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);
}
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);
}
// 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();
}
}