class TestPartitionofUnity(TestCase):
"""Test that elements form a partition of unity."""
elems = [
ElementLineP1(),
ElementLineP2(),
ElementTriP1(),
ElementTriP2(),
ElementQuad1(),
ElementQuad2(),
ElementQuadS2(),
ElementTetP1(),
ElementTetP2(),
ElementHex1(),
ElementHexS2(),
ElementHex2(),
]
def runTest(self):
for elem in self.elems:
if elem.dim == 1:
y = np.array([[.15]])
elif elem.dim == 2:
y = np.array([[.15], [.15]])
elif elem.dim == 3:
y = np.array([[.15], [.15], [.15]])
out = 0.
for i in range(elem.doflocs.shape[0]):
out += elem.lbasis(y, i)[0][0]
self.assertAlmostEqual(out, 1, msg='failed for {}'.format(elem))
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)))
class TestDerivatives(TestCase):
"""Test values of derivatives."""
elems = [
ElementLineP1(),
ElementLineP2(),
ElementTriP1(),
ElementTriP2(),
ElementTriMini(),
ElementQuad1(),
ElementQuad2(),
ElementQuadS2(),
ElementTetP1(),
ElementTetP2(),
ElementTetMini(),
ElementHex1(),
ElementHexS2(),
]
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
class LineNegative1DP2(LineNegative1D):
e = ElementLineP2()
class Line1DP2(Line1D):
e = ElementLineP2()
class LineNeumann1DP2(LineNeumann1D):
e = ElementLineP2()
def create_basis(self, m):
e = ElementLineP2()
return Basis(m, e)
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(), 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