void test_assembly()
{
// Set some parameters
parameters["reorder_dofs_serial"] = false;
// Some parameters
const std::size_t N = 4;
const std::size_t n = 2;
const double b1 = 1.0;
const double b2 = 1.0;
// Right-hand side
class Source : public Expression
{
public:
Source() : Expression(2) {}
void eval(Array<double>& values, const Array<double>& x) const
{
values[0] = 2*DOLFIN_PI*sin(2*DOLFIN_PI*x[1])*
(cos(2*DOLFIN_PI*x[0]) -
2*DOLFIN_PI*DOLFIN_PI*cos(2*DOLFIN_PI*x[0]) +
DOLFIN_PI*DOLFIN_PI);
values[1] = 2*DOLFIN_PI*sin(2*DOLFIN_PI*x[0])*
(cos(2*DOLFIN_PI*x[1]) +
2*DOLFIN_PI*DOLFIN_PI*cos(2*DOLFIN_PI*x[1]) -
DOLFIN_PI*DOLFIN_PI);
}
} source;
// Subdomain for no-slip boundary
class DirichletBoundary : public SubDomain
{
bool inside(const Array<double>& x, bool on_boundary) const
{
return on_boundary and
(near(x[0], 0) || near(x[0], 1) ||
near(x[1], 0) || near(x[1], 1));
}
} dirichlet_boundary;
// Create meshes
UnitSquareMesh mesh_0(N, N);
const double c = 0.123123;
RectangleMesh mesh_1(Point(0.5 - c, 0.5 - c), Point(0.5 + c, 0.5 + c), n, n);
mesh_1.rotate(37, 2);
// Create function spaces
MultiMeshStokes2D::FunctionSpace W0(mesh_0);
MultiMeshStokes2D::FunctionSpace W1(mesh_1);
// Create forms
MultiMeshStokes2D::BilinearForm a0(W0, W0);
MultiMeshStokes2D::BilinearForm a1(W1, W1);
MultiMeshStokes2D::LinearForm L0(W0);
MultiMeshStokes2D::LinearForm L1(W1);
MultiMeshStokes2D::Functional M0(mesh_0);
MultiMeshStokes2D::Functional M1(mesh_1);
// Build multimesh function space
MultiMeshFunctionSpace W;
W.parameters("multimesh")["quadrature_order"] = 3;
W.add(W0);
W.add(W1);
W.build();
// Create constants
Constant beta_1(b1);
Constant beta_2(b2);
// Create solution function
MultiMeshFunction w(W);
// Set coefficients
a0.w0 = beta_1;
a1.w0 = beta_1;
a0.w1 = beta_2;
a1.w1 = beta_2;
L0.w0 = source;
L1.w0 = source;
L0.w1 = beta_2;
L1.w1 = beta_2;
M0.w0 = *w.part(0);
M1.w0 = *w.part(1);
// Build multimesh forms
MultiMeshForm a(W, W);
MultiMeshForm L(W);
MultiMeshForm M(W);
a.add(a0);
a.add(a1);
L.add(L0);
L.add(L1);
M.add(M0);
M.add(M1);
a.build();
L.build();
M.build();
// Create subspaces for boundary conditions
MultiMeshSubSpace V(W, 0);
MultiMeshSubSpace Q(W, 1);
// Create boundary condition
Constant zero(0, 0);
MultiMeshDirichletBC bc(V, zero, dirichlet_boundary);
// Assemble system matrix and right-hand side
Matrix A;
Vector b;
MultiMeshAssembler assembler;
assembler.assemble(A, a);
assembler.assemble(b, L);
// Apply boundary condition
bc.apply(A, b);
// Compute solutipon
solve(A, *w.vector(), b);
// Compute squared L2 norm of solution
Scalar m;
assembler.assemble(m, M);
// Check value
CPPUNIT_ASSERT_DOUBLES_EQUAL(2.217133856286212, m.get_scalar_value(), 1e-12);
}
// Compute solution for given mesh configuration
void solve(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);
// Create function spaces
MultiMeshPoisson::FunctionSpace V0(mesh_0);
MultiMeshPoisson::FunctionSpace V1(mesh_1);
MultiMeshPoisson::FunctionSpace V2(mesh_2);
// FIXME: Some of this stuff may be wrapped or automated later to
// avoid needing to explicitly call add() and build()
// Create forms
MultiMeshPoisson::BilinearForm a0(V0, V0);
MultiMeshPoisson::BilinearForm a1(V1, V1);
MultiMeshPoisson::BilinearForm a2(V2, V2);
MultiMeshPoisson::LinearForm L0(V0);
MultiMeshPoisson::LinearForm L1(V1);
MultiMeshPoisson::LinearForm L2(V2);
// Build multimesh function space
MultiMeshFunctionSpace V;
V.parameters("multimesh")["quadrature_order"] = 2;
V.add(V0);
V.add(V1);
V.add(V2);
V.build();
// Set coefficients
Source f;
L0.f = f;
L1.f = f;
L2.f = f;
// Build multimesh forms
MultiMeshForm a(V, V);
MultiMeshForm L(V);
a.add(a0);
a.add(a1);
a.add(a2);
L.add(L0);
L.add(L1);
L.add(L2);
a.build();
L.build();
// Create boundary condition
Constant zero(0);
DirichletBoundary boundary;
MultiMeshDirichletBC bc(V, zero, boundary);
// Assemble linear system
Matrix A;
Vector b;
MultiMeshAssembler assembler;
assembler.assemble(A, a);
assembler.assemble(b, L);
// Apply boundary condition
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();
}
}