def test_point_source(etype):
mesh = MeshLine1().refined()
basis = CellBasis(mesh, etype())
source = np.array([0.7])
u = solve(*condense(asm(laplace, basis), basis.point_source(source), D=basis.find_dofs()))
exact = np.stack([(1 - source) * mesh.p, (1 - mesh.p) * source]).min(0)
assert_almost_equal(u[basis.nodal_dofs], exact)
def runTest(self):
"""Solve Stokes problem, try splitting and other small things."""
m = MeshTri().refined()
m = m.refined(3).with_boundaries({
'up': lambda x: x[1] == 1.,
'rest': lambda x: x[1] != 1.,
})
e = ElementVectorH1(ElementTriP2()) * ElementTriP1()
basis = CellBasis(m, e)
@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, 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(P.shape[0] == m.nelements)
self.assertTrue((basis.doflocs[:, D['up'].all()][1] == 1.).all())
# test blocks splitting of forms while at it
C1 = asm(bilinf.block(1, 1), CellBasis(m, ElementTriP1()))
C2 = S[basis.nodal_dofs[-1]].T[basis.nodal_dofs[-1]].T
self.assertTrue(abs((C1 - C2).min()) < 1e-10)
self.assertTrue(abs((C1 - C2).max()) < 1e-10)
# test splitting ElementVector
(ux, uxbasis), (uy, uybasis) = u_basis.split(u)
assert_allclose(ux[uxbasis.nodal_dofs[0]], u[u_basis.nodal_dofs[0]])
assert_allclose(ux[uxbasis.facet_dofs[0]], u[u_basis.facet_dofs[0]])
assert_allclose(uy[uybasis.nodal_dofs[0]], u[u_basis.nodal_dofs[1]])
assert_allclose(uy[uybasis.facet_dofs[0]], u[u_basis.facet_dofs[1]])
def runTest(self):
m = self.mesh_type().refined(2)
basis = CellBasis(m, self.elem_type())
for fun in [
lambda x: x[0] == 0, lambda x: x[0] == 1, lambda x: x[1] == 0,
lambda x: x[1] == 1, lambda x: x[2] == 0, lambda x: x[2] == 1
]:
arr1 = basis.find_dofs({'kek':
m.facets_satisfying(fun)})['kek'].edge['u']
arr2 = basis.edge_dofs[:, m.edges_satisfying(fun)]
assert_allclose(arr1, arr2.flatten())
def runTest(self):
"""Solve Stokes problem, try splitting and other small things."""
m = MeshTri().refined()
m = m.refined(3).with_boundaries({
'up': lambda x: x[1] == 1.,
'rest': lambda x: x[1] != 1.,
})
e = ElementVectorH1(ElementTriP2()) * ElementTriP1()
basis = CellBasis(m, e)
@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, 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())