def test_subdomain_facet_assembly():
def subdomain(x):
return np.logical_and(
np.logical_and(x[0] > .25, x[0] < .75),
np.logical_and(x[1] > .25, x[1] < .75),
)
m, e = MeshTri().refined(4), ElementTriP2()
cbasis = CellBasis(m, e)
cbasis_p0 = cbasis.with_element(ElementTriP0())
sfbasis = FacetBasis(m, e, facets=m.facets_around(subdomain, flip=True))
sfbasis_p0 = sfbasis.with_element(ElementTriP0())
sigma = cbasis_p0.zeros() + 1
@BilinearForm
def laplace(u, v, w):
return dot(w.sigma * grad(u), grad(v))
A = laplace.assemble(cbasis, sigma=cbasis_p0.interpolate(sigma))
u0 = cbasis.zeros()
u0[cbasis.get_dofs(elements=subdomain)] = 1
u0_dofs = cbasis.get_dofs() + cbasis.get_dofs(elements=subdomain)
A, b = enforce(A, D=u0_dofs, x=u0)
u = solve(A, b)
@Functional
def measure_current(w):
return dot(w.n, w.sigma * grad(w.u))
meas = measure_current.assemble(sfbasis,
sigma=sfbasis_p0.interpolate(sigma),
u=sfbasis.interpolate(u))
assert_almost_equal(meas, 9.751915526759191)
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.get_dofs()))
exact = np.stack([(1 - source) * mesh.p, (1 - mesh.p) * source]).min(0)
assert_almost_equal(u[basis.nodal_dofs], exact)