예제 #1
0
static void process_region(img** volume, img** orig, ushort thresh,
	vector<ushort>& rar, vector<ushort>& car, vector<ushort>& zar)
{
	static num dmap[6][512][512];	
	
	// if the region is too small...
	if (rar.size() < 600) {
		cout << "--> deleted an unlikely region (size: " << rar.size() << ")\n";
		return;
	}
	
	// if the region spans too many slices vertically...
	int region_zmin = *min_element(zar.begin(), zar.end());
	if (*max_element(zar.begin(), zar.end()) - region_zmin > 5) {
		dp("--> deleted an unlikely region (z-interval > 5)");
		return;
	}
	
	// find the boundary of the region
	vector<ushort> edge_rar, edge_car, edge_zar;
	
	for (ushort i=0; i < zar.size(); ++i) {
		for (ushort q=zar[i]-1; q < zar[i]+2; ++q) {
			for (ushort k=rar[i]-1; k < rar[i]+2; ++k) {
				for (ushort j=car[i]-1; j < car[i]+2; ++j) {
					if (volume[q]->pix[k][j] == white) {
						edge_rar.push_back(rar[i]);
						edge_car.push_back(car[i]);
						edge_zar.push_back(zar[i]);
						volume[zar[i]]->pix[rar[i]][car[i]] = 0;
						break;
					}
				}
				
				if (volume[zar[i]]->pix[rar[i]][car[i]] == 0) {
					break;
				}
			}
			
			if (volume[zar[i]]->pix[rar[i]][car[i]] == 0) {
				break;
			}
		}
	}
	
	ar("--> region-boundary z-vec", edge_zar, edge_zar.size()); 
	
	// create a distance map
	uint blen = edge_rar.size();
	
	num *erar, *ecar, *ezar, *dvec, *tmp;
	try {
		erar = new num[blen];
		ecar = new num[blen];
		ezar = new num[blen];
		dvec = new num[blen];
		tmp = new num[blen];
	} catch (bad_alloc& err) {
		dp("Fatal memory allocation error; results may be unreliable!");
		return;
	}
	
	for (uint i=0; i < blen; ++i) {
		// copy the boundary voxels into num-arrays to make things simple
		erar[i] = (num) edge_rar[i];
		ecar[i] = (num) edge_car[i];
		ezar[i] = (num) edge_zar[i];
	}
	
	// find the minimum distance from the boundary for each point
	for (uint i=0; i < zar.size(); ++i) {
		mat_op(erar, (num) rar[i], blen, sub, tmp);
		mat_op(tmp, dx, blen, mul, tmp);
		m_apply(tmp, square, blen, dvec);

		mat_op(ecar, (num) car[i], blen, sub, tmp);
		mat_op(tmp, dy, blen, mul, tmp);
		m_apply(tmp, square, blen, tmp);
		mat_op(tmp, dvec, blen, add, dvec);
		
		mat_op(ezar, (num) zar[i], blen, sub, tmp);
		mat_op(tmp, dz, blen, mul, tmp);
		m_apply(tmp, square, blen, tmp);
		mat_op(tmp, dvec, blen, add, dvec);
		
		m_apply(dvec, sqrt, blen, dvec);
		
		// store the distance into the distance map
		dmap[zar[i] - region_zmin][rar[i]][car[i]] = *min_element(dvec, dvec+blen);
	}
	
	// find the 'centroid' of the region
	num cen_max = 0;
	ushort cenz=0, cenx=0, ceny=0;
	
	for (ushort i=0; i < zar.size(); ++i) {
		num cur_val = dmap[zar[i] - region_zmin][rar[i]][car[i]];
		if (cur_val > cen_max) {
			cen_max = cur_val;
			cenz = zar[i] - region_zmin;
			cenx = rar[i];
			ceny = car[i];
		}
	}
	
	cout << "--> region centroid: [" << cenx << ", " << ceny << ", " << region_zmin + cenz << "]\n"; 
	
	// find the variance of the distance from the boundary to the centroid
	for (ushort i=0; i < blen; ++i) {
		tmp[i] = sqrt(square((erar[i] - cenx) * dx)
					+ square((ecar[i] - ceny) * dy)
					+ square((ezar[i] - cenz) * dz));
	}
	
	num edge_u = sum_of(tmp, blen) / blen;
	mat_op(tmp, edge_u, blen, sub, tmp);
	m_apply(tmp, square, blen, tmp);
	num stddev = sqrt(sum_of(tmp, blen) / blen);
	cout << "--> (stddev, mean) distance from centroid: (" << stddev << ", " << edge_u << ")\n";
	
	/* My thinking is that 85% or more of the distances should lie within 3 to
	 * 7 units of the mean distance to have a sphere (roughly). According to
	 * Chebyshev's rule [p = 1 - k^-2 => k = sqrt(1 / (1 - p))], 85% of the
	 * distances should lie within 2.582 standard deviations of the mean
	 * distance. So to be spherical, 3 < u - [u - (2.582 * stddev)] < 7.
	 */

	num dist_delta =  edge_u - (edge_u - (CHEBY_DELTA * stddev));
	bool tumor = (dist_delta > 3) && (dist_delta < 7);
	cout << "--> dist_delta: " << dist_delta << endl;
	cout << "--> size: " << rar.size() << endl;
	
	if (tumor) {
		uint64_t sum_shade = 0;
		for (uint i=0; i < zar.size(); ++i) {
			sum_shade += orig[zar[i]]->pix[rar[i]][car[i]];
		}
	
		tumor = (sum_shade / zar.size()) > thresh; // 67% empirically
	}
	
	for (uint i=0; i < zar.size(); ++i) {
		volume[zar[i]]->pix[rar[i]][car[i]] = tumor ? 1 : BENIGN;
	}
	
	cout << "--> " << tumor  << " tumor.\n";
	
	delete[] dvec;
	delete[] tmp;
	delete[] erar;
	delete[] ecar;
	delete[] ezar;
}
예제 #2
0
int main(int argc, char* argv[])
{
  // Load the mesh.
  MeshSharedPtr mesh(new Mesh);
  MeshReaderH2D mloader;
  mloader.load("square.mesh", mesh);

  // Initial mesh refinements.
  for (int i = 0; i < INIT_GLOB_REF_NUM; i++) mesh->refine_all_elements();
  mesh->refine_towards_boundary("Top", INIT_REF_NUM_BDY);

  // Initialize boundary conditions.
  CustomEssentialBCNonConst bc_essential({ "Bottom", "Right", "Top", "Left" });
  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);

  // Zero initial solutions. This is why we use H_OFFSET.
  MeshFunctionSharedPtr<double> h_time_prev(new ZeroSolution<double>(mesh));

  // Initialize views.
  ScalarView view("Initial condition", new WinGeom(0, 0, 600, 500));
  view.fix_scale_width(80);

  // Visualize the initial condition.
  view.show(h_time_prev);

  // Initialize the constitutive relations.
  ConstitutiveRelations* constitutive_relations;
  if (constitutive_relations_type == CONSTITUTIVE_GENUCHTEN)
    constitutive_relations = new ConstitutiveRelationsGenuchten(ALPHA, M, N, THETA_S, THETA_R, K_S, STORATIVITY);
  else
    constitutive_relations = new ConstitutiveRelationsGardner(ALPHA, THETA_S, THETA_R, K_S);

  // Initialize the weak formulation.
  double current_time = 0;
  WeakFormSharedPtr<double> wf(new CustomWeakFormRichardsIE(time_step, h_time_prev, constitutive_relations));

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

  // Initialize Newton solver.
  NewtonSolver<double> newton(&dp);
  newton.set_verbose_output(true);

  // Time stepping:
  int ts = 1;
  do
  {
    Hermes::Mixins::Loggable::Static::info("---- Time step %d, time %3.5f s", ts, current_time);

    // Perform Newton's iteration.
    try
    {
      newton.set_max_allowed_iterations(NEWTON_MAX_ITER);
      newton.solve();
    }
    catch (Hermes::Exceptions::Exception e)
    {
      e.print_msg();
      throw Hermes::Exceptions::Exception("Newton's iteration failed.");
    };

    // Translate the resulting coefficient vector into the Solution<double> sln->
    Solution<double>::vector_to_solution(newton.get_sln_vector(), space, h_time_prev);

    // Visualize the solution.
    char title[100];
    sprintf(title, "Time %g s", current_time);
    view.set_title(title);
    view.show(h_time_prev);

    // 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;
}
예제 #3
0
int main(int argc, char **args) 
{
  // Test variable.
  int success_test = 1;

	if (argc < 3) 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 according to the
  // command-line parameters passed.
	int o;
	sscanf(args[2], "%d", &o);
	Ord3 order(o, o, o);
	HcurlSpace space(&mesh, bc_types, NULL, order);

  // Initialize the weak formulation.
	WeakForm wf;
	wf.add_matrix_form(callback(bilinear_form), HERMES_SYM);
	wf.add_vector_form(callback(linear_form));

  // 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 the preconditioner in the case of SOLVER_AZTECOO.
  if (matrix_solver == SOLVER_AZTECOO) 
  {
    ((AztecOOSolver*) solver)->set_solver(iterative_method);
    ((AztecOOSolver*) solver)->set_precond(preconditioner);
    // Using default iteration parameters (see solver/aztecoo.h).
  }

  // Assemble the linear problem.
  info("Assembling (ndof: %d).", Space::get_num_dofs(&space));
  dp.assemble(matrix, rhs);

  // Solve the linear system. If successful, obtain the solution.
  info("Solving.");
		Solution sln(&mesh);
  if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln);
  else error ("Matrix solver failed.\n");

  ExactSolution ex_sln(&mesh, exact_solution);

  // Calculate exact error.
  info("Calculating exact error.");
  Adapt *adaptivity = new Adapt(&space, HERMES_HCURL_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;

  // Clean up.
  delete matrix;
  delete rhs;
  delete solver;
  delete adaptivity;
  
  if (success_test) {
    info("Success!");
    return ERR_SUCCESS;
	}
	else {
    info("Failure!");
    return ERR_FAILURE;
	}
}
예제 #4
0
파일: main.cpp 프로젝트: michalkuraz/hermes
int main(int argc, char **args)
{
  // Check the number of command-line parameters.
  if (argc < 2) {
    info("Use x, y, z, xy, xz, yz, or xyz as a command-line parameter.");
    error("Not enough command-line parameters.");
  }

  // Determine anisotropy type from the command-line parameter.
  ANISO_TYPE = parse_aniso_type(args[1]);

  // Load the mesh.
  Mesh mesh;
  H3DReader mesh_loader;
  mesh_loader.load("hex-0-1.mesh3d", &mesh);

  // Assign the lowest possible directional polynomial degrees so that the problem's NDOF >= 1.
  assign_poly_degrees();

  // Create an H1 space with default shapeset.
  info("Setting directional polynomial degrees %d, %d, %d.", P_INIT_X, P_INIT_Y, P_INIT_Z);
  H1Space space(&mesh, bc_types, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));

  // Initialize weak formulation.
  WeakForm wf;
  wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<Ord, Ord>, HERMES_SYM, HERMES_ANY);
  wf.add_vector_form(linear_form<double, scalar>, linear_form<Ord, Ord>, HERMES_ANY);

  // Set exact solution.
  ExactSolution exact(&mesh, fndd);

  // 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.
    Space* ref_space = construct_refined_space(&space,1 , H3D_H3D_H3D_REFT_HEX_XYZ);

    // Initialize discrete problem.
    bool is_linear = true;
    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);
    
    // Initialize the preconditioner in the case of SOLVER_AZTECOO.
    if (matrix_solver == SOLVER_AZTECOO) 
    {
      ((AztecOOSolver*) solver)->set_solver(iterative_method);
      ((AztecOOSolver*) solver)->set_precond(preconditioner);
      // Using default iteration parameters (see solver/aztecoo.h).
    }
  
    // Assemble the reference problem.
    info("Assembling on reference mesh (ndof: %d).", Space::get_num_dofs(ref_space));
    dp.assemble(matrix, rhs);

    // Time measurement.
    cpu_time.tick();

    // Solve the linear system on reference mesh. If successful, obtain the solution.
    info("Solving on reference mesh.");
    Solution ref_sln(ref_space->get_mesh());
    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 reference solution on the coarse mesh.
    Solution sln(space.get_mesh());
    info("Projecting reference solution on coarse mesh.");
    OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);

    // Time measurement.
    cpu_time.tick();

    // Output solution and mesh with polynomial orders.
    if (solution_output) 
    {
      out_fn_vtk(&sln, "sln", as);
      out_orders_vtk(&space, "order", as);
    }

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

    // Calculate element errors and total error estimate.
    info("Calculating error estimate and exact error.");
    Adapt *adaptivity = new Adapt(&space, HERMES_H1_NORM);
    bool solutions_for_adapt = true;
    double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln, solutions_for_adapt) * 100;

    // Calculate exact error.
    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("err_est_rel: %g%%, err_exact_rel: %g%%.", err_est_rel, err_exact_rel);

    // Add entry to DOF and CPU convergence graphs.
    graph_dof_est.add_values(Space::get_num_dofs(&space), err_est_rel);
    graph_dof_est.save("conv_dof_est.dat");
    graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel);
    graph_cpu_est.save("conv_cpu_est.dat");
    graph_dof_exact.add_values(Space::get_num_dofs(&space), err_exact_rel);
    graph_dof_exact.save("conv_dof_exact.dat");
    graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact_rel);
    graph_cpu_exact.save("conv_cpu_exact.dat");

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

    // Clean up.
    delete ref_space->get_mesh();
    delete ref_space;
    delete matrix;
    delete rhs;
    delete solver;
    delete adaptivity;

    // Increase the counter of performed adaptivity steps.
    as++;
  } while (!done);

  return 0;
}
예제 #5
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;
}
예제 #6
0
파일: Robber_II.cpp 프로젝트: ShellyCode/AP
int main(){
	int numTests;
	cin >> numTests;
	while(numTests--){
		int N; //  assume knowing the length of the array as N
		cin >> N; 
		std::vector<int> v;
		for (int i = 0; i < N; ++i)
		{
			int t;
			cin >> t;
			v.push_back(t);
		}

		if(v.size() <= 1){
			// trivial case
		}
		if(v.size() == 2){
			cout << max(v[0],v[1]) << endl;
			cout << v[0] < v[1] ? 1 : 0 << endl;
			cout << v[0] < v[1] ? v[1] : v[0] << endl;
		}

		// dp[i] is the maximum ending at ith house
		std::vector<int> dp(N,0);
		std::vector<std::vector<int> > record(N, std::vector<int>());
		dp[0] = v[0];
		dp[1] = v[1];
		record[0].push_back(0);
		record[1].push_back(1);

		int final_max = 0, final_idx;
		for (int i = 2; i < N; ++i)
		{
			// dp[i] = max(dp[i-1], dp[i-2]+v[i]);
			
			if (dp[i-1] > dp[i-2] + v[i])
			{

				dp[i] = dp[i-1];
				record[i] = record[i-1];
			}
			else{

				// if not considering the last one, it is exact the same as rob I
				// considering last if only the first and the last is possible exist together

				if (i == N - 1  && record[i-2][0] == 0) // the last one and the first one is already chosen
				{
					if (v[i] > v[0]) // if last one is bigger than first one, simple replace it
					{
						dp[i] = dp[i-2] + v[i] - v[0];
						record[i] = record[i-2];
						record[i].erase(record[i].begin());
						record[i].push_back(i);
					}
					// otherwise do nothing
				}
				else{
					dp[i] = dp[i-2] + v[i];
					record[i] = record[i-2];
					record[i].push_back(i);
				}
			}
			if (final_max < dp[i])
			{
				final_max = dp[i];
				final_idx = i;
			}
		}
		// output the results
		cout << final_max << endl;
		for (int i = 0; i < record[final_idx].size(); ++i)
		{
			cout << record[final_idx][i] << " ";
		}
		cout << endl
		for (int i = 0; i < record[final_idx].size(); ++i)
		{
			cout << v[record[final_idx][i]] << " ";
		}
		cout << endl;

	}
}
예제 #7
0
int main(int argc, char* argv[])
{
  // Time measurement.
  Hermes::Mixins::TimeMeasurable cpu_time;
  cpu_time.tick();

  // Load the mesh.
  Mesh mesh;
  if (USE_XML_FORMAT == true)
  {
    MeshReaderH2DXML mloader;  
    Hermes::Mixins::Loggable::Static::info("Reading mesh in XML format.");
    mloader.load("domain.xml", &mesh);
  }
  else 
  {
    MeshReaderH2D mloader;
    Hermes::Mixins::Loggable::Static::info("Reading mesh in original format.");
    mloader.load("domain.mesh", &mesh);
  }

  // Perform initial mesh refinements.
  for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
  
  // Initialize boundary conditions
  CustomEssentialBCNonConst bc_essential("Horizontal");
  EssentialBCs<double> bcs(&bc_essential);

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

  // Initialize the weak formulation.
  CustomWeakFormGeneral wf("Horizontal");

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

  // Initialize Newton solver.
  NewtonSolver<double> newton(&dp);

  // Perform Newton's iteration.
  try
  {
    newton.solve();
  }
  catch(std::exception& e)
  {
    std::cout << e.what();
    
  }

  // Translate the resulting coefficient vector into a Solution.
  Solution<double> sln;
  Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);

  // Time measurement.
  cpu_time.tick();

  // View the solution and mesh.
  ScalarView sview("Solution", new WinGeom(0, 0, 440, 350));
  sview.show(&sln);
  OrderView oview("Polynomial orders", new WinGeom(450, 0, 405, 350));
  oview.show(&space);

  // Print timing information.
  Hermes::Mixins::Loggable::Static::info("Total running time: %g s", cpu_time.accumulated());

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

  return 0;
}
예제 #8
0
int main(int argc, char **args) 
{
  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();

  // Load the mesh. 
  Mesh mesh;
  ExodusIIReader mloader;
  mloader.load("brick_with_holes_tet.e", &mesh);

  // Create H1 space with default shapeset for x-displacement component. 
  H1Space xdisp(&mesh, bc_types_x, essential_bc_values, Ord3(P_INIT));
  
  // Create H1 space with default shapeset for y-displacement component. 
  H1Space ydisp(&mesh, bc_types_y, essential_bc_values, Ord3(P_INIT));
  
  // Create H1 space with default shapeset for z-displacement component. 
  H1Space zdisp(&mesh, bc_types_z, essential_bc_values, Ord3(P_INIT));
  
  // Initialize weak formulation.
  WeakForm wf(3);
  wf.add_matrix_form(0, 0, callback(bilinear_form_0_0), HERMES_SYM);
  wf.add_matrix_form(0, 1, callback(bilinear_form_0_1), HERMES_SYM);
  wf.add_matrix_form(0, 2, callback(bilinear_form_0_2), HERMES_SYM);
  wf.add_vector_form_surf(0, callback(surf_linear_form_x), bdy_force);

  wf.add_matrix_form(1, 1, callback(bilinear_form_1_1), HERMES_SYM);
  wf.add_matrix_form(1, 2, callback(bilinear_form_1_2), HERMES_SYM);
  wf.add_vector_form_surf(1, callback(surf_linear_form_y), bdy_force);

  wf.add_matrix_form(2, 2, callback(bilinear_form_2_2), HERMES_SYM);
  wf.add_vector_form_surf(2, callback(surf_linear_form_z), bdy_force);

  // Initialize discrete problem.
  bool is_linear = true;
  DiscreteProblem dp(&wf, Tuple<Space *>(&xdisp, &ydisp, &zdisp), is_linear);

  // Initialize the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
  initialize_solution_environment(matrix_solver, argc, args);

  // 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 the preconditioner in the case of SOLVER_AZTECOO.
  if (matrix_solver == SOLVER_AZTECOO) 
  {
    ((AztecOOSolver*) solver)->set_solver(iterative_method);
    ((AztecOOSolver*) solver)->set_precond(preconditioner);
    // Using default iteration parameters (see solver/aztecoo.h).
  }

  // Assemble stiffness matrix and load vector.
  info("Assembling the linear problem (ndof: %d).", Space::get_num_dofs(Tuple<Space *>(&xdisp, &ydisp, &zdisp)));
  dp.assemble(matrix, rhs);

  // Solve the linear system. If successful, obtain the solution.
  info("Solving the linear problem.");
  Solution xsln(xdisp.get_mesh());
  Solution ysln(ydisp.get_mesh());
  Solution zsln(zdisp.get_mesh());
  if(solver->solve()) Solution::vector_to_solutions(solver->get_solution(), 
                      Tuple<Space *>(&xdisp, &ydisp, &zdisp), Tuple<Solution *>(&xsln, &ysln, &zsln));
  else error ("Matrix solver failed.\n");

  // Output all components of the solution.
  if (solution_output) out_fn_vtk(&xsln, &ysln, &zsln, "sln");
  
  // Time measurement.
  cpu_time.tick();

  // Print timing information.
  info("Solutions saved. Total running time: %g s.", cpu_time.accumulated());

  // Clean up.
  delete matrix;
  delete rhs;
  delete solver;
  
  // Properly terminate the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
  finalize_solution_environment(matrix_solver);

  return 0;
}
예제 #9
0
int main(int argc, char* argv[])
{
  // Instantiate a class with global functions.
  Hermes2D hermes2d;

  // Load the mesh.
  Mesh mesh, mesh1;
  H2DReader mloader;
  mloader.load("domain.mesh", &mesh);

  // Perform uniform mesh refinement.
  mesh.refine_all_elements();

  // Initialize boundary conditions.
  DefaultEssentialBCConst zero_disp("Bottom", 0.0);
  EssentialBCs bcs(&zero_disp);

  // Create x- and y- displacement space using the default H1 shapeset.
  H1Space u1_space(&mesh, &bcs, P_INIT);
  H1Space u2_space(&mesh, &bcs, P_INIT);
  int ndof = Space::get_num_dofs(Hermes::vector<Space *>(&u1_space, &u2_space));
  info("ndof = %d", ndof);

  // Initialize the weak formulation.
  CustomWeakFormLinearElasticity wf(E, nu, rho*g1, "Top", f0, f1);

  // Initialize the FE problem.
  DiscreteProblem dp(&wf, Hermes::vector<Space *>(&u1_space, &u2_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);

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

  // Perform Newton's iteration.
  bool verbose = true;
  bool jacobian_changed = true;
  if (!hermes2d.solve_newton(coeff_vec, &dp, solver, matrix, rhs, jacobian_changed,
      NEWTON_TOL, NEWTON_MAX_ITER, verbose)) error("Newton's iteration failed.");

  // Translate the resulting coefficient vector into the Solution sln.
  Solution u1_sln, u2_sln;
  Solution::vector_to_solutions(coeff_vec, Hermes::vector<Space *>(&u1_space, &u2_space), 
                                Hermes::vector<Solution *>(&u1_sln, &u2_sln));
  
  // Visualize the solution.
  ScalarView view("Von Mises stress [Pa]", new WinGeom(0, 0, 800, 400));
  double lambda = (E * nu) / ((1 + nu) * (1 - 2*nu));  // First Lame constant.
  double mu = E / (2*(1 + nu));                        // Second Lame constant.
  VonMisesFilter stress(Hermes::vector<MeshFunction *>(&u1_sln, &u2_sln), lambda, mu);
  view.show_mesh(false);
  view.show(&stress, HERMES_EPS_HIGH, H2D_FN_VAL_0, &u1_sln, &u2_sln, 1.5e5);

  // Wait for the view to be closed.
  View::wait();

  // Clean up.
  delete [] coeff_vec;
  delete solver;
  delete matrix;
  delete rhs;

  return 0;
}
예제 #10
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, basemesh;
  MeshReaderH2D mloader;
  mloader.load("square.mesh", &basemesh);
  mesh.copy(&basemesh);

  // Initial mesh refinements.
  for(int i = 0; i < INIT_GLOB_REF_NUM; i++) mesh.refine_all_elements();
  mesh.refine_towards_boundary("Top", INIT_REF_NUM_BDY);

  // Initialize boundary conditions.
  CustomEssentialBCNonConst bc_essential(Hermes::vector<std::string>("Bottom", "Right", "Top", "Left"));
  EssentialBCs<double> bcs(&bc_essential);

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

  // Zero initial solution. This is why we use H_OFFSET.
  ZeroSolution h_time_prev(&mesh), h_time_new(&mesh);

  // Initialize the constitutive relations.
  ConstitutiveRelations* constitutive_relations;
  if(constitutive_relations_type == CONSTITUTIVE_GENUCHTEN)
    constitutive_relations = new ConstitutiveRelationsGenuchten(ALPHA, M, N, THETA_S, THETA_R, K_S, STORATIVITY);
  else
    constitutive_relations = new ConstitutiveRelationsGardner(ALPHA, THETA_S, THETA_R, K_S);

  // Initialize the weak formulation.
  CustomWeakFormRichardsRK wf(constitutive_relations);

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

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

  // Visualize initial condition.
  char title[100];
  ScalarView view("Initial condition", new WinGeom(0, 0, 440, 350));
  OrderView ordview("Initial mesh", new WinGeom(445, 0, 440, 350));
  view.show(&h_time_prev);
  ordview.show(&space);

  // DOF and CPU convergence graphs initialization.
  SimpleGraph graph_dof, graph_cpu;
  
  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();
  
  // Time stepping loop.
  double current_time = 0; int ts = 1;
  do 
  {
    // 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: space.unrefine_all_mesh_elements();
                space.adjust_element_order(-1, -1, P_INIT, P_INIT);
                break;
        default: error("Wrong global derefinement method.");
      }

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

    // Spatial adaptivity loop. Note: h_time_prev 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<double>* ref_space = Space<double>::construct_refined_space(&space);
      int ndof_ref = Space<double>::get_num_dofs(ref_space);

      // Time measurement.
      cpu_time.tick();

      // Initialize Runge-Kutta time stepping.
      RungeKutta<double> runge_kutta(&wf, ref_space, &bt, matrix_solver);

      // 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 freeze_jacobian = false;
      bool block_diagonal_jacobian = false;
      bool verbose = true;
      double damping_coeff = 1.0;
      double max_allowed_residual_norm = 1e10;

      try
      {
        runge_kutta.rk_time_step_newton(current_time, time_step, &h_time_prev, 
            &h_time_new, freeze_jacobian, block_diagonal_jacobian, verbose,
            NEWTON_TOL, NEWTON_MAX_ITER, damping_coeff, max_allowed_residual_norm);
      }
      catch(Exceptions::Exception& e)
      {
        e.printMsg();
        error("Runge-Kutta time step failed");
      }

      // Project the fine mesh solution onto the coarse mesh.
      Solution<double> sln_coarse;
      info("Projecting fine mesh solution on coarse mesh for error estimation.");
      OGProjection<double>::project_global(&space, &h_time_new, &sln_coarse, matrix_solver); 

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

      // Report results.
      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);

      // Time measurement.
      cpu_time.tick();

      // 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<double>::get_num_dofs(&space) >= NDOF_STOP) 
          done = true;
        else
          // Increase the counter of performed adaptivity steps.
          as++;
      }
      
      // Clean up.
      delete adaptivity;
      if(!done)
      {
        delete h_time_new.get_space();
        delete h_time_new.get_mesh();
      }
    }
    while (done == false);

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

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

    // Copy last reference solution into h_time_prev.
    h_time_prev.copy(&h_time_new);
    delete h_time_new.get_mesh();

    // 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;
}
dgFloat32 dgCollisionChamferCylinder::RayCast(const dgVector& q0, const dgVector& q1, dgFloat32 maxT, dgContactPoint& contactOut, const dgBody* const body, void* const userData, OnRayPrecastAction preFilter) const
{
	if (q0.m_x > m_height) {
		if (q1.m_x < m_height) {
			dgFloat32 t1 = (m_height - q0.m_x) / (q1.m_x - q0.m_x);
			dgFloat32 y = q0.m_y + (q1.m_y - q0.m_y) * t1;
			dgFloat32 z = q0.m_z + (q1.m_z - q0.m_z) * t1;
			if ((y * y + z * z) < m_radius * m_radius) {
				contactOut.m_normal = dgVector(dgFloat32(1.0f), dgFloat32(0.0f), dgFloat32(0.0f), dgFloat32(0.0f));
				return t1;
			}
		}
	}

	if (q0.m_x < -m_height) {
		if (q1.m_x > -m_height) {
			dgFloat32 t1 = (-m_height - q0.m_x) / (q1.m_x - q0.m_x);
			dgFloat32 y = q0.m_y + (q1.m_y - q0.m_y) * t1;
			dgFloat32 z = q0.m_z + (q1.m_z - q0.m_z) * t1;
			if ((y * y + z * z) < m_radius * m_radius) {
				contactOut.m_normal = dgVector(dgFloat32(-1.0f), dgFloat32(0.0f), dgFloat32(0.0f), dgFloat32(0.0f));
				return t1;
			}
		}
	}

	dgVector dq((q1 - q0) & dgVector::m_triplexMask);

	// avoid NaN as a result of a division by zero
	if ((dq % dq) <= 0.0f) {
		return dgFloat32(1.2f);
	}

	dgVector dir(dq.CompProduct4(dq.InvMagSqrt()));
	if (dgAbsf(dir.m_x) > 0.9999f) {
		return dgCollisionConvex::RayCast(q0, q1, maxT, contactOut, body, NULL, NULL);
	}

	dgVector p0(q0 & dgVector::m_triplexMask);
	dgVector p1(q1 & dgVector::m_triplexMask);

	p0.m_x = dgFloat32 (0.0f);
	p1.m_x = dgFloat32 (0.0f);

	dgVector dp (p1 - p0);
	dgFloat32 a = dp.DotProduct4(dp).GetScalar();
	dgFloat32 b = dgFloat32 (2.0f) * dp.DotProduct4(p0).GetScalar();
	dgFloat32 c = p0.DotProduct4(p0).GetScalar() - m_radius * m_radius;

	dgFloat32 disc = b * b - dgFloat32 (4.0f) * a * c;
	if (disc >= dgFloat32 (0.0f)) {
		disc = dgSqrt (disc);
		dgVector origin0(p0 + dp.Scale4 ((-b + disc) / (dgFloat32 (2.0f) * a)));
		dgVector origin1(p0 + dp.Scale4 ((-b - disc) / (dgFloat32 (2.0f) * a)));
		dgFloat32 t0 = dgRayCastSphere(q0, q1, origin0, m_height);
		dgFloat32 t1 = dgRayCastSphere(q0, q1, origin1, m_height);
		if(t1 < t0) {
			t0 = t1;
			origin0 = origin1;
		}

		if ((t0 >= 0.0f) && (t0 <= 1.0f)) {
			contactOut.m_normal = q0 + dq.Scale4(t0) - origin0;
			dgAssert(contactOut.m_normal.m_w == dgFloat32(0.0f));
			contactOut.m_normal = contactOut.m_normal.CompProduct4(contactOut.m_normal.DotProduct4(contactOut.m_normal).InvSqrt());
			return t0;
		}
	} else {
		dgVector origin0 (dgPointToRayDistance (dgVector::m_zero, p0, p1)); 
		origin0 = origin0.Scale4(m_radius / dgSqrt(origin0.DotProduct4(origin0).GetScalar()));
		dgFloat32 t0 = dgRayCastSphere(q0, q1, origin0, m_height);
		if ((t0 >= 0.0f) && (t0 <= 1.0f)) {
			contactOut.m_normal = q0 + dq.Scale4(t0) - origin0;
			dgAssert(contactOut.m_normal.m_w == dgFloat32(0.0f));
			contactOut.m_normal = contactOut.m_normal.CompProduct4(contactOut.m_normal.DotProduct4(contactOut.m_normal).InvSqrt());
			return t0;
		}
	}

	return dgFloat32(1.2f);
}
예제 #12
0
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.
  for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();

  // Enter boundary markers.
  BCTypes bc_types;
  bc_types.add_bc_dirichlet(BDY_HORIZONTAL);
  bc_types.add_bc_neumann(BDY_VERTICAL);

  BCValues bc_values;
  bc_values.add_function(BDY_HORIZONTAL, essential_bc_values);

  // Create 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 weak formulation.
  bool matrix_free = false;
  WeakForm wf;
  wf.add_matrix_form(bilinear_form, bilinear_form_ord, HERMES_SYM);
  wf.add_vector_form(linear_form, linear_form_ord);
  wf.add_vector_form_surf(linear_form_surf, linear_form_surf_ord, BDY_VERTICAL);

  // Initialize the FE problem.
  bool is_linear = true;
  DiscreteProblem dp(&wf, &space, is_linear);
   
  SparseMatrix* matrix = create_matrix(matrix_solver);
  Vector* rhs = create_vector(matrix_solver);
  Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);

  if (matrix_solver == SOLVER_AZTECOO) 
  {
    ((AztecOOSolver*) solver)->set_solver(iterative_method);
    ((AztecOOSolver*) solver)->set_precond(preconditioner);
    // Using default iteration parameters (see solver/aztecoo.h).
  }
    
  // Initialize the solution.
  Solution sln;
  
  // Assemble the stiffness matrix and right-hand side vector.
  info("Assembling the stiffness matrix and right-hand side vector.");
  dp.assemble(matrix, rhs);

  // 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, &sln);
  else
    error ("Matrix solver failed.\n");
  
  // Time measurement.
  cpu_time.tick();
  
  // Clean up.
  delete solver;
  delete matrix;
  delete rhs;

  // View the solution and mesh.
  ScalarView sview("Solution", new WinGeom(0, 0, 440, 350));
  sview.show(&sln);
  OrderView  oview("Polynomial orders", new WinGeom(450, 0, 400, 350));
  oview.show(&space);

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

  // Print timing information.
  verbose("Total running time: %g s", cpu_time.accumulated());

  // Wait for all views to be closed.
  View::wait();
  
  return 0;
}
예제 #13
0
void StrandBlockSolver::lhsDissipation()
{
  int jj=nPstr+2,nn=nFaces+nBedges;
  Array4D<double> aa(nq,nq,jj,nn);
  for (int n=0; n<nFaces+nBedges; n++)
    for (int j=0; j<nPstr+2; j++)
      for (int k=0; k<nq; k++)
	for (int l=0; l<nq; l++) aa(l,k,j,n) = 0.;


  // unstructured faces
  int c1,c2,n1,n2,jp,fc,m,mm,m1l,m1u,m2l,m2u,npts=1;
  double a[nq*nq];
  for (int n=0; n<nEdges; n++){
    c1            = edge(0,n);
    c2            = edge(1,n);
    m1l           = ncsc(c1  );
    m1u           = ncsc(c1+1);
    m2l           = ncsc(c2  );
    m2u           = ncsc(c2+1);
    fc            = fClip(c1);
    if (fClip(c2) > fc) fc = fClip(c2);
  for (int j=1; j<fc+1; j++){
    sys->lhsDisFluxJacobian(npts,&facs(0,j,n),&xvs(j,n),
			    &q(0,j,c1),&q(0,j,c2),&a[0]);

    for (int k=0; k<nq*nq; k++) a[k] *= .5;

    // diagonal contributions
    for (int k=0; k<nq; k++){
      m             = k*nq;
    for (int l=0; l<nq; l++){
      dd(l,k,j,c1) += a[m+l];
      dd(l,k,j,c2) += a[m+l];
    }}

    // off-diagonal contributions
    for (int k=0; k<nq; k++){
      m             = k*nq;
    for (int l=0; l<nq; l++){
      aa(l,k,j,c1)  = a[m+l];
      aa(l,k,j,c2)  = a[m+l];
    }}

    for (int mm=m1l; mm<m1u; mm++){
      nn            = csc(mm);
      for (int k=0; k<nq; k++){
	m           = k*nq;
      for (int l=0; l<nq; l++)
	bu(l,k,j,mm) -= aa(l,k,j,nn);
      }}

    for (int mm=m2l; mm<m2u; mm++){
      nn            = csc(mm);
      for (int k=0; k<nq; k++){
	m           = k*nq;
      for (int l=0; l<nq; l++)
	bu(l,k,j,mm) -= aa(l,k,j,nn);
      }}

    // reset working array to zero
    for (int k=0; k<nq; k++){
      m             = k*nq;
    for (int l=0; l<nq; l++){
      aa(l,k,j,c1)  = 0.;
      aa(l,k,j,c2)  = 0.;
    }}
  }}

  aa.deallocate();


  // structured faces
  double Ax,Ay,ds,eps=1.e-14;
  for (int n=0; n<nFaces-nGfaces; n++){
    n1            = face(0,n);
    n2            = face(1,n);
  for (int j=0; j<fClip(n)+1; j++){
    jp            = j+1;
    Ax            = facu(0,j,n);
    Ay            = facu(1,j,n);
    ds            = Ax*Ax+Ay*Ay;
    if (fabs(ds) < eps){
      for (int k=0; k<nq; k++){
	m         = k*nq;
      for (int l=0; l<nq; l++)
	a[m+l]    = 0.;
      }}
    else
      sys->lhsDisFluxJacobian(npts,&facu(0,j,n),&xvu(j,n),
			      &q(0,j,n),&q(0,jp,n),&a[0]);
    for (int k=0; k<nq; k++){
      m             = k*nq;
    for (int l=0; l<nq; l++){
      dd(l,k,j ,n) += (a[m+l]*.5);
      dp(l,k,j ,n) -= (a[m+l]*.5);
      dd(l,k,jp,n) += (a[m+l]*.5);
      dm(l,k,jp,n) -= (a[m+l]*.5);
    }}}}
}
예제 #14
0
int main(int argc, char* argv[])
{
  // Load the mesh.
  Mesh mesh;
  H2DReader mloader;
  mloader.load("domain.mesh", &mesh);

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

  // Enter boundary markers.
  BCTypes bc_types;
  bc_types.add_bc_dirichlet(Hermes::Tuple<int>(BDY_BOTTOM, BDY_OUTER, BDY_LEFT, BDY_INNER));

  // Enter Dirichlet boudnary values.
  BCValues bc_values;
  bc_values.add_function(Hermes::Tuple<int>(BDY_BOTTOM, BDY_OUTER, BDY_LEFT, BDY_INNER), essential_bc_values);

  // Create 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 weak formulation.
  WeakForm wf;
  wf.add_matrix_form(callback(bilinear_form));
  wf.add_vector_form(callback(linear_form));

  // 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 the solution.
  Solution sln;

  // Assemble the stiffness matrix and right-hand side vector.
  info("Assembling the stiffness matrix and right-hand side vector.");
  dp.assemble(matrix, rhs);

  // Solve the linear system and if successful, obtain the and solution.
  info("Solving the matrix problem.");
  if(solver->solve())
    Solution::vector_to_solution(solver->get_solution(), &space, &sln);
  else
    error ("Matrix solver failed.\n");

  // Visualize the solution.
  ScalarView view("Solution", new WinGeom(0, 0, 440, 350));
  view.show(&sln);

  // Wait for the view to be closed.
  View::wait();

  // Clean up.
  delete solver;
  delete matrix;
  delete rhs;

  return 0;
}
예제 #15
0
파일: main.cpp 프로젝트: navi-vonavi/hermes
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'\n", args[1]);

  // Initialize the space 1.
	Ord3 o1(2, 2, 2);
	H1Space space1(&mesh, bc_types, essential_bc_values, o1);

	// Initialize the space 2.
	Ord3 o2(4, 4, 4);
	H1Space space2(&mesh, bc_types, essential_bc_values, o2);

  // Initialize the weak formulation.
  WeakForm wf(2);
	wf.add_matrix_form(0, 0, bilinear_form_1<double, scalar>, bilinear_form_1<Ord, Ord>, HERMES_SYM);
	wf.add_vector_form(0, linear_form_1<double, scalar>, linear_form_1<Ord, Ord>);
	wf.add_matrix_form(1, 1, bilinear_form_2<double, scalar>, bilinear_form_2<Ord, Ord>, HERMES_SYM);
	wf.add_vector_form(1, linear_form_2<double, scalar>, linear_form_2<Ord, Ord>);

  // Initialize the FE problem.
  bool is_linear = true;
  DiscreteProblem dp(&wf, Tuple<Space *>(&space1, &space2), is_linear);

  // Initialize the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
  initialize_solution_environment(matrix_solver, argc, args);

  // 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 the preconditioner in the case of SOLVER_AZTECOO.
  if (matrix_solver == SOLVER_AZTECOO) 
  {
    ((AztecOOSolver*) solver)->set_solver(iterative_method);
    ((AztecOOSolver*) solver)->set_precond(preconditioner);
    // Using default iteration parameters (see solver/aztecoo.h).
  }

  // Assemble the linear problem.
  info("Assembling (ndof: %d).", Space::get_num_dofs(Tuple<Space *>(&space1, &space2)));
  dp.assemble(matrix, rhs);
    
  // Solve the linear system. If successful, obtain the solution.
  info("Solving.");
  Solution sln1(&mesh);
  Solution sln2(&mesh);
  if(solver->solve()) Solution::vector_to_solutions(solver->get_solution(), Tuple<Space *>(&space1, &space2), Tuple<Solution *>(&sln1, &sln2));
  else error ("Matrix solver failed.\n");
    
  ExactSolution ex_sln1(&mesh, exact_sln_fn_1);
  ExactSolution ex_sln2(&mesh, exact_sln_fn_2);

  // Calculate exact error.
  info("Calculating exact error.");
  Adapt *adaptivity = new Adapt(Tuple<Space *>(&space1, &space2), Tuple<ProjNormType>(HERMES_H1_NORM, HERMES_H1_NORM));
  bool solutions_for_adapt = false;
  double err_exact = adaptivity->calc_err_exact(Tuple<Solution *>(&sln1, &sln2), Tuple<Solution *>(&ex_sln1, &ex_sln2), solutions_for_adapt, HERMES_TOTAL_ERROR_ABS);

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

  // Clean up.
  delete matrix;
  delete rhs;
  delete solver;
  delete adaptivity;

  // Properly terminate the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
  finalize_solution_environment(matrix_solver);
  
  if (success_test) {
    info("Success!");
    return ERR_SUCCESS;
  }
  else {
    info("Failure!");
    return ERR_FAILURE;
  }
}
예제 #16
0
void writeFrames(const Kinect::FrameSource::IntrinsicParameters& ip,const Kinect::FrameBuffer& color,const Kinect::MeshBuffer& mesh,const char* lwoFileName)
	{
	/* Create the texture file name: */
	std::string textureFileName(lwoFileName,Misc::getExtension(lwoFileName));
	textureFileName.append("-color.png");
	
	/* Write the color frame as a texture image: */
	{
	Images::RGBImage texImage(color.getSize(0),color.getSize(1));
	Images::RGBImage::Color* tiPtr=texImage.modifyPixels();
	const unsigned char* cfPtr=color.getTypedBuffer<unsigned char>();
	for(int y=0;y<color.getSize(1);++y)
		for(int x=0;x<color.getSize(0);++x,++tiPtr,cfPtr+=3)
			*tiPtr=Images::RGBImage::Color(cfPtr);
	
	Images::writeImageFile(texImage,textureFileName.c_str());
	}
	
	/* Open the LWO file: */
	IO::FilePtr lwoFile=IO::openFile(lwoFileName,IO::File::WriteOnly);
	lwoFile->setEndianness(Misc::BigEndian);
	
	/* Create the LWO file structure via the FORM chunk: */
	{
	IFFChunkWriter form(lwoFile,"FORM");
	form.write<char>("LWO2",4);
	
	/* Create the TAGS chunk: */
	{
	IFFChunkWriter tags(&form,"TAGS");
	tags.writeString("ColorImage");
	tags.writeChunk();
	}
	
	/* Create the LAYR chunk: */
	{
	IFFChunkWriter layr(&form,"LAYR");
	layr.write<Misc::UInt16>(0U);
	layr.write<Misc::UInt16>(0x0U);
	for(int i=0;i<3;++i)
		layr.write<Misc::Float32>(0.0f);
	layr.writeString("DepthImage");
	layr.writeChunk();
	}
	
	/* Create an index map for all vertices to omit unused vertices: */
	unsigned int* indices=new unsigned int[mesh.numVertices];
	for(unsigned int i=0;i<mesh.numVertices;++i)
		indices[i]=~0x0U;
	unsigned int numUsedVertices=0;
	
	/* Create the PNTS, BBOX and VMAP chunks in one go: */
	{
	typedef Kinect::FrameSource::IntrinsicParameters::PTransform PTransform;
	typedef PTransform::Point Point;
	typedef Geometry::Box<Point::Scalar,3> Box;
	
	IFFChunkWriter bbox(&form,"BBOX");
	IFFChunkWriter pnts(&form,"PNTS");
	IFFChunkWriter vmap(&form,"VMAP");
	
	/* Write the VMAP header: */
	vmap.write<char>("TXUV",4);
	vmap.write<Misc::UInt16>(2U);
	vmap.writeString("ColorImageUV");
	
	/* Process all triangle vertices: */
	Box pBox=Box::empty;
	const Kinect::MeshBuffer::Vertex* vertices=mesh.getVertices();
	const Kinect::MeshBuffer::Index* tiPtr=mesh.getTriangleIndices();
	for(unsigned int i=0;i<mesh.numTriangles*3;++i,++tiPtr)
		{
		/* Check if the triangle vertex doesn't already have an index: */
		if(indices[*tiPtr]==~0x0U)
			{
			/* Assign an index to the triangle vertex: */
			indices[*tiPtr]=numUsedVertices;
			
			/* Transform the mesh vertex to camera space using the depth projection matrix: */
			Point dp(vertices[*tiPtr].position.getXyzw());
			Point cp=ip.depthProjection.transform(dp);
			
			/* Transform the depth-space point to texture space using the color projection matrix: */
			Point tp=ip.colorProjection.transform(dp);
			
			/* Add the point to the bounding box: */
			pBox.addPoint(cp);
			
			/* Store the point and its texture coordinates: */
			pnts.writePoint(cp);
			vmap.writeVarIndex(numUsedVertices);
			for(int i=0;i<2;++i)
				vmap.write<Misc::Float32>(tp[i]);
			
			++numUsedVertices;
			}
		}
	
	/* Write the bounding box: */
	bbox.writeBox(pBox);
	
	/* Write the BBOX, PNTS, and VMAP chunks: */
	bbox.writeChunk();
	pnts.writeChunk();
	vmap.writeChunk();
	}
	
	/* Create the POLS chunk: */
	{
	IFFChunkWriter pols(&form,"POLS");
	pols.write<char>("FACE",4);
	const Kinect::MeshBuffer::Index* tiPtr=mesh.getTriangleIndices();
	for(unsigned int triangleIndex=0;triangleIndex<mesh.numTriangles;++triangleIndex,tiPtr+=3)
		{
		pols.write<Misc::UInt16>(3U);
		for(int i=0;i<3;++i)
			pols.writeVarIndex(indices[tiPtr[2-i]]);
		}
	pols.writeChunk();
	}
	
	/* Delete the vertex index map: */
	delete[] indices;
	
	/* Create the PTAG chunk: */
	{
	IFFChunkWriter ptag(&form,"PTAG");
	ptag.write<char>("SURF",4);
	for(unsigned int triangleIndex=0;triangleIndex<mesh.numTriangles;++triangleIndex)
		{
		ptag.writeVarIndex(triangleIndex);
		ptag.write<Misc::UInt16>(0U);
		}
	ptag.writeChunk();
	}
	
	/* Create the CLIP chunk: */
	{
	IFFChunkWriter clip(&form,"CLIP");
	clip.write<Misc::UInt32>(1U);
	
	/* Create the STIL chunk: */
	{
	IFFChunkWriter stil(&clip,"STIL",true);
	stil.writeString(textureFileName.c_str());
	stil.writeChunk();
	}
	
	clip.writeChunk();
	}
	
	/* Create the SURF chunk: */
	{
	IFFChunkWriter surf(&form,"SURF");
	surf.writeString("ColorImage");
	surf.writeString("");
	
	/* Create the SIDE subchunk: */
	{
	IFFChunkWriter side(&surf,"SIDE",true);
	side.write<Misc::UInt16>(3U);
	side.writeChunk();
	}
	
	/* Create the SMAN subchunk: */
	{
	IFFChunkWriter sman(&surf,"SMAN",true);
	sman.write<Misc::Float32>(Math::rad(90.0f));
	sman.writeChunk();
	}
	
	/* Create the COLR subchunk: */
	{
	IFFChunkWriter colr(&surf,"COLR",true);
	// colr.writeColor(1.0f,1.0f,1.0f);
	colr.writeColor(0.5f,0.6f,0.8f);
	colr.writeVarIndex(0U);
	colr.writeChunk();
	}
	
	/* Create the DIFF subchunk: */
	{
	IFFChunkWriter diff(&surf,"DIFF",true);
	diff.write<Misc::Float32>(1.0f);
	diff.writeVarIndex(0U);
	diff.writeChunk();
	}
	
	/* Create the LUMI subchunk: */
	{
	IFFChunkWriter lumi(&surf,"LUMI",true);
	lumi.write<Misc::Float32>(0.0f);
	lumi.writeVarIndex(0U);
	lumi.writeChunk();
	}
	
	/* Create the BLOK subchunk: */
	{
	IFFChunkWriter blok(&surf,"BLOK",true);
	
	/* Create the IMAP subchunk: */
	{
	IFFChunkWriter imap(&blok,"IMAP",true);
	imap.writeString("1");
	
	/* Create the CHAN subchunk: */
	{
	IFFChunkWriter chan(&imap,"CHAN",true);
	chan.write<char>("COLR",4);
	chan.writeChunk();
	}
	
	imap.writeChunk();
	}
	
	/* Create the PROJ subchunk: */
	{
	IFFChunkWriter proj(&blok,"PROJ",true);
	proj.write<Misc::UInt16>(5U);
	proj.writeChunk();
	}
	
	/* Create the IMAG subchunk: */
	{
	IFFChunkWriter imag(&blok,"IMAG",true);
	imag.writeVarIndex(1U);
	imag.writeChunk();
	}
	
	/* Create the VMAP subchunk: */
	{
	IFFChunkWriter vmap(&blok,"VMAP",true);
	vmap.writeString("ColorImageUV");
	vmap.writeChunk();
	}
	
	blok.writeChunk();
	}
	
	/* Write the SURF chunk: */
	surf.writeChunk();
	}
	
	/* Write the FORM chunk: */
	form.writeChunk();
	}
	}
예제 #17
0
int main(int argc, char* argv[])
{
  // Instantiate a class with global functions.
  Hermes2D hermes2d;

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

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

  // Perform initial mesh refinements.
  for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
  
  // Initialize boundary conditions
  CustomEssentialBCNonConst bc_essential("Boundary 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("Boundary horizontal");

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

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

  if (matrix_solver == SOLVER_AZTECOO)
  {
    ((AztecOOSolver*) solver)->set_solver(iterative_method);
    ((AztecOOSolver*) solver)->set_precond(preconditioner);
    // Using default iteration parameters (see solver/aztecoo.h).
  }

  // Initial coefficient vector for the Newton's method.  
  scalar* coeff_vec = new scalar[ndof];
  memset(coeff_vec, 0, ndof*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 sln;
  Solution::vector_to_solution(coeff_vec, &space, &sln);

  // Time measurement.
  cpu_time.tick();

  // Clean up.
  delete solver;
  delete matrix;
  delete rhs;
  delete [] coeff_vec;

  // View the solution and mesh.
  ScalarView sview("Solution", new WinGeom(0, 0, 440, 350));
  sview.show(&sln);
  OrderView  oview("Polynomial orders", new WinGeom(450, 0, 400, 350));
  oview.show(&space);

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

  // Print timing information.
  verbose("Total running time: %g s", cpu_time.accumulated());

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

  return 0;
}
예제 #18
0
int main(int argc, char* argv[])
{
  // Load the mesh.
  Mesh mesh_whole_domain, mesh_with_hole;
  Hermes::vector<Mesh*> meshes (&mesh_whole_domain, &mesh_with_hole);
  MeshReaderH2DXML mloader;
  mloader.load("domain.xml", meshes);

  // Temperature mesh: Initial uniform mesh refinements in graphite.
  meshes[0]->refine_by_criterion(element_in_graphite, INIT_REF_NUM_TEMPERATURE_GRAPHITE);

  // Temperature mesh: Initial uniform mesh refinements in fluid.
  meshes[0]->refine_by_criterion(element_in_fluid, INIT_REF_NUM_TEMPERATURE_FLUID);

  // Fluid mesh: Initial uniform mesh refinements.
  for(int i = 0; i < INIT_REF_NUM_FLUID; i++)
    meshes[1]->refine_all_elements();

  // Initial refinements towards boundary of graphite.
  for(unsigned int meshes_i = 0; meshes_i < meshes.size(); meshes_i++)
    meshes[meshes_i]->refine_towards_boundary("Inner Wall", INIT_REF_NUM_BDY_GRAPHITE);

  // Initial refinements towards the top and bottom edges.
  for(unsigned int meshes_i = 0; meshes_i < meshes.size(); meshes_i++)
    meshes[meshes_i]->refine_towards_boundary("Outer Wall", INIT_REF_NUM_BDY_WALL);

  /* View both meshes. */
  MeshView m1("Mesh for temperature"), m2("Mesh for fluid");
  m1.show(&mesh_whole_domain);
  m2.show(&mesh_with_hole);

  // Initialize boundary conditions.
  EssentialBCNonConst bc_inlet_vel_x("Inlet", VEL_INLET, H, STARTUP_TIME);
  DefaultEssentialBCConst<double> bc_other_vel_x(Hermes::vector<std::string>("Outer Wall", "Inner Wall"), 0.0);
  EssentialBCs<double> bcs_vel_x(Hermes::vector<EssentialBoundaryCondition<double> *>(&bc_inlet_vel_x, &bc_other_vel_x));
  DefaultEssentialBCConst<double> bc_vel_y(Hermes::vector<std::string>("Inlet", "Outer Wall", "Inner Wall"), 0.0);
  EssentialBCs<double> bcs_vel_y(&bc_vel_y);
  EssentialBCs<double> bcs_pressure;
  DefaultEssentialBCConst<double> bc_temperature(Hermes::vector<std::string>("Outer Wall", "Inlet"), 20.0);
  EssentialBCs<double> bcs_temperature(&bc_temperature);

  // Spaces for velocity components, pressure and temperature.
  H1Space<double> xvel_space(&mesh_with_hole, &bcs_vel_x, P_INIT_VEL);
  H1Space<double> yvel_space(&mesh_with_hole, &bcs_vel_y, P_INIT_VEL);
#ifdef PRESSURE_IN_L2
  L2Space<double> p_space(&mesh_with_hole, P_INIT_PRESSURE);
#else
  H1Space<double> p_space(&mesh_with_hole, &bcs_pressure, P_INIT_PRESSURE);
#endif
  H1Space<double> temperature_space(&mesh_whole_domain, &bcs_temperature, P_INIT_TEMPERATURE);
  Hermes::vector<Space<double> *> all_spaces(&xvel_space, 
      &yvel_space, &p_space, &temperature_space);
  Hermes::vector<const Space<double> *> all_spaces_const(&xvel_space, 
      &yvel_space, &p_space, &temperature_space);

  // Calculate and report the number of degrees of freedom.
  int ndof = Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&xvel_space, 
      &yvel_space, &p_space, &temperature_space));
  info("ndof = %d.", ndof);

  // Define projection norms.
  ProjNormType vel_proj_norm = HERMES_H1_NORM;
#ifdef PRESSURE_IN_L2
  ProjNormType p_proj_norm = HERMES_L2_NORM;
#else
  ProjNormType p_proj_norm = HERMES_H1_NORM;
#endif
  ProjNormType temperature_proj_norm = HERMES_H1_NORM;
  Hermes::vector<ProjNormType> all_proj_norms = Hermes::vector<ProjNormType>(vel_proj_norm, 
      vel_proj_norm, p_proj_norm, temperature_proj_norm);

  // Initial conditions and such.
  info("Setting initial conditions.");
  ZeroSolution xvel_prev_time(&mesh_with_hole), yvel_prev_time(&mesh_with_hole), p_prev_time(&mesh_with_hole);
  CustomInitialConditionTemperature temperature_init_cond(&mesh_whole_domain, HOLE_MID_X, HOLE_MID_Y, 
      0.5*OBSTACLE_DIAMETER, TEMPERATURE_INIT_FLUID, TEMPERATURE_INIT_GRAPHITE); 
  Solution<double> temperature_prev_time;
  Hermes::vector<Solution<double> *> all_solutions = Hermes::vector<Solution<double> *>(&xvel_prev_time, 
      &yvel_prev_time, &p_prev_time, &temperature_prev_time);
  Hermes::vector<MeshFunction<double> *> all_meshfns = Hermes::vector<MeshFunction<double> *>(&xvel_prev_time, 
      &yvel_prev_time, &p_prev_time, &temperature_init_cond);

  // Project all initial conditions on their FE spaces to obtain aninitial
  // coefficient vector for the Newton's method. We use local projection
  // to avoid oscillations in temperature on the graphite-fluid interface
  // FIXME - currently the LocalProjection only does the lowest-order part (linear
  // interpolation) at the moment. Higher-order part needs to be added.
  double* coeff_vec = new double[ndof];
  info("Projecting initial condition to obtain initial vector for the Newton's method.");
  //OGProjection<double>::project_global(all_spaces, all_meshfns, coeff_vec, matrix_solver, all_proj_norms);
  LocalProjection<double>::project_local(all_spaces_const, all_meshfns, coeff_vec, matrix_solver, all_proj_norms);

  // Translate the solution vector back to Solutions. This is needed to replace
  // the discontinuous initial condition for temperature_prev_time with its projection.
  Solution<double>::vector_to_solutions(coeff_vec, all_spaces_const, all_solutions);

  // Calculate Reynolds number.
  double reynolds_number = VEL_INLET * OBSTACLE_DIAMETER / KINEMATIC_VISCOSITY_FLUID;
  info("RE = %g", reynolds_number);
  if (reynolds_number < 1e-8) error("Re == 0 will not work - the equations use 1/Re.");

  // Initialize weak formulation.
  CustomWeakFormHeatAndFlow wf(STOKES, reynolds_number, time_step, &xvel_prev_time, &yvel_prev_time, &temperature_prev_time, 
      HEAT_SOURCE_GRAPHITE, SPECIFIC_HEAT_GRAPHITE, SPECIFIC_HEAT_FLUID, RHO_GRAPHITE, RHO_FLUID, 
      THERMAL_CONDUCTIVITY_GRAPHITE, THERMAL_CONDUCTIVITY_FLUID, SIMPLE_TEMPERATURE_ADVECTION);
  
  // Initialize the FE problem.
  DiscreteProblem<double> dp(&wf, all_spaces_const);

  // Initialize the Newton solver.
  NewtonSolver<double> newton(&dp, matrix_solver);

  // Initialize views.
  Views::VectorView vview("velocity [m/s]", new Views::WinGeom(0, 0, 700, 360));
  Views::ScalarView pview("pressure [Pa]", new Views::WinGeom(0, 415, 700, 350));
  Views::ScalarView tempview("temperature [C]", new Views::WinGeom(0, 795, 700, 350));
  //vview.set_min_max_range(0, 0.5);
  vview.fix_scale_width(80);
  //pview.set_min_max_range(-0.9, 1.0);
  pview.fix_scale_width(80);
  pview.show_mesh(false);
  tempview.fix_scale_width(80);
  tempview.show_mesh(false);

  // Time-stepping loop:
  char title[100];
  int num_time_steps = T_FINAL / time_step;
  double current_time = 0.0;
  for (int ts = 1; ts <= num_time_steps; ts++)
  {
    current_time += time_step;
    info("---- Time step %d, time = %g:", ts, current_time);

    // Update time-dependent essential BCs.
    if (current_time <= STARTUP_TIME) 
    {
      info("Updating time-dependent essential BC.");
      Space<double>::update_essential_bc_values(Hermes::vector<Space<double> *>(&xvel_space, &yvel_space, &p_space, 
                                                &temperature_space), current_time);
    }

    // Perform Newton's iteration.
    info("Solving nonlinear problem:");
    bool verbose = true;
    // Perform Newton's iteration and translate the resulting coefficient vector into previous time level solutions.
    newton.set_verbose_output(verbose);
    try
    {
      newton.solve(coeff_vec, NEWTON_TOL, NEWTON_MAX_ITER);
    }
    catch(Hermes::Exceptions::Exception e)
    {
      e.printMsg();
      error("Newton's iteration failed.");
    };
    {
      Hermes::vector<Solution<double> *> tmp(&xvel_prev_time, &yvel_prev_time, &p_prev_time, &temperature_prev_time);
      Solution<double>::vector_to_solutions(newton.get_sln_vector(), Hermes::vector<const Space<double> *>(&xvel_space, 
          &yvel_space, &p_space, &temperature_space), tmp);
    }
    
    // Show the solution at the end of time step.
    sprintf(title, "Velocity [m/s], time %g s", current_time);
    vview.set_title(title);
    vview.show(&xvel_prev_time, &yvel_prev_time);
    sprintf(title, "Pressure [Pa], time %g s", current_time);
    pview.set_title(title);
    pview.show(&p_prev_time);
    sprintf(title, "Temperature [C], time %g s", current_time);
    tempview.set_title(title);
    tempview.show(&temperature_prev_time,  Views::HERMES_EPS_HIGH);
  }

  delete [] coeff_vec;

  // Wait for all views to be closed.
  Views::View::wait();
  return 0;
}
예제 #19
0
파일: main.cpp 프로젝트: kameari/hermes
int main(int argc, char **args) 
{
  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();

  // Load the mesh. 
  Mesh mesh;
  H3DReader mloader;
  mloader.load("lshape_hex.mesh3d", &mesh);

  // Perform initial mesh refinement.
  for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);

  // Create an Hcurl space with default shapeset.
  HcurlSpace space(&mesh, bc_types, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));

  // Initialize weak formulation.
  WeakForm wf;
  wf.add_matrix_form(biform<double, scalar>, biform<Ord, Ord>, HERMES_SYM);
  wf.add_matrix_form_surf(biform_surf, biform_surf_ord);
  wf.add_vector_form_surf(liform_surf, liform_surf_ord);

  // Initialize discrete problem.
  bool is_linear = true;
  DiscreteProblem dp(&wf, &space, is_linear);

  // Initialize the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
  initialize_solution_environment(matrix_solver, argc, args);
  
  // 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 the preconditioner in the case of SOLVER_AZTECOO.
  if (matrix_solver == SOLVER_AZTECOO) 
  {
    ((AztecOOSolver*) solver)->set_solver(iterative_method);
    ((AztecOOSolver*) solver)->set_precond(preconditioner);
    // Using default iteration parameters (see solver/aztecoo.h).
  }

  // Assemble stiffness matrix and load vector.
  info("Assembling the linear problem (ndof: %d).", Space::get_num_dofs(&space));
  dp.assemble(matrix, rhs);

  // Solve the linear system. If successful, obtain the solution.
  info("Solving the linear problem.");
  Solution sln(space.get_mesh());
  if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln);
  else error ("Matrix solver failed.\n");

  // Output solution and mesh with polynomial orders.
  if (solution_output) 
  {
    out_fn_vtk(&sln, "sln");
    out_orders_vtk(&space, "order");
  }
  
  // Time measurement.
  cpu_time.tick();

  // Print timing information.
  info("Solution and mesh with polynomial orders saved. Total running time: %g s", cpu_time.accumulated());

  // Clean up.
  delete matrix;
  delete rhs;
  delete solver;

  // Properly terminate the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
  finalize_solution_environment(matrix_solver);

  return 0;
}
예제 #20
0
dgInt32 dgCollisionBox::CalculatePlaneIntersection (const dgVector& normal, const dgVector& point, dgVector* const contactsOut, dgFloat32 normalSign) const
{
	dgVector support[4];
	dgInt32 featureCount = 3;
	
	const dgConvexSimplexEdge** const vertToEdgeMapping = GetVertexToEdgeMapping();
	if (vertToEdgeMapping) {
		dgInt32 edgeIndex;
		support[0] = SupportVertex (normal.Scale4(normalSign), &edgeIndex);

		dgFloat32 dist = normal.DotProduct4(support[0] - point).GetScalar();
		if (dist <= DG_IMPULSIVE_CONTACT_PENETRATION) {
			dgVector normalAlgin (normal.Abs());
			if (!((normalAlgin.m_x > dgFloat32 (0.9999f)) || (normalAlgin.m_y > dgFloat32 (0.9999f)) || (normalAlgin.m_x > dgFloat32 (0.9999f)))) {
				// 0.25 degrees
				const dgFloat32 tiltAngle = dgFloat32 (0.005f);
				const dgFloat32 tiltAngle2 = tiltAngle * tiltAngle ;
				dgPlane testPlane (normal, - (normal.DotProduct4(support[0]).GetScalar()));

				featureCount = 1;
				const dgConvexSimplexEdge* const edge = vertToEdgeMapping[edgeIndex];
				const dgConvexSimplexEdge* ptr = edge;
				do {
					const dgVector& p = m_vertex[ptr->m_twin->m_vertex];
					dgFloat32 test1 = testPlane.Evalue(p);
					dgVector dist (p - support[0]);
					dgFloat32 angle2 = test1 * test1 / (dist.DotProduct4(dist).GetScalar());
					if (angle2 < tiltAngle2) {
						support[featureCount] = p;
						featureCount ++;
					}
					ptr = ptr->m_twin->m_next;
				} while ((ptr != edge) && (featureCount < 3));
			}
		}
	}

	dgInt32 count = 0;
	switch (featureCount)
	{
		case 1:
		{
			contactsOut[0] = support[0] - normal.CompProduct4(normal.DotProduct4(support[0] - point));
			count = 1;
			break;
		}

		case 2:
		{
			contactsOut[0] = support[0] - normal.CompProduct4(normal.DotProduct4(support[0] - point));
			contactsOut[1] = support[1] - normal.CompProduct4(normal.DotProduct4(support[1] - point));
			count = 2;
			break;
		}

		default:
		{
			dgFloat32 test[8];
			dgAssert(normal.m_w == dgFloat32(0.0f));
			dgPlane plane(normal, -(normal.DotProduct4(point).GetScalar()));
			for (dgInt32 i = 0; i < 8; i++) {
				dgAssert(m_vertex[i].m_w == dgFloat32(0.0f));
				test[i] = plane.DotProduct4(m_vertex[i] | dgVector::m_wOne).m_x;
			}

			dgConvexSimplexEdge* edge = NULL;
			for (dgInt32 i = 0; i < dgInt32 (sizeof (m_edgeEdgeMap) / sizeof (m_edgeEdgeMap[0])); i ++) {
				dgConvexSimplexEdge* const ptr = m_edgeEdgeMap[i];
				dgFloat32 side0 = test[ptr->m_vertex];
				dgFloat32 side1 = test[ptr->m_twin->m_vertex];
				if ((side0 * side1) < dgFloat32 (0.0f)) {
					edge = ptr;
					break;
				}
			}

			if (edge) {
				if (test[edge->m_vertex] < dgFloat32 (0.0f)) {
					edge = edge->m_twin;
				}
				dgAssert (test[edge->m_vertex] > dgFloat32 (0.0f));

				dgConvexSimplexEdge* ptr = edge;
				dgConvexSimplexEdge* firstEdge = NULL;
				dgFloat32 side0 = test[edge->m_vertex];
				do {
					dgAssert (m_vertex[ptr->m_twin->m_vertex].m_w == dgFloat32 (0.0f));
					dgFloat32 side1 = test[ptr->m_twin->m_vertex];
					if (side1 < side0) {
						if (side1 < dgFloat32 (0.0f)) {
							firstEdge = ptr;
							break;
						}

						side0 = side1;
						edge = ptr->m_twin;
						ptr = edge;
					}
					ptr = ptr->m_twin->m_next;
				} while (ptr != edge);

				if (firstEdge) {
					edge = firstEdge;
					ptr = edge;
					do {
						dgVector dp (m_vertex[ptr->m_twin->m_vertex] - m_vertex[ptr->m_vertex]);
						dgFloat32 t = plane.DotProduct4(dp).m_x;
						if (t >= dgFloat32 (-1.e-24f)) {
							t = dgFloat32 (0.0f);
						} else {
							t = test[ptr->m_vertex] / t;
							if (t > dgFloat32 (0.0f)) {
								t = dgFloat32 (0.0f);
							}
							if (t < dgFloat32 (-1.0f)) {
								t = dgFloat32 (-1.0f);
							}
						}

						dgAssert (t <= dgFloat32 (0.01f));
						dgAssert (t >= dgFloat32 (-1.05f));
						contactsOut[count] = m_vertex[ptr->m_vertex] - dp.Scale4 (t);
						count ++;

						dgConvexSimplexEdge* ptr1 = ptr->m_next;
						for (; ptr1 != ptr; ptr1 = ptr1->m_next) {
							dgInt32 index0 = ptr1->m_twin->m_vertex;
							if (test[index0] >= dgFloat32 (0.0f)) {
								dgAssert (test[ptr1->m_vertex] <= dgFloat32 (0.0f));
								break;
							}
						}
						dgAssert (ptr != ptr1);
						ptr = ptr1->m_twin;

					} while ((ptr != edge) && (count < 8));
				}
			}
		}
	}

	if (count > 2) {
		count = RectifyConvexSlice (count, normal, contactsOut);
	}
	return count;
}
예제 #21
0
파일: main.cpp 프로젝트: michalkuraz/hermes
int main(int argc, char* argv[])
{
  // Load the mesh file.
  Mesh mesh;
  H2DReader mloader;
  mloader.load("sample.mesh", &mesh);

  // Enter boundary markers.
  BCTypes bc_types;
  bc_types.add_bc_dirichlet(BDY_1);
  bc_types.add_bc_neumann(Hermes::Tuple<int>(BDY_2, BDY_3, BDY_4, BDY_5));

  // Enter Dirichlet boundary values;
  BCValues bc_values;
  bc_values.add_zero(BDY_1);

  // Create x- and y- displacement space using the default H1 shapeset.
  H1Space u_space(&mesh, &bc_types, &bc_values, P_INIT);
  H1Space v_space(&mesh, &bc_types, &bc_values, P_INIT);
  info("ndof = %d.", Space::get_num_dofs(Hermes::Tuple<Space *>(&u_space, &v_space)));

  // Initialize the weak formulation.
  WeakForm wf(2);
  wf.add_matrix_form(0, 0, callback(bilinear_form_0_0), HERMES_SYM);  // Note that only one symmetric part is
  wf.add_matrix_form(0, 1, callback(bilinear_form_0_1), HERMES_SYM);  // added in the case of symmetric bilinear
  wf.add_matrix_form(1, 1, callback(bilinear_form_1_1), HERMES_SYM);  // forms.
  wf.add_vector_form_surf(0, callback(linear_form_surf_0), BDY_3);
  wf.add_vector_form_surf(1, callback(linear_form_surf_1), BDY_3);

  // Testing n_dof and correctness of solution vector
  // for p_init = 1, 2, ..., 10
  int success = 1;
  Solution xsln, ysln;
  for (int p_init = 1; p_init <= 10; p_init++) {
    printf("********* p_init = %d *********\n", p_init);
    u_space.set_uniform_order(p_init);
    v_space.set_uniform_order(p_init);

    // Initialize the FE problem.
    bool is_linear = true;
    DiscreteProblem dp(&wf, Hermes::Tuple<Space *>(&u_space, &v_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 the solutions.
    Solution u_sln, v_sln;

    // Assemble the stiffness matrix and right-hand side vector.
    info("Assembling the stiffness matrix and right-hand side vector.");
    dp.assemble(matrix, rhs);

    // Solve the linear system and if successful, obtain the solutions.
    info("Solving the matrix problem.");
    if(solver->solve())
      Solution::vector_to_solutions(solver->get_solution(), Hermes::Tuple<Space *>(&u_space, &v_space), Hermes::Tuple<Solution *>(&u_sln, &v_sln));
    else
      error ("Matrix solver failed.\n");

    int ndof = Space::get_num_dofs(Hermes::Tuple<Space *>(&u_space, &v_space));
    printf("ndof = %d\n", ndof);
    double sum = 0;
    for (int i=0; i < ndof; i++) sum += solver->get_solution()[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 - 3.50185e-06) > 1e-3) success = 0;
    if (p_init == 2 && fabs(sum - 4.34916e-06) > 1e-3) success = 0;
    if (p_init == 3 && fabs(sum - 4.60553e-06) > 1e-3) success = 0;
    if (p_init == 4 && fabs(sum - 4.65616e-06) > 1e-3) success = 0;
    if (p_init == 5 && fabs(sum - 4.62893e-06) > 1e-3) success = 0;
    if (p_init == 6 && fabs(sum - 4.64336e-06) > 1e-3) success = 0;
    if (p_init == 7 && fabs(sum - 4.63724e-06) > 1e-3) success = 0;
    if (p_init == 8 && fabs(sum - 4.64491e-06) > 1e-3) success = 0;
    if (p_init == 9 && fabs(sum - 4.64582e-06) > 1e-3) success = 0;
    if (p_init == 10 && fabs(sum - 4.65028e-06) > 1e-3) success = 0;
  }

  if (success == 1) {
    printf("Success!\n");
    return ERR_SUCCESS;
  }
  else {
    printf("Failure!\n");
    return ERR_FAILURE;
  }
}
예제 #22
0
파일: poly.cpp 프로젝트: barak/CppAD-1
bool link_poly(
	size_t                     size     ,
	size_t                     repeat   ,
	CppAD::vector<double>     &a        ,  // coefficients of polynomial
	CppAD::vector<double>     &z        ,  // polynomial argument value
	CppAD::vector<double>     &ddp      )  // second derivative w.r.t z
{
	// speed test global option values
	if( global_atomic )
		return false;

	// -----------------------------------------------------
	// setup
	typedef CppAD::AD<double>     ADScalar;
	typedef CppAD::vector<ADScalar> ADVector;

	size_t i;      // temporary index
	size_t m = 1;  // number of dependent variables
	size_t n = 1;  // number of independent variables
	ADVector Z(n); // AD domain space vector
	ADVector P(m); // AD range space vector

	// choose the polynomial coefficients
	CppAD::uniform_01(size, a);

	// AD copy of the polynomial coefficients
	ADVector A(size);
	for(i = 0; i < size; i++)
		A[i] = a[i];

	// forward mode first and second differentials
	CppAD::vector<double> p(1), dp(1), dz(1), ddz(1);
	dz[0]  = 1.;
	ddz[0] = 0.;

	// AD function object
	CppAD::ADFun<double> f;

	// --------------------------------------------------------------------
	if( ! global_onetape ) while(repeat--)
	{
		// choose an argument value
		CppAD::uniform_01(1, z);
		Z[0] = z[0];

		// declare independent variables
		Independent(Z);

		// AD computation of the function value
		P[0] = CppAD::Poly(0, A, Z[0]);

		// create function object f : A -> detA
		f.Dependent(Z, P);

		if( global_optimize )
			f.optimize();

		// skip comparison operators
		f.compare_change_count(0);

		// pre-allocate memory for three forward mode calculations
		f.capacity_order(3);

		// evaluate the polynomial
		p = f.Forward(0, z);

		// evaluate first order Taylor coefficient
		dp = f.Forward(1, dz);

		// second derivative is twice second order Taylor coef
		ddp     = f.Forward(2, ddz);
		ddp[0] *= 2.;
	}
	else
	{
		// choose an argument value
		CppAD::uniform_01(1, z);
		Z[0] = z[0];

		// declare independent variables
		Independent(Z);

		// AD computation of the function value
		P[0] = CppAD::Poly(0, A, Z[0]);

		// create function object f : A -> detA
		f.Dependent(Z, P);

		if( global_optimize )
			f.optimize();

		// skip comparison operators
		f.compare_change_count(0);

		while(repeat--)
		{	// sufficient memory is allocated by second repetition

			// get the next argument value
			CppAD::uniform_01(1, z);

			// evaluate the polynomial at the new argument value
			p = f.Forward(0, z);

			// evaluate first order Taylor coefficient
			dp = f.Forward(1, dz);

			// second derivative is twice second order Taylor coef
			ddp     = f.Forward(2, ddz);
			ddp[0] *= 2.;
		}
	}
	return true;
}
예제 #23
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.
#if defined NONLIN1
	Ord3 order(1, 1, 1);
#else
	Ord3 order(2, 2, 2);
#endif
	H1Space space(&mesh, bc_types, essential_bc_values, order);

#if defined NONLIN2
	// Do L2 projection of zero function.
	WeakForm proj_wf;
	proj_wf.add_matrix_form(biproj_form<double, scalar>, biproj_form<Ord, Ord>, HERMES_SYM);
	proj_wf.add_vector_form(liproj_form<double, scalar>, liproj_form<Ord, Ord>);

	bool is_linear = true;
	DiscreteProblem lp(&proj_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_proj = create_linear_solver(matrix_solver, matrix, rhs);
  
  // Initialize the preconditioner in the case of SOLVER_AZTECOO.
  if (matrix_solver == SOLVER_AZTECOO) 
  {
    ((AztecOOSolver*) solver_proj)->set_solver(iterative_method);
    ((AztecOOSolver*) solver_proj)->set_precond(preconditioner);
    // Using default iteration parameters (see solver/aztecoo.h).
  }
  
  // Assemble the linear problem.
  info("Assembling (ndof: %d).", Space::get_num_dofs(&space));
  lp.assemble(matrix, rhs);
    
  // Solve the linear system.
  info("Solving.");
  if(!solver_proj->solve()) error ("Matrix solver failed.\n");

  delete matrix;
  delete rhs;
#endif

	// Initialize the weak formulation.
	WeakForm wf(1);
	wf.add_matrix_form(0, 0, jacobi_form<double, scalar>, jacobi_form<Ord, Ord>, HERMES_NONSYM);
	wf.add_vector_form(0, resid_form<double, scalar>, resid_form<Ord, Ord>);

	// Initialize the FE problem.
#if defined NONLIN2
  is_linear = false;
#else
  bool is_linear = false;
#endif
	DiscreteProblem dp(&wf, &space, is_linear);

	NoxSolver solver(&dp);

#if defined NONLIN2
solver.set_init_sln(solver_proj->get_solution());
delete solver_proj;
#endif

solver.set_conv_iters(10);
	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);
#ifdef NONLIN1
		ex_sln.set_const(100.0);
#else
		ex_sln.set_exact(exact_solution);
#endif
		// 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;
  }
}
예제 #24
0
int main(int argc, char* argv[])
{
  // Define nonlinear magnetic permeability via a cubic spline.
  Hermes::vector<double> mu_inv_pts(0.0,      0.5,      0.9,      1.0,      1.1,      1.2,      1.3,
                                    1.4,      1.6,      1.7,      1.8,      1.9,      3.0,      5.0,     10.0);
  Hermes::vector<double> mu_inv_val(1/1500.0, 1/1480.0, 1/1440.0, 1/1400.0, 1/1300.0, 1/1150.0, 1/950.0,
                                    1/750.0,  1/250.0,  1/180.0,  1/175.0,  1/150.0,  1/20.0,   1/10.0,  1/5.0);
  /*
  // This is for debugging (iron is assumed linear with mu_r = 300.0
  Hermes::vector<double> mu_inv_pts(0.0,      10.0);
  Hermes::vector<double> mu_inv_val(1/300.0,   1/300.0);
  */

  // Create the cubic spline (and plot it for visual control).
  double bc_left = 0.0;
  double bc_right = 0.0;
  bool first_der_left = false;
  bool first_der_right = false;
  bool extrapolate_der_left = false;
  bool extrapolate_der_right = false;
  CubicSpline mu_inv_iron(mu_inv_pts, mu_inv_val, bc_left, bc_right, first_der_left, first_der_right,
                          extrapolate_der_left, extrapolate_der_right);
  info("Saving cubic spline into a Pylab file spline.dat.");
  // The interval of definition of the spline will be
  // extended by "interval_extension" on both sides.
  double interval_extension = 1.0; 
  bool plot_derivative = false;
  mu_inv_iron.plot("spline.dat", interval_extension, plot_derivative);
  plot_derivative = true;
  mu_inv_iron.plot("spline_der.dat", interval_extension, plot_derivative);

  // Load the mesh.
  Mesh mesh;
  MeshReaderH2D mloader;
  mloader.load("actuator.mesh", &mesh);

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

  //MeshView mv("Mesh", new WinGeom(0, 0, 400, 400));
  //mv.show(&mesh);

  // Initialize boundary conditions.
  DefaultEssentialBCConst<double> bc_essential(BDY_DIRICHLET, 0.0);
  EssentialBCs<double> bcs(&bc_essential);

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

  // Initialize the weak formulation
  // This determines the increase of integration order
  // for the axisymmetric term containing 1/r. Default is 3.
  int order_inc = 3; 
  CustomWeakFormMagnetostatics wf(MAT_IRON_1, MAT_IRON_2, &mu_inv_iron, MAT_AIR,
                                  MAT_COPPER, MU_VACUUM, CURRENT_DENSITY, order_inc);

  // Initialize the FE problem.
  DiscreteProblem<double> dp(&wf, &space);
  
  // Initialize the solution.
  ConstantSolution<double> sln(&mesh, INIT_COND);

  // Project the initial condition on the FE space to obtain initial
  // coefficient vector for the Newton's method.
  info("Projecting to obtain initial vector for the Newton's method.");
  double* coeff_vec = new double[Space<double>::get_num_dofs(&space)] ;
  OGProjection<double>::project_global(&space, &sln, coeff_vec, matrix_solver_type);

  // Perform Newton's iteration.
  Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
  bool verbose = true;
  newton.set_verbose_output(verbose);
  try
  {
    newton.solve(coeff_vec, NEWTON_TOL, NEWTON_MAX_ITER);
  }
  catch(Hermes::Exceptions::Exception e)
  {
    e.printMsg();
    error("Newton's iteration failed.");
  };

  // Translate the resulting coefficient vector into the Solution sln.
  Solution<double>::vector_to_solution(coeff_vec, &space, &sln);

  // Cleanup.
  delete [] coeff_vec;

  // Visualise the solution and mesh.
  ScalarView s_view1("Vector potencial", new WinGeom(0, 0, 350, 450));
  FilterVectorPotencial vector_potencial(Hermes::vector<MeshFunction<double> *>(&sln, &sln),
                                         Hermes::vector<int>(H2D_FN_VAL, H2D_FN_VAL));
  s_view1.show_mesh(false);
  s_view1.show(&vector_potencial);

  ScalarView s_view2("Flux density", new WinGeom(360, 0, 350, 450));
  FilterFluxDensity flux_density(Hermes::vector<MeshFunction<double> *>(&sln, &sln));
  s_view2.show_mesh(false);
  s_view2.show(&flux_density);

  OrderView o_view("Mesh", new WinGeom(720, 0, 350, 450));
  o_view.show(&space);

  // Wait for all views to be closed.
  View::wait();
  return 0;
}
예제 #25
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("../domain.mesh", &mesh);

  // Convert to quadrilaterals.
  mesh.convert_triangles_to_quads();

  // Refine towards boundary.
  mesh.refine_towards_boundary("Bdy", 1, true);

  // Refine once towards vertex #4.
  mesh.refine_towards_vertex(4, 1);

  // Initialize solutions.
  CustomInitialConditionWave u_sln(&mesh);
  Solution v_sln(&mesh, 0.0);
  Hermes::vector<Solution*> slns(&u_sln, &v_sln);

  // Initialize the weak formulation.
  CustomWeakFormWave wf(time_step, C_SQUARED, &u_sln, &v_sln);
  
  // Initialize boundary conditions
  DefaultEssentialBCConst bc_essential("Bdy", 0.0);
  EssentialBCs bcs(&bc_essential);

  // Create x- and y- displacement space using the default H1 shapeset.
  H1Space u_space(&mesh, &bcs, P_INIT);
  H1Space v_space(&mesh, &bcs, P_INIT);
  info("ndof = %d.", Space::get_num_dofs(Hermes::vector<Space *>(&u_space, &v_space)));

  // Initialize the FE problem.
  DiscreteProblem dp(&wf, Hermes::vector<Space *>(&u_space, &v_space));

  // Initialize Runge-Kutta time stepping.
  RungeKutta runge_kutta(&dp, &bt, matrix_solver);

  // 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, time_step = %g s, stages: %d).", 
         current_time, time_step, bt.get_size());
    bool jacobian_changed = false;
    bool verbose = true;

    if (!runge_kutta.rk_time_step(current_time, time_step, slns, 
                                  slns, jacobian_changed, verbose))
      error("Runge-Kutta time step failed, try to decrease time step size.");

    // Update time.
    current_time += time_step;

  } while (current_time < T_FINAL);

  double coord_x[4] = {1, 3, 5, 7};
  double coord_y[4] = {1, 3, 5, 7};

  info("Coordinate (1.0, 0.0) value = %lf", u_sln.get_pt_value(coord_x[0], coord_y[0]));
  info("Coordinate (3.0, 3.0) value = %lf", u_sln.get_pt_value(coord_x[1], coord_y[1]));
  info("Coordinate (5.0, 5.0) value = %lf", u_sln.get_pt_value(coord_x[2], coord_y[2]));
  info("Coordinate (7.0, 7.0) value = %lf", u_sln.get_pt_value(coord_x[3], coord_y[3]));

  info("Coordinate (1.0, 0.0) value = %lf", v_sln.get_pt_value(coord_x[0], coord_y[0]));
  info("Coordinate (3.0, 3.0) value = %lf", v_sln.get_pt_value(coord_x[1], coord_y[1]));
  info("Coordinate (5.0, 5.0) value = %lf", v_sln.get_pt_value(coord_x[2], coord_y[2]));
  info("Coordinate (7.0, 7.0) value = %lf", v_sln.get_pt_value(coord_x[3], coord_y[3]));

  double t_value[8] = {0.212655, 0.000163, 0.000000, 0.000000, -0.793316, 0.007255, 0.000001, 0.000000};
  bool success = true;

  for (int i = 0; i < 4; i++)
  {
    if (fabs(t_value[i] - u_sln.get_pt_value(coord_x[i], coord_y[i])) > 1E-6) success = false;
  }

  for (int i = 4; i < 8; i++)
  {
    if (fabs(t_value[i] - v_sln.get_pt_value(coord_x[i-4], coord_y[i-4])) > 1E-6) success = false;
  }

  if (success) {
    printf("Success!\n");
    return ERR_SUCCESS;
  }
  else {
    printf("Failure!\n");
    return ERR_FAILURE;
  }

  // Wait for the view to be closed.
  View::wait();

  return 0;
}
예제 #26
0
// 于是按照这个思路写了一个,果断超时
// 然后又用 DP 加了一个 cache 解答,结果还是超时,为什么呢,看注释
    int minDistance(string word1, string word2) {
        vector<vector<int> > dp(word1.length(), vector<int>(word2.length(), -1));
        return minDistanceRecursion(word1, word2, word1.length(), word2.length(), dp);
    }
예제 #27
0
int main(int argc, char* argv[])
{
  // Time measurement.
  TimePeriod cpu_time;
  cpu_time.tick();

  // Load the mesh.
  Mesh u_mesh, v_mesh;
  MeshReaderH2D mloader;
  mloader.load("domain.mesh", &u_mesh);
  if (MULTI == false) u_mesh.refine_towards_boundary("Bdy", 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("Bdy", INIT_REF_BDY);

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

  // Define right-hand sides.
  CustomRightHandSide1 g1(K, D_u, SIGMA);
  CustomRightHandSide2 g2(K, D_v);

  // Initialize the weak formulation.
  CustomWeakForm wf(&g1, &g2);
  
  // Initialize boundary conditions
  DefaultEssentialBCConst<double> bc_u("Bdy", 0.0);
  EssentialBCs<double> bcs_u(&bc_u);
  DefaultEssentialBCConst<double> bc_v("Bdy", 0.0);
  EssentialBCs<double> bcs_v(&bc_v);

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


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

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

  // Initialize views.
  Views::ScalarView s_view_0("Solution[0]", new Views::WinGeom(0, 0, 440, 350));
  s_view_0.show_mesh(false);
  Views::OrderView  o_view_0("Mesh[0]", new Views::WinGeom(450, 0, 420, 350));
  Views::ScalarView s_view_1("Solution[1]", new Views::WinGeom(880, 0, 440, 350));
  s_view_1.show_mesh(false);
  Views::OrderView o_view_1("Mesh[1]", new Views::WinGeom(1330, 0, 420, 350));

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

  // 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<double> *>* ref_spaces = 
      Space<double>::construct_refined_spaces(Hermes::vector<Space<double> *>(&u_space, &v_space));
    Space<double>* u_ref_space = (*ref_spaces)[0];
    Space<double>* v_ref_space = (*ref_spaces)[1];
   
    Hermes::vector<const Space<double> *> ref_spaces_const((*ref_spaces)[0], (*ref_spaces)[1]);

    int ndof_ref = Space<double>::get_num_dofs(ref_spaces_const);

    // Initialize reference problem.
    info("Solving on reference mesh.");
    DiscreteProblem<double> dp(&wf, ref_spaces_const);

    NewtonSolver<double> newton(&dp, matrix_solver);
    //newton.set_verbose_output(false);

    // Time measurement.
    cpu_time.tick();
    
    // Perform Newton's iteration.
    try
    {
      newton.solve();
    }
    catch(Hermes::Exceptions::Exception e)
    {
      e.printMsg();
      error("Newton's iteration failed.");
    }

    // Translate the resulting coefficient vector into the instance of Solution.
    Solution<double>::vector_to_solutions(newton.get_sln_vector(), ref_spaces_const, 
                                          Hermes::vector<Solution<double> *>(&u_ref_sln, &v_ref_sln));

    // Project the fine mesh solution onto the coarse mesh.
    info("Projecting reference solution on coarse mesh.");
    OGProjection<double>::project_global(Hermes::vector<const Space<double> *>(&u_space, &v_space), 
                                 Hermes::vector<Solution<double> *>(&u_ref_sln, &v_ref_sln), 
                                 Hermes::vector<Solution<double> *>(&u_sln, &v_sln), matrix_solver); 
   
    cpu_time.tick();

    // View the coarse mesh solution and polynomial orders.
    s_view_0.show(&u_sln); 
    o_view_0.show(&u_space);
    s_view_1.show(&v_sln); 
    o_view_1.show(&v_space);

    // Calculate element errors.
    info("Calculating error estimate and exact error."); 
    Adapt<double>* adaptivity = new Adapt<double>(Hermes::vector<Space<double> *>(&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<double> *>(&u_sln, &v_sln), 
                                                        Hermes::vector<Solution<double> *>(&u_ref_sln, &v_ref_sln), 
                                                        &err_est_rel) * 100;

    // Calculate exact error for each solution component and the total exact error.
    Hermes::vector<double> err_exact_rel;
    bool solutions_for_adapt = false;
    double err_exact_rel_total = adaptivity->calc_err_exact(Hermes::vector<Solution<double> *>(&u_sln, &v_sln), 
                                                            Hermes::vector<Solution<double> *>(&exact_u, &exact_v), 
                                                            &err_exact_rel, solutions_for_adapt) * 100;

    // Time measurement.
    cpu_time.tick();

    // Report results.
    info("ndof_coarse[0]: %d, ndof_fine[0]: %d",
         u_space.get_num_dofs(), u_ref_space->get_num_dofs());
    info("err_est_rel[0]: %g%%, err_exact_rel[0]: %g%%", err_est_rel[0]*100, err_exact_rel[0]*100);
    info("ndof_coarse[1]: %d, ndof_fine[1]: %d",
         v_space.get_num_dofs(), v_ref_space->get_num_dofs());
    info("err_est_rel[1]: %g%%, err_exact_rel[1]: %g%%", err_est_rel[1]*100, err_exact_rel[1]*100);
    info("ndof_coarse_total: %d, ndof_fine_total: %d",
         Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&u_space, &v_space)), 
         Space<double>::get_num_dofs(ref_spaces_const));
    info("err_est_rel_total: %g%%, err_est_exact_total: %g%%", err_est_rel_total, err_exact_rel_total);

    // Add entry to DOF and CPU convergence graphs.
    graph_dof_est.add_values(Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&u_space, &v_space)), 
                             err_est_rel_total);
    graph_dof_est.save("conv_dof_est.dat");
    graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel_total);
    graph_cpu_est.save("conv_cpu_est.dat");

    graph_dof_exact.add_values(Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&u_space, &v_space)), 
                               err_exact_rel_total);
    graph_dof_exact.save("conv_dof_exact.dat");
    graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact_rel_total);
    graph_cpu_exact.save("conv_cpu_exact.dat");

    // If err_est too large, adapt the mesh.
    if (err_est_rel_total < ERR_STOP) 
      done = true;
    else 
    {
      info("Adapting coarse mesh.");
      done = adaptivity->adapt(Hermes::vector<RefinementSelectors::Selector<double> *>(&selector, &selector), 
                               THRESHOLD, STRATEGY, MESH_REGULARITY);
    }
    if (Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&u_space, &v_space)) >= NDOF_STOP) done = true;

    // Clean up.
    delete adaptivity;
    for(unsigned int i = 0; i < ref_spaces->size(); i++)
      delete (*ref_spaces)[i]->get_mesh();
    delete ref_spaces;
    
    // Increase counter.
    as++;
  }
  while (done == false);

  verbose("Total running time: %g s", cpu_time.accumulated());

  // Wait for all views to be closed.
  Views::View::wait();
  return 0;
}
예제 #28
0
/**
 * This function performs the publisher role in this example.
 * @return 0 if a sample is successfully written, 1 otherwise.
 */
int publisher(int argc, char *argv[])
{
    int result = 0;
    try
    {
        /** A dds::domain::DomainParticipant is created for the default domain. */
        dds::domain::DomainParticipant dp(org::opensplice::domain::default_id());

        /** The Durability::Transient policy is specified as a dds::topic::qos::TopicQos
         * so that even if the subscriber does not join until after the sample is written
         * then the DDS will still retain the sample for it. The Reliability::Reliable
         * policy is also specified to guarantee delivery and a policy::Deadline() of 1 second is
         * used to trigger the ExampleDataReaderListener::on_request_deadline_missed method
         * after no message  has been received for that duration. */
        dds::topic::qos::TopicQos topicQos
             = dp.default_topic_qos()
                << dds::core::policy::Durability::Transient()
                << dds::core::policy::Reliability::Reliable()
                << dds::core::policy::Deadline(dds::core::Duration(1, 0));

        /** These tailored QoS are made the new participant default */
        dp.default_topic_qos(topicQos);

        /** A dds::topic::Topic is created for our sample type on the domain participant. */
        dds::topic::Topic<ListenerData::Msg> topic(dp, "ListenerData_Msg", topicQos);

        /** A dds::pub::Publisher is created on the domain participant. */
        std::string name = "Listener example";
        dds::pub::qos::PublisherQos pubQos
            = dp.default_publisher_qos()
                << dds::core::policy::Partition(name);
        dds::pub::Publisher pub(dp, pubQos);

        /** The dds::pub::qos::DataWriterQos is derived from the topic qos and the
         * WriterDataLifecycle::ManuallyDisposeUnregisteredInstances policy is
         * specified as an addition. This is so the publisher can optionally be run (and
         * exit) before the subscriber. It prevents the middleware default 'clean up' of
         * the topic instance after the writer deletion, this deletion implicitly performs
         * DataWriter::unregister_instance */
        dds::pub::qos::DataWriterQos dwqos = topic.qos();
        dwqos << dds::core::policy::WriterDataLifecycle::ManuallyDisposeUnregisteredInstances();

        /** A dds::pub::DataWriter is created on the Publisher & Topic with the modififed Qos. */
        dds::pub::DataWriter<ListenerData::Msg> dw(pub, topic, dwqos);

        /** A sample is created on the stack and then written. */
        ListenerData::Msg msgInstance(1, "Hello World");
        dw << msgInstance;

        std::cout << "=== [Publisher] written a message containing :" << std::endl;
        std::cout << "    userID  : " << msgInstance.userID() << std::endl;
        std::cout << "    Message : \"" << msgInstance.message() << "\"" << std::endl;

        /* A short sleep ensures time is allowed for the sample to be written to the network.
        If the example is running in *Single Process Mode* exiting immediately might
        otherwise shutdown the domain services before this could occur */
        exampleSleepMilliseconds(1500);
    }
    catch (const dds::core::Exception& e)
    {
        std::cerr << "ERROR: Exception: " << e.what() << std::endl;
        result = 1;
    }

    return result;
}
예제 #29
0
int main(int argc, char **args)
{
	int res = ERR_SUCCESS;

#ifdef WITH_PETSC
	PetscInitialize(&argc, &args, (char *) PETSC_NULL, PETSC_NULL);
#endif

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

	printf("* Loading mesh '%s'\n", args[1]);
	Mesh mesh1;
	H3DReader mesh_loader;
	if (!mesh_loader.load(args[1], &mesh1)) error("Loading mesh file '%s'\n", args[1]);

#if defined RHS2

	Ord3 order(P_INIT_X, P_INIT_Y, P_INIT_Z);
	printf("  - Setting uniform order to (%d, %d, %d)\n", order.x, order.y, order.z);
	
	// Create an H1 space with default shapeset.
	printf("* Setting the space up\n");
	H1Space space(&mesh1, bc_types, essential_bc_values, order);

	int ndofs = space.assign_dofs();
	printf("  - Number of DOFs: %d\n", ndofs);

	printf("* Calculating a solution\n");

	// duplicate the mesh
	Mesh mesh2;
	mesh2.copy(mesh1);
	// do some changes
	mesh2.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
	mesh2.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);

	Solution fsln(&mesh2);
	fsln.set_const(-6.0);
#else
	// duplicate the mesh
	Mesh mesh2;
	mesh2.copy(mesh1);

	Mesh mesh3;
	mesh3.copy(mesh1);

	// change meshes
	mesh1.refine_all_elements(H3D_REFT_HEX_X);
	mesh2.refine_all_elements(H3D_REFT_HEX_Y);
	mesh3.refine_all_elements(H3D_REFT_HEX_Z);

	printf("* Setup spaces\n");
	Ord3 o1(2, 2, 2);
	printf("  - Setting uniform order to (%d, %d, %d)\n", o1.x, o1.y, o1.z);
	H1Space space1(&mesh1, bc_types_1, essential_bc_values_1, o1);

	Ord3 o2(2, 2, 2);
	printf("  - Setting uniform order to (%d, %d, %d)\n", o2.x, o2.y, o2.z);
	H1Space space2(&mesh2, bc_types_2, essential_bc_values_2, o2);

	Ord3 o3(1, 1, 1);
	printf("  - Setting uniform order to (%d, %d, %d)\n", o3.x, o3.y, o3.z);
	H1Space space3(&mesh3, bc_types_3, essential_bc_values_3, o3);

	int ndofs = 0;
	ndofs += space1.assign_dofs();
	ndofs += space2.assign_dofs(ndofs);
	ndofs += space3.assign_dofs(ndofs);
	printf("  - Number of DOFs: %d\n", ndofs);
#endif

#if defined WITH_UMFPACK
	MatrixSolverType matrix_solver = SOLVER_UMFPACK; 
#elif defined WITH_PETSC
	MatrixSolverType matrix_solver = SOLVER_PETSC; 
#elif defined WITH_MUMPS
	MatrixSolverType matrix_solver = SOLVER_MUMPS; 
#endif

#ifdef RHS2
	WeakForm wf;
	wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<Ord, Ord>, HERMES_SYM);
	wf.add_vector_form(linear_form<double, scalar>, linear_form<Ord, Ord>, HERMES_ANY_INT, &fsln);

	// Initialize discrete problem.
	bool is_linear = true;
	DiscreteProblem dp(&wf, &space, is_linear);
#elif defined SYS3
	WeakForm wf(3);
	wf.add_matrix_form(0, 0, biform_1_1<double, scalar>, biform_1_1<Ord, Ord>, HERMES_SYM);
	wf.add_matrix_form(0, 1, biform_1_2<double, scalar>, biform_1_2<Ord, Ord>, HERMES_NONSYM);
	wf.add_vector_form(0, liform_1<double, scalar>, liform_1<Ord, Ord>);

	wf.add_matrix_form(1, 1, biform_2_2<double, scalar>, biform_2_2<Ord, Ord>, HERMES_SYM);
	wf.add_matrix_form(1, 2, biform_2_3<double, scalar>, biform_2_3<Ord, Ord>, HERMES_NONSYM);
	wf.add_vector_form(1, liform_2<double, scalar>, liform_2<Ord, Ord>);

	wf.add_matrix_form(2, 2, biform_3_3<double, scalar>, biform_3_3<Ord, Ord>, HERMES_SYM);

	// Initialize discrete problem.
	bool is_linear = true;
	DiscreteProblem dp(&wf, Hermes::vector<Space *>(&space1, &space2, &space3), is_linear);
#endif
	// Time measurement.
	TimePeriod cpu_time;
	cpu_time.tick();
  
	// 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 the preconditioner in the case of SOLVER_AZTECOO.
	if (matrix_solver == SOLVER_AZTECOO) 
	{
		((AztecOOSolver*) solver)->set_solver(iterative_method);
		((AztecOOSolver*) solver)->set_precond(preconditioner);
		// Using default iteration parameters (see solver/aztecoo.h).
	}

	// Assemble stiffness matrix and load vector.
	dp.assemble(matrix, rhs);

	// Solve the linear system. If successful, obtain the solution.
	info("Solving the linear problem.");
	bool solved = solver->solve();

	// Time measurement.
	cpu_time.tick();
	// Print timing information.
	info("Solution and mesh with polynomial orders saved. Total running time: %g s", cpu_time.accumulated());

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

	if (solved) {
#ifdef RHS2
		// Solve the linear system. If successful, obtain the solution.
		info("Solving the linear problem.");
                Solution sln(&mesh1);
		Solution::vector_to_solution(solver->get_solution(), &space, &sln);

		// Set exact solution.
		ExactSolution ex_sln(&mesh1, exact_solution);

		// Norm.
		double h1_sln_norm = h1_norm(&sln);
		double h1_err_norm = h1_error(&sln, &ex_sln);
		printf("  - H1 solution norm:   % le\n", h1_sln_norm);
		printf("  - H1 error norm:      % le\n", h1_err_norm);

		double l2_sln_norm = l2_norm(&sln);
		double l2_err_norm = l2_error(&sln, &ex_sln);
		printf("  - L2 solution norm:   % le\n", l2_sln_norm);
		printf("  - L2 error norm:      % le\n", l2_err_norm);

		if (h1_err_norm > EPS || l2_err_norm > EPS) {
			// Calculated solution is not enough precise.
			res = ERR_FAILURE;
		}
#elif defined SYS3
		// Solution 1.
		Solution sln1(&mesh1);
		Solution sln2(&mesh2);
		Solution sln3(&mesh3);

		Solution::vector_to_solution(solver->get_solution(), &space1, &sln1);
		Solution::vector_to_solution(solver->get_solution(), &space2, &sln2);
		Solution::vector_to_solution(solver->get_solution(), &space3, &sln3);

		ExactSolution esln1(&mesh1, exact_sln_fn_1);
		ExactSolution esln2(&mesh2, exact_sln_fn_2);
		ExactSolution esln3(&mesh3, exact_sln_fn_3);

		// Norm.
		double h1_err_norm1 = h1_error(&sln1, &esln1);
		double h1_err_norm2 = h1_error(&sln2, &esln2);
		double h1_err_norm3 = h1_error(&sln3, &esln3);

		double l2_err_norm1 = l2_error(&sln1, &esln1);
		double l2_err_norm2 = l2_error(&sln2, &esln2);
		double l2_err_norm3 = l2_error(&sln3, &esln3);

		printf("  - H1 error norm:      % le\n", h1_err_norm1);
		printf("  - L2 error norm:      % le\n", l2_err_norm1);
		if (h1_err_norm1 > EPS || l2_err_norm1 > EPS) {
			// Calculated solution is not enough precise.
			res = ERR_FAILURE;
		}

		printf("  - H1 error norm:      % le\n", h1_err_norm2);
		printf("  - L2 error norm:      % le\n", l2_err_norm2);
		if (h1_err_norm2 > EPS || l2_err_norm2 > EPS) {
			// Calculated solution is not enough precise.
			res = ERR_FAILURE;
		}

		printf("  - H1 error norm:      % le\n", h1_err_norm3);
		printf("  - L2 error norm:      % le\n", l2_err_norm3);
		if (h1_err_norm3 > EPS || l2_err_norm3 > EPS) {
			// Calculated solution is not enough precise.
			res = ERR_FAILURE;
		}
#endif

#ifdef RHS2
		out_fn_vtk(&sln, "solution");
#elif defined SYS3
		out_fn_vtk(&sln1, "sln1");
		out_fn_vtk(&sln2, "sln2");
		out_fn_vtk(&sln3, "sln3");
#endif
	}
	else
		res = ERR_FAILURE;

	// Print timing information.
	info("Solution and mesh with polynomial orders saved. Total running time: %g s", sln_time.accumulated());

	// Clean up.
	delete matrix;
	delete rhs;
	delete solver;

	return res;
}
예제 #30
0
int main(int argc, char* argv[])
{
    // Load the mesh.
    Mesh mesh;
    H2DReader mloader;
    mloader.load("domain.mesh", &mesh);

    // Perform uniform mesh refinement.
    for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(2); // 2 is for vertical split.

    // Initialize boundary conditions
    DefaultEssentialBCConst bc1(BDY_PERFECT, 0.0);
    EssentialBCNonConst bc2(BDY_LEFT);
    EssentialBCs bcs(Hermes::vector<EssentialBoundaryCondition *>(&bc1, &bc2));

    // Create an H1 space with default shapeset.
    H1Space e_r_space(&mesh, &bcs, P_INIT);
    H1Space e_i_space(&mesh, &bcs, P_INIT);
    int ndof = Space::get_num_dofs(&e_r_space);
    info("ndof = %d", ndof);

    // Initialize the weak formulation
    // Weak forms for real and imaginary parts

    // Initialize the weak formulation.
    WeakFormHelmholtz wf(eps, mu, omega, sigma, beta, E0, h);

    // Initialize the FE problem.
    bool is_linear = true;
    DiscreteProblem dp(&wf, Hermes::vector<Space *>(&e_r_space, &e_i_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 the solutions.
    Solution e_r_sln, e_i_sln;

    // Assemble the stiffness matrix and right-hand side vector.
    info("Assembling the stiffness matrix and right-hand side vector.");
    dp.assemble(matrix, rhs);

    // Solve the linear system and if successful, obtain the solutions.
    info("Solving the matrix problem.");
    if(solver->solve())
        Solution::vector_to_solutions(solver->get_solution(),
                                      Hermes::vector<Space *>(&e_r_space, &e_i_space),
                                      Hermes::vector<Solution *>(&e_r_sln, &e_i_sln));
    else
        error ("Matrix solver failed.\n");

    // Visualize the solution.
    ScalarView viewEr("Er [V/m]", new WinGeom(0, 0, 800, 400));
    viewEr.show(&e_r_sln);
    // viewEr.save_screenshot("real_part.bmp");

    ScalarView viewEi("Ei [V/m]", new WinGeom(0, 450, 800, 400));
    viewEi.show(&e_i_sln);
    // viewEi.save_screenshot("imaginary_part.bmp");

    // Wait for the view to be closed.
    View::wait();

    // Clean up.
    delete solver;
    delete matrix;
    delete rhs;

    return 0;
}