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))
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
def runTest(self):
m = MeshHex()
# check that these assemble to the same matrix
ec = ElementHex1() * ElementHex1() * ElementHex1()
ev = ElementVectorH1(ElementHex1())
basisc = Basis(m, ec)
basisv = Basis(m, ev)
@BilinearForm
def bilinf_ev(u, v, w):
from skfem.helpers import dot
return dot(u, v)
@BilinearForm
def bilinf_ec(ux, uy, uz, vx, vy, vz, w):
return ux * vx + uy * vy + uz * vz
Kv = asm(bilinf_ev, basisv)
Kc = asm(bilinf_ec, basisc)
self.assertAlmostEqual(np.sum(np.sum((Kv - Kc).todense())), 0.)
def createBasis(self):
m = MeshHex().refined(3)
self.fbasis = FacetBasis(m, ElementHex1())
self.boundary_area = 6.000
class NormalVectorTestQuad(NormalVectorTestTri):
case = (MeshQuad(), ElementQuad1())
class NormalVectorTestQuadP(NormalVectorTestTri):
case = (MeshQuad(), ElementQuadP(3))
test_integrate_volume = False
class NormalVectorTestHex(NormalVectorTestTri):
case = (MeshHex(), ElementHex1())
intorder = 3
class NormalVectorTestHexS2(NormalVectorTestTri):
case = (MeshHex(), ElementHexS2())
intorder = 3
test_integrate_volume = False
class NormalVectorTestHex2(NormalVectorTestTri):
case = (MeshHex(), ElementHex2())
intorder = 3
test_integrate_volume = False
ElementQuad2(),
),
(
MeshTri().refined(2),
MeshTri1DG,
ElementTriP2(),
),
(
MeshLine().refined(5),
MeshLine1DG,
ElementLineP1(),
),
(
MeshHex().refined(3),
MeshHex1DG,
ElementHex1(),
),
(
MeshLine().refined(),
MeshLine1DG,
ElementLinePp(5),
),
])
def test_periodic_loading(m, mdgtype, e):
def _sort(ix):
# sort index arrays so that ix[0] matches
return ix[np.argsort(np.sum(m.p, axis=0)[ix])]
mp = mdgtype.periodic(m, _sort(m.nodes_satisfying(lambda x: x[0] == 0)),
_sort(m.nodes_satisfying(lambda x: x[0] == 1)))
basis = Basis(mp, e)
def create_basis(self, m):
e = ElementHex1()
return Basis(m, e)
def mapping(self):
return MappingIsoparametric(self, ElementHex1(), ElementQuad1())
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))
basis = CellBasis(m, e)
y = projection(lambda x: x[0] + x[1], basis)
class NormalVectorTestQuad(NormalVectorTestTri):
case = (MeshQuad(), ElementQuad1())
class NormalVectorTestQuadP(NormalVectorTestTri):
case = (MeshQuad(), ElementQuadP(3))
test_integrate_volume = False
class NormalVectorTestHex(NormalVectorTestTri):
case = (MeshHex(), ElementHex1())
intorder = 3
class NormalVectorTestHexS2(NormalVectorTestTri):
case = (MeshHex(), ElementHexS2())
intorder = 3
test_integrate_volume = False
class NormalVectorTestHex2(NormalVectorTestTri):
case = (MeshHex(), ElementHex2())
intorder = 3
test_integrate_volume = False
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
basis = InteriorBasis(m, e)
basisdg = InteriorBasis(m, edg)
assert_allclose(
square.assemble(basis, random=basis.interpolate(basis.zeros() + 1)),
def mapping(self):
from skfem.mapping import MappingIsoparametric
from skfem.element import ElementHex1, ElementQuad1
return MappingIsoparametric(self, ElementHex1(), ElementQuad1())
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)],
target_elem=e2)
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)],
target_elem=e2)