def runTest(self): """Solve Stokes problem, try splitting and other small things.""" m = MeshTri() m.refine() m.define_boundary('centreline', lambda x: x[0] == .5, boundaries_only=False) m.refine(3) e = ElementVectorH1(ElementTriP2()) * ElementTriP1() m.define_boundary('up', lambda x: x[1] == 1.) m.define_boundary('rest', lambda x: x[1] != 1.) basis = InteriorBasis(m, e) self.assertEqual( basis.get_dofs(m.boundaries['centreline']).all().size, (2 + 1) * (2**(1 + 3) + 1) + 2 * 2**(1 + 3)) self.assertEqual(basis.find_dofs()['centreline'].all().size, (2 + 1) * (2**(1 + 3) + 1) + 2 * 2**(1 + 3)) @BilinearForm def bilinf(u, p, v, q, w): from skfem.helpers import grad, ddot, div return (ddot(grad(u), grad(v)) - div(u) * q - div(v) * p - 1e-2 * p * q) S = asm(bilinf, basis) D = basis.find_dofs(skip=['u^2']) x = basis.zeros() x[D['up'].all('u^1^1')] = .1 x = solve(*condense(S, basis.zeros(), x=x, D=D)) (u, u_basis), (p, p_basis) = basis.split(x) self.assertEqual(len(u), m.p.shape[1] * 2 + m.facets.shape[1] * 2) self.assertEqual(len(p), m.p.shape[1]) self.assertTrue(np.sum(p - x[basis.nodal_dofs[2]]) < 1e-8) U, P = basis.interpolate(x) self.assertTrue(isinstance(U.value, np.ndarray)) self.assertTrue(isinstance(P.value, np.ndarray)) self.assertTrue((basis.doflocs[:, D['up'].all()][1] == 1.).all())
def runTest(self): m = self.mesh().refined(4) basis = InteriorBasis(m, self.elem) boundary_basis = FacetBasis(m, self.elem) boundary_dofs = boundary_basis.get_dofs().flatten() def dirichlet(x): """return a harmonic function""" return ((x[0] + 1.j * x[1])**2).real u = basis.zeros() A = laplace.assemble(basis) u[boundary_dofs] = projection(dirichlet, boundary_basis, I=boundary_dofs) u = solve(*enforce(A, x=u, D=boundary_dofs)) @Functional def gradu(w): gradu = w['sol'].grad return dot(gradu, gradu) self.assertAlmostEqual( gradu.assemble(basis, sol=basis.interpolate(u)), 8 / 3, delta=1e-10, )
def test_dg_element(m, e, edg): edg = edg(e) @Functional def square(w): return w['random']**2 basis = InteriorBasis(m, e) basisdg = InteriorBasis(m, edg) assert_allclose( square.assemble(basis, random=basis.interpolate(basis.zeros() + 1)), square.assemble(basisdg, random=basisdg.interpolate(basisdg.zeros() + 1)), )