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)
class TestNodality(TestCase):
"""Test for Element.doflocs."""
elems = [
ElementLineP0(),
ElementLineP1(),
ElementLineP2(),
ElementLinePp(1),
ElementLinePp(3),
ElementLineMini(),
ElementTriP0(),
ElementTriP1(),
ElementTriP2(),
ElementTriP3(),
ElementTriP4(),
ElementTriMini(),
ElementQuad0(),
ElementQuad1(),
ElementQuad2(),
ElementQuadS2(),
ElementQuadP(1),
ElementQuadP(3),
ElementTetP0(),
ElementTetP1(),
ElementTetP2(),
ElementTetMini(),
ElementHex1(),
ElementHexS2(),
ElementHex2(),
ElementTetCR(),
ElementTetCCR(),
ElementTriCR(),
ElementTriCCR(),
ElementWedge1(),
]
def runTest(self):
for e in self.elems:
N = e.doflocs.shape[0]
Ih = np.zeros((N, N))
for itr in range(N):
Ih[itr] = e.lbasis(e.doflocs.T, itr)[0]
# Remove nan-rows: test nodality only on non-nan doflocs.
#
# Some elements, such as ElementTriMini might have a combination
# of nodal dofs and non-nodal dofs.
#
# Nodal dof is defined so that there exists a point where the
# corresponding basis function is one, and other basis functions
# are zero. Non-nodal dof does not satisfy this property.
ix = np.isnan(np.sum(Ih, axis=1))
Nnan = np.sum(ix)
ixs = np.nonzero(~ix)[0]
Ih = Ih[ixs].T[ixs].T
assert_allclose(Ih,
np.eye(N - Nnan),
atol=1e-13,
err_msg="{}".format(type(e)))
def create_basis(self, m):
e = ElementTriRT0()
e0 = ElementTriP0()
return (InteriorBasis(m, e,
intorder=2), InteriorBasis(m, e0, intorder=2))
def create_basis(self, m):
e = ElementTriBDM1()
e0 = ElementTriP0()
return (CellBasis(m, e, intorder=4), CellBasis(m, e0, intorder=4))
np.random.seed(0)
X = np.random.rand(m.p.shape[0], int(npoints))
basis = CellBasis(m, e)
y = projection(lambda x: x[0] + x[1], basis)
assert_allclose(basis.probes(X) @ y, basis.interpolator(y)(X))
assert_allclose(basis.probes(X) @ y, X[0] + X[1])
@pytest.mark.parametrize(
"mtype,e1,e2,flat",
[
(MeshTri, ElementTriP1(), ElementTriP0(), False),
(MeshTri, ElementTriP1(), ElementTriP1(), False),
(MeshTri, ElementTriP2(), ElementTriP1(), False),
(MeshTri, ElementTriP2(), ElementTriP2(), False),
(MeshTri, ElementTriP1(), ElementTriP0(), True),
(MeshTri, ElementTriP1(), ElementTriP1(), True),
(MeshTri, ElementTriP2(), ElementTriP1(), True),
(MeshTri, ElementTriP2(), ElementTriP2(), True),
(MeshTri, ElementTriP2(), None, False),
(MeshTri, ElementTriP2(), None, True),
(MeshQuad, ElementQuad1(), ElementQuad0(), False),
(MeshQuad, ElementQuad1(), ElementQuad1(), False),
(MeshQuad, ElementQuad2(), ElementQuad2(), False),
(MeshQuad, ElementQuad1(), ElementQuad0(), True),
(MeshQuad, ElementQuad1(), ElementQuad1(), True),
(MeshQuad, ElementQuad2(), ElementQuad2(), True),
class TestDerivatives(TestCase):
"""Test values of derivatives."""
elems = [
ElementLineP0(),
ElementLineP1(),
ElementLineP2(),
ElementLineMini(),
ElementTriP0(),
ElementTriP1(),
ElementTriP2(),
ElementTriP3(),
ElementTriP4(),
ElementTriMini(),
ElementQuad0(),
ElementQuad1(),
ElementQuad2(),
ElementQuadS2(),
ElementTetP0(),
ElementTetP1(),
ElementTetP2(),
ElementTetMini(),
ElementHex1(),
ElementHexS2(),
ElementHex2(),
ElementTriCR(),
ElementTriCCR(),
ElementTetCR(),
ElementTetCCR(),
ElementWedge1(),
]
def runTest(self):
for elem in self.elems:
eps = 1e-6
for base in [0., .3, .6, .9]:
if elem.dim == 1:
y = np.array([[base, base + eps]])
elif elem.dim == 2:
y = np.array([[base, base + eps, base, base],
[base, base, base, base + eps]])
elif elem.dim == 3:
y = np.array([[base, base + eps, base, base, base, base],
[base, base, base, base + eps, base, base],
[base, base, base, base, base, base + eps]])
i = 0
while True:
try:
out = elem.lbasis(y, i)
except ValueError:
break
diff = (out[0][1] - out[0][0]) / eps
errmsg = 'x-derivative for {}th bfun failed for {}'
self.assertAlmostEqual(diff,
out[1][0][0],
delta=1e-3,
msg=errmsg.format(i, elem))
if elem.dim > 1:
diff = (out[0][3] - out[0][2]) / eps
errmsg = 'y-derivative for {}th bfun failed for {}'
self.assertAlmostEqual(diff,
out[1][1][3],
delta=1e-3,
msg=errmsg.format(i, elem))
if elem.dim == 3:
diff = (out[0][5] - out[0][4]) / eps
errmsg = 'z-derivative for {}th bfun failed for {}'
self.assertAlmostEqual(diff,
out[1][2][4],
delta=1e-3,
msg=errmsg.format(i, elem))
i += 1
mesh_type = MeshLine
element_type = ElementLineP2
nrefs = 5
class TestIncompatibleMeshElement(TestCase):
def runTest(self):
with self.assertRaises(ValueError):
m = MeshTri()
e = ElementTetP2()
basis = InteriorBasis(m, e)
@pytest.mark.parametrize("mtype,e1,e2", [
(MeshTri, ElementTriP1(), ElementTriP0()),
(MeshTri, ElementTriP1(), ElementTriP1()),
(MeshTri, ElementTriP2(), ElementTriP1()),
(MeshTri, ElementTriP2(), ElementTriP2()),
(MeshTri, ElementTriP2(), None),
(MeshQuad, ElementQuad1(), ElementQuad0()),
(MeshQuad, ElementQuad1(), ElementQuad1()),
(MeshQuad, ElementQuad2(), ElementQuad2()),
(MeshTet, ElementTetP1(), ElementTetP0()),
(MeshTet, ElementTetP2(), ElementTetP2()),
(MeshHex, ElementHex1(), ElementHex0()),
(MeshHex, ElementHex1(), ElementHex1()),
(MeshHex, ElementHex2(), ElementHex2()),
])
def test_trace(mtype, e1, e2):
with self.assertRaises(ValueError):
m = MeshTri()
e = ElementTetP2()
basis = InteriorBasis(m, e)
@pytest.mark.parametrize("mtype,e1,e2", [
(MeshTri, ElementTriP1(), ElementLineP0()),
(MeshTri, ElementTriP1(), ElementLineP1()),
(MeshTri, ElementTriP2(), ElementLineP1()),
(MeshTri, ElementTriP2(), ElementLineP2()),
(MeshTri, ElementTriP2(), None),
(MeshQuad, ElementQuad1(), ElementLineP0()),
(MeshQuad, ElementQuad1(), ElementLineP1()),
(MeshQuad, ElementQuad2(), ElementLineP2()),
(MeshTet, ElementTetP1(), ElementTriP0()),
(MeshTet, ElementTetP2(), ElementTriP2()),
(MeshHex, ElementHex1(), ElementQuad0()),
(MeshHex, ElementHex1(), ElementQuad1()),
(MeshHex, ElementHex2(), ElementQuad2()),
])
def test_trace(mtype, e1, e2):
m = mtype().refined(3)
# use the boundary where last coordinate is zero
basis = FacetBasis(
m, e1, facets=m.facets_satisfying(lambda x: x[x.shape[0] - 1] == 0.0))
xfun = project(lambda x: x[0], basis_to=InteriorBasis(m, e1))
nbasis, y = basis.trace(xfun,
lambda p: p[0:(p.shape[0] - 1)],
