix_form(precond_0_0<double, scalar>, precond_0_0<Ord, Ord>, HERMES_SYM);
#endif

	// Initialize the FE problem.
	DiscreteProblem fep(&wf, &space);

#if defined LIN_DIRICHLET || defined NLN_DIRICHLET
	// use ML preconditioner to speed-up things
	MlPrecond pc("sa");
	pc.set_param("max levels", 6);
	pc.set_param("increasing or decreasing", "decreasing");
	pc.set_param("aggregation: type", "MIS");
	pc.set_param("coarse: type", "Amesos-KLU");
#endif

	NoxSolver solver(&fep);
#if defined LIN_DIRICHLET || defined NLN_DIRICHLET
//	solver.set_precond(&pc);
#endif

	info("Solving.");
	Solution sln(&mesh);
	if(solver.solve()) Solution::vector_to_solution(solver.get_solution(), &space, &sln);
  else error ("Matrix solver failed.\n");
	

		Solution ex_sln(&mesh);
		ex_sln.set_exact(exact_solution);

		// Calculate exact error.
  info("Calculating exact error.");
  Adapt *adaptivity = new Adapt(&space, HERMES_H1_NORM);
  bool solutions_for_adapt = false;
  double err_exact = adaptivity->calc_err_exact(&sln, &ex_sln, solutions_for_adapt, HERMES_TOTAL_ERROR_ABS);

  if (err_exact > EPS)
		// Calculated solution is not precise enough.
		success_test = 0;

  if (success_test) {
    info("Success!");
    return ERR_SUCCESS;
  }
  else {
    info("Failure!");
    return ERR_FAILURE;
  }
}

int main(int argc, char* argv[])
{
  // Instantiate a class with global functions.
  Hermes2D hermes2d;

  // Load the mesh.
  Mesh mesh;
  H2DReader mloader;
  mloader.load("domain.mesh", &mesh);
  
  // Perform initial uniform mesh refinement.
  for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();

  // Set essential boundary conditions.
  DefaultEssentialBCConst bc_essential(Hermes::vector<std::string>("right", "top"), 0.0);
  EssentialBCs bcs(&bc_essential);
  
  // Create an H1 space with default shapeset.
  H1Space space(&mesh, &bcs, P_INIT);

  // Associate element markers (corresponding to physical regions) 
  // with material properties (diffusion coefficient, absorption 
  // cross-section, external sources).
  Hermes::vector<std::string> regions("e1", "e2", "e3", "e4", "e5");
  Hermes::vector<double> D_map(D_1, D_2, D_3, D_4, D_5);
  Hermes::vector<double> Sigma_a_map(SIGMA_A_1, SIGMA_A_2, SIGMA_A_3, SIGMA_A_4, SIGMA_A_5);
  Hermes::vector<double> Sources_map(Q_EXT_1, 0.0, Q_EXT_3, 0.0, 0.0);
  
  // Initialize the weak formulation.
  WeakFormsNeutronics::Monoenergetic::Diffusion::DefaultWeakFormFixedSource
    wf(regions, D_map, Sigma_a_map, Sources_map);

  // Initialize coarse and reference mesh solution.
  Solution sln, ref_sln;
  
  // Initialize refinement selector.
  H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);

  // Initialize views.
  ScalarView sview("Solution", new WinGeom(0, 0, 440, 350));
  sview.fix_scale_width(50);
  sview.show_mesh(false);
  OrderView  oview("Polynomial orders", new WinGeom(450, 0, 400, 350));
  
  // DOF and CPU convergence graphs initialization.
  SimpleGraph graph_dof, graph_cpu;
  
  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();

  // Adaptivity loop:
  int as = 1; bool done = false;
  do
  {
    info("---- Adaptivity step %d:", as);

    // Construct globally refined reference mesh and setup reference space.
    Space* ref_space = Space::construct_refined_space(&space);
    int ndof_ref = Space::get_num_dofs(ref_space);

    // Initialize the FE problem.
    DiscreteProblem dp(&wf, ref_space);

    // Initialize the FE problem.
    SparseMatrix* matrix = create_matrix(matrix_solver);
    Vector* rhs = create_vector(matrix_solver);
    Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);

    // Initial coefficient vector for the Newton's method.  
    scalar* coeff_vec = new scalar[ndof_ref];
    memset(coeff_vec, 0, ndof_ref*sizeof(scalar));

    // Perform Newton's iteration on reference emesh.
    info("Solving on reference mesh.");
    if (!hermes2d.solve_newton(coeff_vec, &dp, solver, matrix, rhs)) error("Newton's iteration failed.");

    // Translate the resulting coefficient vector into the Solution sln.
    Solution::vector_to_solution(coeff_vec, ref_space, &ref_sln);

    // Project the fine mesh solution onto the coarse mesh.
    Solution sln;
    info("Projecting reference solution on coarse mesh.");
    OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver); 

    // Time measurement.
    cpu_time.tick();
   
    // View the coarse mesh solution and polynomial orders.
    sview.show(&sln);
    oview.show(&space);

    // Skip visualization time.
    cpu_time.tick(HERMES_SKIP);

    // Calculate element errors and total error estimate.
    info("Calculating error estimate."); 
    Adapt* adaptivity = new Adapt(&space);
    double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln) * 100;

//.........这里部分代码省略.........

int main(int argc, char* argv[])
{
  // Instantiate a class with global functions.
  Hermes2D hermes2d;

  // Load the mesh.
  Mesh mesh;
  H2DReader mloader;
  mloader.load("motor.mesh", &mesh);

  // Initialize the weak formulation.
  CustomWeakFormPoisson wf("Motor", EPS_MOTOR, "Air", EPS_AIR);
  
  // Initialize boundary conditions
  DefaultEssentialBCConst bc_essential_out("Outer", 0.0);
  DefaultEssentialBCConst bc_essential_stator("Stator", VOLTAGE);
  EssentialBCs bcs(Hermes::vector<EssentialBoundaryCondition *>(&bc_essential_out, &bc_essential_stator));

  // Create an H1 space with default shapeset.
  H1Space space(&mesh, &bcs, P_INIT);

  // Initialize coarse and reference mesh solution.
  Solution sln, ref_sln;

  // Initialize refinement selector.
  H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);

  // Initialize views.
  ScalarView sview("Solution", new WinGeom(0, 0, 410, 600));
  sview.fix_scale_width(50);
  sview.show_mesh(false);
  OrderView  oview("Polynomial orders", new WinGeom(420, 0, 400, 600));

  // DOF and CPU convergence graphs initialization.
  SimpleGraph graph_dof, graph_cpu;

  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();

  // Adaptivity loop:
  int as = 1;
  bool done = false;
  do
  {
    info("---- Adaptivity step %d:", as);

    // Construct globally refined reference mesh and setup reference space.
    Space* ref_space = Space::construct_refined_space(&space);
    int ndof_ref = Space::get_num_dofs(ref_space);

    // Initialize matrix solver.
    SparseMatrix* matrix = create_matrix(matrix_solver);
    Vector* rhs = create_vector(matrix_solver);
    Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);

    // Initialize reference problem.
    info("Solving on reference mesh.");
    DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space);

    // Time measurement.
    cpu_time.tick();

    // Initial coefficient vector for the Newton's method.  
    scalar* coeff_vec = new scalar[ndof_ref];
    memset(coeff_vec, 0, ndof_ref * sizeof(scalar));

    // Perform Newton's iteration.
    if (!hermes2d.solve_newton(coeff_vec, dp, solver, matrix, rhs)) error("Newton's iteration failed.");

    // Translate the resulting coefficient vector into the Solution sln.
    Solution::vector_to_solution(coeff_vec, ref_space, &ref_sln);

    // Project the fine mesh solution onto the coarse mesh.
    info("Projecting reference solution on coarse mesh.");
    OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);

    // Time measurement.
    cpu_time.tick();

    // VTK output.
    if (VTK_VISUALIZATION) {
      // Output solution in VTK format.
      Linearizer lin;
      char* title = new char[100];
      sprintf(title, "sln-%d.vtk", as);
      lin.save_solution_vtk(&sln, title, "Potential", false);
      info("Solution in VTK format saved to file %s.", title);

      // Output mesh and element orders in VTK format.
      Orderizer ord;
      sprintf(title, "ord-%d.vtk", as);
      ord.save_orders_vtk(&space, title);
      info("Element orders in VTK format saved to file %s.", title);
    }

    // View the coarse mesh solution and polynomial orders.
    if (HERMES_VISUALIZATION) {
      sview.show(&sln);
      oview.show(&space);
//.........这里部分代码省略.........

int main(int argc, char* args[])
{
  // Load the mesh.
  MeshSharedPtr mesh(new Mesh);
  MeshReaderH2D mloader;
  mloader.load("square.mesh", mesh);

  // Perform initial mesh refinement.
  for (int i = 0; i < INIT_REF; i++)
    mesh->refine_all_elements();

  // Create an L2 space.
  SpaceSharedPtr<double> fine_space(new L2Space<double>(mesh, USE_TAYLOR_SHAPESET ? std::max(P_INIT, 2) : P_INIT, (USE_TAYLOR_SHAPESET ? (Shapeset*)(new L2ShapesetTaylor) : (Shapeset*)(new L2ShapesetLegendre))));

  // Initialize refinement selector.
  L2ProjBasedSelector<double> selector(CAND_LIST);
  selector.set_error_weights(1., 1., 1.);

  MeshFunctionSharedPtr<double> sln(new Solution<double>);
  MeshFunctionSharedPtr<double> refsln(new Solution<double>);

  // Initialize the weak formulation.
  WeakFormSharedPtr<double> wf(new CustomWeakForm("Bdy_bottom_left", mesh));
  ScalarView view1("Solution", new WinGeom(900, 0, 450, 350));
  view1.fix_scale_width(60);

  // Initialize linear solver.
  Hermes::Hermes2D::LinearSolver<double> linear_solver;
  linear_solver.set_weak_formulation(wf);

  adaptivity.set_space(fine_space);

  int as = 1; bool done = false;
  do
  {
    // Construct globally refined reference mesh
    // and setup reference space->
    Mesh::ReferenceMeshCreator ref_mesh_creator(mesh);
    MeshSharedPtr ref_mesh = ref_mesh_creator.create_ref_mesh();

    Space<double>::ReferenceSpaceCreator refspace_creator(fine_space, ref_mesh, 0);
    SpaceSharedPtr<double> refspace = refspace_creator.create_ref_space();

    try
    {
      linear_solver.set_space(refspace);
      linear_solver.solve();

      if (USE_TAYLOR_SHAPESET)
      {
        PostProcessing::VertexBasedLimiter limiter(refspace, linear_solver.get_sln_vector(), P_INIT);
        refsln = limiter.get_solution();
      }
      else
      {
        Solution<double>::vector_to_solution(linear_solver.get_sln_vector(), refspace, refsln);
      }

      view1.show(refsln);
      OGProjection<double>::project_global(fine_space, refsln, sln, HERMES_L2_NORM);
    }
    catch (Exceptions::Exception& e)
    {
      std::cout << e.info();
    }
    catch (std::exception& e)
    {
      std::cout << e.what();
    }

    // Calculate element errors and total error estimate.
    errorCalculator.calculate_errors(sln, refsln);
    double err_est_rel = errorCalculator.get_total_error_squared() * 100;

    std::cout << "Error: " << err_est_rel << "%." << std::endl;

    // If err_est_rel too large, adapt the mesh.
    if (err_est_rel < ERR_STOP)
      done = true;
    else
      done = adaptivity.adapt(&selector);
    as++;
  } while (done == false);

  // Wait for keyboard or mouse input.
  View::wait();
  return 0;
}