Example #1
0
  void test_multiple_meshes_interface_quadrature()
  {
    // // These three meshes are ok
    // UnitSquareMesh mesh_0(1, 1);
    // RectangleMesh mesh_1(Point(0.1, 0.1), Point(0.9, 0.9), 1, 1);
    // RectangleMesh mesh_2(Point(0.2, 0.2), Point(0.8, 0.8), 1, 1);
    // double exact_volume = 4*(0.9-0.1); // mesh0 and mesh1
    // exact_volume += 4*(0.8-0.2); // mesh1 and mesh2

    // UnitCubeMesh mesh_0(1, 2, 3);
    // BoxMesh mesh_1(Point(0.1, 0.1, 0.1),    Point(0.9, 0.9, 0.9),  2,3,4); //2, 3, 4);
    // BoxMesh mesh_2(Point(-0.1, -0.1, -0.1), Point(0.7, 0.7, 0.7),  4, 3, 2);
    // BoxMesh mesh_3(Point(0.51, 0.51, 0.51), Point( 0.7, 0.7, 0.7), 1, 1, 1); //4, 3, 2);
    // BoxMesh mesh_4(Point(0.3, 0.3, 0.3),    Point(0.7, 0.7, 0.7),  1, 1, 1);
    // double exact_volume = 0.8*0.8*6; // for mesh_0 and mesh_1
    // exact_volume += 0.4*0.4*6; // for mesh_1 and mesh_4

    UnitCubeMesh mesh_0(1, 1, 1);
    BoxMesh mesh_1(Point(0.1, 0.1, 0.1), Point(0.9, 0.9, 0.9), 1, 1, 1);
    BoxMesh mesh_2(Point(0.2, 0.2, 0.2), Point(0.8, 0.8, 0.8), 1, 1, 1);
    // BoxMesh mesh_3(Point(0.51, 0.51, 0.51), Point(0.7, 0.7, 0.7), 1, 1, 1); //4, 3, 2);
    // BoxMesh mesh_4(Point(0.3, 0.3, 0.3),    Point(0.7, 0.7, 0.7), 1, 1, 1);
    double exact_volume = (0.9 - 0.1)*(0.9 - 0.1)*6; // for mesh_0 and mesh_1
    exact_volume += (0.8 - 0.2)*(0.8 - 0.2)*6; // mesh_1 and mesh_2

    // UnitCubeMesh mesh_0(1, 1, 1);
    // MeshEditor editor;
    // Mesh mesh_1;
    // editor.open(mesh_1, 3, 3);
    // editor.init_vertices(4);
    // editor.init_cells(1);
    // editor.add_vertex(0, Point(0.7, 0.1, -0.1));
    // editor.add_vertex(1, Point(0.7, 0.3, -0.1));
    // editor.add_vertex(2, Point(0.5, 0.1, -0.1));
    // editor.add_vertex(3, Point(0.7, 0.1, 0.1));
    // editor.add_cell(0, 0,1,2,3);
    // editor.close();

    // Mesh mesh_2;
    // editor.open(mesh_2, 3,3);
    // editor.init_vertices(4);
    // editor.init_cells(1);
    // editor.add_vertex(0, Point(0.7, 0.1, -0.2));
    // editor.add_vertex(1, Point(0.7, 0.3, -0.2));
    // editor.add_vertex(2, Point(0.5, 0.1, -0.2));
    // editor.add_vertex(3, Point(0.7, 0.1, 0.05));
    // editor.add_cell(0, 0,1,2,3);
    // editor.close();

    //double exact_volume = 0.8*0.8*6; // for mesh_0 and mesh_1
    //exact_volume += 0.4*0.4*6; // for mesh_1 and mesh_4

    // MeshEditor editor;
    // Mesh mesh_0;
    // editor.open(mesh_0, 2, 2);
    // editor.init_vertices(3);
    // editor.init_cells(1);
    // editor.add_vertex(0, Point(0.,0.));
    // editor.add_vertex(1, Point(2.,0.));
    // editor.add_vertex(2, Point(1.,2.));
    // editor.add_cell(0, 0,1,2);
    // editor.close();

    // Mesh mesh_1;
    // editor.open(mesh_1, 2, 2);
    // editor.init_vertices(3);
    // editor.init_cells(1);
    // editor.add_vertex(0, Point(0.,-0.5));
    // editor.add_vertex(1, Point(2.,-0.5));
    // editor.add_vertex(2, Point(1.,1.5));
    // editor.add_cell(0, 0,1,2);
    // editor.close();

    // Mesh mesh_2;
    // editor.open(mesh_2, 2, 2);
    // editor.init_vertices(3);
    // editor.init_cells(1);
    // editor.add_vertex(0, Point(0.,-1.));
    // editor.add_vertex(1, Point(2.,-1.));
    // editor.add_vertex(2, Point(1.,1.));
    // editor.add_cell(0, 0,1,2);
    // editor.close();

    // double exact_volume = 2*std::sqrt(0.75*0.75 + 1.5*1.5); // mesh_0 and mesh_1
    // exact_volume += 2*std::sqrt(0.5*0.5 + 1*1); // mesh_0 and mesh_2
    // exact_volume += 2*std::sqrt(0.75*0.75 + 1.5*1.5); // mesh_1and mesh_2
    // double volume = 0;

    // // These three meshes are ok.
    // MeshEditor editor;
    // Mesh mesh_0;
    // editor.open(mesh_0, 2, 2);
    // editor.init_vertices(3);
    // editor.init_cells(1);
    // editor.add_vertex(0, Point(0.,0.));
    // editor.add_vertex(1, Point(2.,0.));
    // editor.add_vertex(2, Point(1.,2.));
    // editor.add_cell(0, 0,1,2);
    // editor.close();

    // Mesh mesh_1;
    // editor.open(mesh_1, 2, 2);
    // editor.init_vertices(3);
    // editor.init_cells(1);
    // editor.add_vertex(0, Point(1.5,-2.));
    // editor.add_vertex(1, Point(4.,0.));
    // editor.add_vertex(2, Point(1.5,2));
    // editor.add_cell(0, 0,1,2);
    // editor.close();

    // Mesh mesh_2;
    // editor.open(mesh_2, 2, 2);
    // editor.init_vertices(3);
    // editor.init_cells(1);
    // editor.add_vertex(0, Point(3.,0.5));
    // editor.add_vertex(1, Point(-1.,0.5));
    // editor.add_vertex(2, Point(1.,-1.5));
    // editor.add_cell(0, 0,1,2);
    // editor.close();

    // double exact_volume = (1.5-0.25) + (1-0.5); // mesh_0, mesh_1 and mesh_2
    // exact_volume += (3-1.5) + std::sqrt(1.5*1.5 + 1.5*1.5); // mesh_1 and mesh_2

    File("mesh_0.xml") << mesh_0;
    File("mesh_1.xml") << mesh_1;
    File("mesh_2.xml") << mesh_2;

    // Build the multimesh
    MultiMesh multimesh;
    multimesh.add(mesh_0);
    multimesh.add(mesh_1);
    multimesh.add(mesh_2);
    //multimesh.add(mesh_3);
    //multimesh.add(mesh_4);
    multimesh.build();

    // Sum contribution from all parts
    std::cout << "\n\n Sum up\n\n";
    double volume = 0;
    for (std::size_t part = 0; part < multimesh.num_parts(); part++)
    {
      std::cout << "% part " << part << '\n';
      double part_volume = 0;

      const auto& quadrature_rules = multimesh.quadrature_rule_interface(part);

      // Get collision map
      const auto& cmap = multimesh.collision_map_cut_cells(part);
      for (auto it = cmap.begin(); it != cmap.end(); ++it)
      {
        const unsigned int cut_cell_index = it->first;

        // Iterate over cutting cells
        const auto& cutting_cells = it->second;
        for (auto jt = cutting_cells.begin(); jt != cutting_cells.end(); jt++)
        {
          //const std::size_t cutting_part = jt->first;
          //const std::size_t cutting_cell_index = jt->second;

          // Get quadrature rule for interface part defined by
          // intersection of the cut and cutting cells
          const std::size_t k = jt - cutting_cells.begin();
          dolfin_assert(k < quadrature_rules.at(cut_cell_index).size());
          const auto& qr = quadrature_rules.at(cut_cell_index)[k];

          for (std::size_t j = 0; j < qr.second.size(); ++j)
          {
            volume += qr.second[j];
            part_volume += qr.second[j];
          }

        }
      }

      std::cout<<"part volume " << part_volume<<std::endl;
    }

    std::cout << "exact volume " << exact_volume<<'\n'
              << "volume " << volume<<std::endl;
    CPPUNIT_ASSERT_DOUBLES_EQUAL(exact_volume, volume, DOLFIN_EPS_LARGE);
  }
Example #2
0
  void test_multiple_meshes_quadrature()
  {
    set_log_level(DEBUG);

    // Create multimesh from three triangle meshes of the unit square

    // Many meshes, but not more than three overlap => this works
    UnitCubeMesh mesh_0(11, 12, 13);
    BoxMesh mesh_1(Point(0.1, 0.1, 0.1),    Point(0.9, 0.9, 0.9),    13, 11, 12);
    BoxMesh mesh_2(Point(0.2, 0.2, 0.2),    Point(0.95, 0.95, 0.8),  11, 13, 11);
    BoxMesh mesh_3(Point(0.94, 0.01, 0.01), Point(0.98, 0.99, 0.99), 1, 11, 11);
    BoxMesh mesh_4(Point(0.01, 0.01, 0.01), Point(0.02, 0.02, 0.02), 1, 1, 1);

    // // Completely nested 2D: can't do no more than three meshes
    // UnitSquareMesh mesh_0(1, 1);
    // RectangleMesh mesh_1(Point(0.1, 0.1), Point(0.9, 0.9, 1, 1);
    // RectangleMesh mesh_2(Point(0.2, 0.2), Point(0.8, 0.8, 1, 1);
    // RectangleMesh mesh_3(Point(0.3, 0.3), Point(0.7, 0.7, 1, 1);
    // RectangleMesh mesh_4(Point(0.4, 0.4), Point(0.6, 0.6, 1, 1);

    // // Completely nested 3D: can't do no more than three meshes
    // UnitCubeMesh mesh_0(2, 3, 4);
    // BoxMesh mesh_1(Point(0.1, 0.1, 0.1),    Point(0.9, 0.9, 0.9),    4, 3, 2);
    // BoxMesh mesh_2(Point(0.2, 0.2, 0.2),    Point(0.8, 0.8, 0.8),    3, 4, 3);
    // BoxMesh mesh_3(Point(0.8, 0.01, 0.01),  Point(0.9, 0.99, 0.99),  4, 2, 3);
    // BoxMesh mesh_4(Point(0.01, 0.01, 0.01), Point(0.02, 0.02, 0.02), 1, 1, 1);

    // Build the multimesh
    MultiMesh multimesh;
    multimesh.add(mesh_0);
    multimesh.add(mesh_1);
    multimesh.add(mesh_2);
    multimesh.add(mesh_3);
    multimesh.add(mesh_4);
    multimesh.build();

    // Exact volume is known
    const double exact_volume = 1;
    double volume = 0;

    // Sum contribution from all parts
    std::cout << "Sum contributions\n";
    for (std::size_t part = 0; part < multimesh.num_parts(); part++)
    {
      std::cout << "% part " << part;
      double part_volume = 0;

      // Uncut cell volume given by function volume
      const auto uncut_cells = multimesh.uncut_cells(part);
      for (auto it = uncut_cells.begin(); it != uncut_cells.end(); ++it)
      {
        const Cell cell(*multimesh.part(part), *it);
        volume += cell.volume();
        part_volume += cell.volume();
      }

      std::cout << "\t uncut volume "<< part_volume<<' ';

      // Cut cell volume given by quadrature rule
      const auto& cut_cells = multimesh.cut_cells(part);
      for (auto it = cut_cells.begin(); it != cut_cells.end(); ++it)
      {
        const auto& qr = multimesh.quadrature_rule_cut_cell(part, *it);
        for (std::size_t i = 0; i < qr.second.size(); ++i)
        {
          volume += qr.second[i];
          part_volume += qr.second[i];
        }
      }
      std::cout << "\ttotal volume " << part_volume<< std::endl;
    }

    std::cout<<std::setprecision(13) << "exact volume " << exact_volume<<'\n'
              << "volume " << volume<<std::endl;
    CPPUNIT_ASSERT_DOUBLES_EQUAL(exact_volume, volume, DOLFIN_EPS_LARGE);
  }
Example #3
0
// Compute solution for given mesh configuration
void solve_poisson(double t,
                   double x1, double y1,
                   double x2, double y2,
                   bool plot_solution,
                   File& u0_file, File& u1_file, File& u2_file)
{
  // Create meshes
  double r = 0.5;
  RectangleMesh mesh_0(Point(-r, -r), Point(r, r), 16, 16);
  RectangleMesh mesh_1(Point(x1 - r, y1 - r), Point(x1 + r, y1 + r), 8, 8);
  RectangleMesh mesh_2(Point(x2 - r, y2 - r), Point(x2 + r, y2 + r), 8, 8);
  mesh_1.rotate(70*t);
  mesh_2.rotate(-70*t);

  // Build multimesh
  MultiMesh multimesh;
  multimesh.add(mesh_0);
  multimesh.add(mesh_1);
  multimesh.add(mesh_2);
  multimesh.build();

  // Create function space
  MultiMeshPoisson::MultiMeshFunctionSpace V(multimesh);

  // Create forms
  MultiMeshPoisson::MultiMeshBilinearForm a(V, V);
  MultiMeshPoisson::MultiMeshLinearForm L(V);

  // Attach coefficients
  Source f;
  L.f = f;

  // Assemble linear system
  Matrix A;
  Vector b;
  assemble_multimesh(A, a);
  assemble_multimesh(b, L);

  // Apply boundary condition
  Constant zero(0);
  DirichletBoundary boundary;
  MultiMeshDirichletBC bc(V, zero, boundary);
  bc.apply(A, b);

  // Compute solution
  MultiMeshFunction u(V);
  solve(A, *u.vector(), b);

  // Save to file
  u0_file << *u.part(0);
  u1_file << *u.part(1);
  u2_file << *u.part(2);

  // Plot solution (last time)
  if (plot_solution)
  {
    plot(V.multimesh());
    plot(u.part(0), "u_0");
    plot(u.part(1), "u_1");
    plot(u.part(2), "u_2");
    interactive();
  }
}