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 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))
def test_adaptive_splitting_3d_3():
# adaptively refine one face of a cube, check that the mesh parameter h
# is approximately linear w.r.t to distance from the face
m = MeshTet.init_tensor(np.linspace(0, 1, 3), np.linspace(0, 1, 3),
np.linspace(0, 1, 3))
for itr in range(15):
m = m.refined(m.f2t[0, m.facets_satisfying(lambda x: x[0] == 0)])
@LinearForm
def hproj(v, w):
return w.h * v
basis = Basis(m, ElementTetP1())
h = projection(hproj, basis)
funh = basis.interpolator(h)
xs = np.vstack((
np.linspace(0, .5, 20),
np.zeros(20) + .5,
np.zeros(20) + .5,
))
hs = funh(xs)
assert np.max(np.abs(hs - xs[0])) < 0.063
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
if self.test_integrate_volume:
# by Gauss theorem this integrates to one
for itr in range(m.p.shape[0]):
@LinearForm
def linf(v, w):
return w.n[itr] * v
b = asm(linf, basis)
self.assertAlmostEqual(b @ m.p[itr, :], 1.0, places=5)
class NormalVectorTestTet(NormalVectorTestTri):
case = (MeshTet(), ElementTetP1())
class NormalVectorTestTetP2(NormalVectorTestTri):
case = (MeshTet(), ElementTetP2())
test_integrate_volume = False
class NormalVectorTestQuad(NormalVectorTestTri):
case = (MeshQuad(), ElementQuad1())
class NormalVectorTestQuadP(NormalVectorTestTri):
def create_basis(self, m):
e = ElementTetP1()
return Basis(m, e)
with self.assertRaises(ValueError):
m = MeshTri()
e = ElementTetP2()
basis = CellBasis(m, e)
@pytest.mark.parametrize(
"mtype,e,nrefs,npoints",
[
(MeshTri, ElementTriP1(), 0, 10),
(MeshTri, ElementTriP2(), 1, 10),
(MeshTri, ElementTriP1(), 5, 10),
(MeshTri, ElementTriP1(), 1, 3e5),
(MeshTet, ElementTetP2(), 1, 10),
(MeshTet, ElementTetP1(), 4, 10),
(MeshTet, ElementTetP1(), 1, 3e4),
(MeshQuad, ElementQuad1(), 1, 10),
(MeshQuad, ElementQuad1(), 1, 3e5),
(MeshHex, ElementHex1(), 1, 1e5),
(MeshWedge1, ElementWedge1(), 0, 10),
]
)
def test_interpolator_probes(mtype, e, nrefs, npoints):
m = mtype()
if nrefs > 0:
m = m.refined(nrefs)
np.random.seed(0)
X = np.random.rand(m.p.shape[0], int(npoints))
if self.test_integrate_volume:
# by Gauss theorem this integrates to one
for itr in range(m.p.shape[0]):
@LinearForm
def linf(v, w):
return w.n[itr] * v
b = asm(linf, basis)
self.assertAlmostEqual(b @ m.p[itr, :], 1.0, places=5)
class NormalVectorTestTet(NormalVectorTestTri):
case = (MeshTet(), ElementTetP1())
class NormalVectorTestTetP2(NormalVectorTestTri):
case = (MeshTet(), ElementTetP2())
test_integrate_volume = False
class NormalVectorTestQuad(NormalVectorTestTri):
case = (MeshQuad(), ElementQuad1())
class NormalVectorTestQuadP(NormalVectorTestTri):
class TestElementQuadBFS(TestCase):
def test_throw_index_error(self):
"""Tests that exception is thrown when i % 4 not in (0, 1, 2, 3)."""
element = ElementQuadBFS()
with self.assertRaises(ValueError):
element.gdof(0, 0, -1)
with self.assertRaises(ValueError):
element.gdof(0, 0, 16)
@pytest.mark.parametrize("m,e,edg", [
(MeshTri().refined(), ElementTriP1(), ElementTriDG),
(MeshTri().refined(), ElementTriP2(), ElementTriDG),
(MeshTet().refined(), ElementTetP1(), ElementTetDG),
(MeshTet().refined(), ElementTetP2(), ElementTetDG),
(MeshTri().refined(), ElementTriArgyris(), ElementTriDG),
(MeshTri().refined(), ElementTriMorley(), ElementTriDG),
(MeshTri().refined(), ElementTriHermite(), ElementTriDG),
(MeshHex().refined(), ElementHex1(), ElementHexDG),
(MeshQuad().refined(), ElementQuad1(), ElementQuadDG),
])
def test_dg_element(m, e, edg):
edg = edg(e)
@Functional
def square(w):
return w['random']**2
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):
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 = projection(lambda x: x[0], InteriorBasis(m, e1))
nbasis, y = basis.trace(xfun,
lambda p: p[0:(p.shape[0] - 1)],
places=10)
if self.test_integrate_volume:
# by Gauss theorem this integrates to one
for itr in range(m.p.shape[0]):
@LinearForm
def linf(v, w):
return w.n[itr] * v
b = asm(linf, basis)
self.assertAlmostEqual(b @ m.p[itr, :], 1.0, places=5)
class NormalVectorTestTet(NormalVectorTestTri):
case = (MeshTet(), ElementTetP1())
class NormalVectorTestTetP2(NormalVectorTestTri):
case = (MeshTet(), ElementTetP2())
test_integrate_volume = False
class NormalVectorTestQuad(NormalVectorTestTri):
case = (MeshQuad(), ElementQuad1())
class NormalVectorTestQuadP(NormalVectorTestTri):
