def runTest(self):
# Mesh.remove_elements
m = MeshTri()
m.refine()
M = m.remove_elements(np.array([0]))
self.assertEqual(M.t.shape[1], 7)
# Mesh.define_boundary
m.define_boundary('foo', lambda x: x[0] == 0.)
self.assertEqual(m.boundaries['foo'].size, 2)
# Mesh.define_boundary (internal)
m.define_boundary('bar',
lambda x: x[0] == 1. / 2,
boundaries_only=False)
self.assertEqual(m.boundaries['bar'].size, 2)
# Mesh.scale, Mesh.translate
m = MeshHex()
m.scale(0.5)
m.translate((0.5, 0.5, 0.5))
self.assertGreater(np.min(m.p), 0.4999)
# Mesh3D.facets_satisfying
self.assertEqual(len(m.facets_satisfying(lambda x: x[0] == 0.5)), 1)
def runTest(self):
m = MeshTri()
M = MeshTri()
M.translate((1.0, 0.0))
M.define_boundary('top', lambda x: x[1] == 1.0)
mesh = m + M
self.assertTrue(mesh.p.shape[1] == 6)
self.assertTrue(mesh.t.shape[1] == 4)
self.assertTrue(mesh.subdomains is None)
self.assertTrue('top' in mesh.boundaries)
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())