def runTest(self):
m = MeshQuad()
m.refine(2)
e = ElementQuad1()
basis = InteriorBasis(m, e)
M, X = basis.refinterp(m.p[0], 3)
self.assertEqual(M.p.shape[1], len(X))
class ConvergenceQ2(ConvergenceQ1):
rateL2 = 3.0
rateH1 = 2.0
def create_basis(self, m):
e = ElementQuad2()
return InteriorBasis(m, e)
def setUp(self):
self.mesh = MeshQuad()
self.mesh.refine(2)
def test_periodic_failure():
# these meshes cannot be made periodic due to insufficient number of
# elements
with pytest.raises(ValueError):
mp = MeshLine1DG.periodic(MeshLine(), [0], [1])
with pytest.raises(ValueError):
mp = MeshQuad1DG.periodic(MeshQuad(), [0], [1])
with pytest.raises(ValueError):
mp = MeshQuad1DG.periodic(MeshQuad().refined(2), [0], [1, 2])
def runTest(self):
m = MeshQuad()
m.refine(3)
e = ElementQuad1()
basis = InteriorBasis(m, e)
@functional
def x_squared(w):
return w.x[0]**2
y = asm(x_squared, basis)
self.assertAlmostEqual(y, 1. / 3.)
self.assertEqual(len(x_squared.elemental(basis)), m.t.shape[1])
def test_pickling():
# some simple checks for pickle
mesh = MeshQuad()
elem = ElementQuad1()
mapping = MappingIsoparametric(mesh, elem)
basis = CellBasis(mesh, elem, mapping)
pickled_mesh = pickle.dumps(mesh)
pickled_elem = pickle.dumps(elem)
pickled_mapping = pickle.dumps(mapping)
pickled_basis = pickle.dumps(basis)
mesh1 = pickle.loads(pickled_mesh)
elem1 = pickle.loads(pickled_elem)
mapping1 = pickle.loads(pickled_mapping)
basis1 = pickle.loads(pickled_basis)
assert_almost_equal(
laplace.assemble(basis).toarray(),
laplace.assemble(basis1).toarray(),
)
assert_almost_equal(
mesh.doflocs,
mesh1.doflocs,
)
assert_almost_equal(
mapping.J(0, 0, np.array([[.3], [.3]])),
mapping1.J(0, 0, np.array([[.3], [.3]])),
)
assert_almost_equal(
elem.doflocs,
elem1.doflocs,
)
def runRefineTest(self):
mesh = MeshQuad()
mesh.define_boundary('left', lambda x: x[0] == 0)
mesh.refine()
mesh_tri = mesh.to_meshtri()
for b in mesh.boundaries:
np.testing.assert_array_equal(*[m.facets.T[m.boundaries[b]]
for m in [mesh, mesh_tri]])
def test_multimesh():
m1 = MeshTri().refined()
m2 = MeshQuad().refined().translated((1., 0.))
m3 = MeshTri().refined().translated((2., 0.))
M = m1 @ m2 @ m3
assert len(M) == 3
E = [ElementTriP1(), ElementQuad1(), ElementTriP1()]
basis = list(map(Basis, M, E))
Mm = asm(mass, basis)
assert Mm.shape[0] == 3 * 7
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)),
square.assemble(basisdg,
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):
case = (MeshQuad(), ElementQuadP(3))
test_integrate_volume = False
class NormalVectorTestHex(NormalVectorTestTri):
case = (MeshHex(), ElementHex1())
intorder = 3
class NormalVectorTestHexS2(NormalVectorTestTri):
def createBasis(self):
m = MeshQuad().refined(6)
self.fbasis = FacetBasis(m, self.elem)
self.boundary_area = 4.0000
def initialize_meshes(self):
m0 = MeshQuad()
m = MeshQuad([[0, 1, 1, 0], [0, .9, 1, 1]], m0.t)
return m
(
MeshTri().refined(2),
MeshTri1DG,
ElementTriP1,
lambda x: x[0] == 1,
lambda x: x[0] == 0,
),
(
MeshTri().refined(3),
MeshTri1DG,
ElementTriP1,
lambda x: x[0] == 1,
lambda x: x[0] == 0,
),
(
MeshQuad().refined(2),
MeshQuad1DG,
ElementQuad1,
lambda x: x[0] == 1,
lambda x: x[0] == 0,
),
(
MeshQuad().refined(2),
MeshQuad1DG,
ElementQuad2,
lambda x: x[0] == 1,
lambda x: x[0] == 0,
),
(
MeshTri().refined(2),
MeshTri1DG,
class ConvergenceQ1(unittest.TestCase):
rateL2 = 2.0
rateH1 = 1.0
eps = 0.1
def runTest(self):
@LinearForm
def load(v, w):
x = w.x
if x.shape[0] == 1:
return (np.sin(np.pi * x[0]) * (np.pi**2) * v)
elif x.shape[0] == 2:
return (np.sin(np.pi * x[0]) * np.sin(np.pi * x[1]) *
(2.0 * np.pi**2) * v)
elif x.shape[0] == 3:
return (np.sin(np.pi * x[0]) * np.sin(np.pi * x[1]) *
np.sin(np.pi * x[2]) * (3.0 * np.pi**2) * v)
else:
raise Exception("The dimension not supported")
m = self.mesh
Nitrs = 3
L2s = np.zeros(Nitrs)
H1s = np.zeros(Nitrs)
hs = np.zeros(Nitrs)
for itr in range(Nitrs):
if itr > 0:
m.refine()
ib = self.create_basis(m)
A = asm(laplace, ib)
b = asm(load, ib)
D = ib.get_dofs().all()
x = solve(*condense(A, b, D=D))
# calculate error
L2s[itr], H1s[itr] = self.compute_error(m, ib, x)
hs[itr] = m.param()
rateL2 = np.polyfit(np.log(hs), np.log(L2s), 1)[0]
rateH1 = np.polyfit(np.log(hs), np.log(H1s), 1)[0]
self.assertLess(np.abs(rateL2 - self.rateL2),
self.eps,
msg='observed L2 rate: {}'.format(rateL2))
self.assertLess(np.abs(rateH1 - self.rateH1),
self.eps,
msg='observed H1 rate: {}'.format(rateH1))
self.assertLess(H1s[-1], 0.3)
self.assertLess(L2s[-1], 0.008)
def compute_error(self, m, basis, U):
uh, duh, *_ = basis.interpolate(U)
dx = basis.dx
x = basis.global_coordinates()
def u(y):
if y.shape[0] == 1:
return np.sin(np.pi * y[0])
elif y.shape[0] == 2:
return (np.sin(np.pi * y[0]) * np.sin(np.pi * y[1]))
elif y.shape[0] == 3:
return (np.sin(np.pi * y[0]) * np.sin(np.pi * y[1]) *
np.sin(np.pi * y[2]))
else:
raise Exception("The dimension not supported")
L2 = np.sqrt(np.sum(np.sum((uh - u(x.f))**2 * dx, axis=1)))
def ux(y):
if y.shape[0] == 1:
return np.pi * np.cos(np.pi * y[0])
elif y.shape[0] == 2:
return np.pi * (np.cos(np.pi * y[0]) * np.sin(np.pi * y[1]))
elif y.shape[0] == 3:
return np.pi * (np.cos(np.pi * y[0]) * np.sin(np.pi * y[1]) *
np.sin(np.pi * y[2]))
else:
raise Exception("The dimension not supported")
if m.dim() >= 2:
def uy(y):
if y.shape[0] == 2:
return np.pi * (np.sin(np.pi * y[0]) *
np.cos(np.pi * y[1]))
elif y.shape[0] == 3:
return np.pi * (np.sin(np.pi * y[0]) * np.cos(np.pi * y[1])
* np.sin(np.pi * y[2]))
else:
raise Exception("The dimension not supported")
if m.dim() == 3:
def uz(y):
return np.pi * (np.sin(np.pi * y[0]) * np.sin(np.pi * y[1]) *
np.cos(np.pi * y[2]))
if m.dim() == 3:
H1 = np.sqrt(
np.sum(
np.sum(((duh[0] - ux(x.f))**2 + (duh[1] - uy(x.f))**2 +
(duh[2] - uz(x.f))**2) * dx,
axis=1)))
elif m.dim() == 2:
H1 = np.sqrt(
np.sum(
np.sum(
((duh[0] - ux(x.f))**2 + (duh[1] - uy(x.f))**2) * dx,
axis=1)))
else:
H1 = np.sqrt(np.sum(np.sum(((duh[0] - ux(x.f))**2) * dx, axis=1)))
return L2, H1
def create_basis(self, m):
e = ElementQuad1()
return InteriorBasis(m, e)
def setUp(self):
self.mesh = MeshQuad()
self.mesh.refine(2)
def setUp(self):
self.mesh = MeshQuad().refined(2)
.dot(m2.p[0] * 0. + 1.)), lenright)
assert_almost_equal((mass.assemble(mb[1], mb[0])
.dot(m2.p[0] * 0. + 1.)
.dot(m1.p[0] * 0. + 1.)), lenright)
assert_allclose(mass.assemble(mb[0], mb[1]).toarray(),
mass.assemble(mb[1], mb[0]).T.toarray())
@pytest.mark.parametrize(
"m, e, fun",
[
(MeshTri(), ElementTriP1(), lambda x: x[0]),
(MeshTri(), ElementTriRT0(), lambda x: x),
(MeshQuad(), ElementQuadRT0(), lambda x: x),
]
)
def test_basis_project(m, e, fun):
basis = CellBasis(m, e)
y = basis.project(fun)
@Functional
def int_y_1(w):
return w.y ** 2
@Functional
def int_y_2(w):
return fun(w.x) ** 2
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):
case = (MeshQuad(), ElementQuadP(3))
test_integrate_volume = False
class NormalVectorTestHex(NormalVectorTestTri):
case = (MeshHex(), ElementHex1())
intorder = 3
class NormalVectorTestHexS2(NormalVectorTestTri):
def setUp(self):
self.mesh = MeshQuad()
self.mesh.refine(2)
self.assertEqual(finder(np.array([0.001]))[0], 0)
self.assertEqual(finder(np.array([0.999]))[0], 2**itr - 1)
class TestFinder1DLinspaced(TestCase):
def runTest(self):
for itr in range(5):
finder = (MeshLine(np.linspace(0, 1, 2**itr + 1)).element_finder())
self.assertEqual(finder(np.array([0.999]))[0], 2**itr - 1)
self.assertEqual(finder(np.array([0.001]))[0], 0)
@pytest.mark.parametrize("m", [
MeshTri.init_circle(),
MeshQuad.init_tensor([0, 1, 3], [0, 1, 3]),
MeshTet().refined(3),
MeshHex.init_tensor([0, 1, 3], [0, 1, 3], [0, 1, 3]),
])
def test_smoothed(m):
M = m.smoothed()
assert M.is_valid()
# points have moved?
assert np.linalg.norm((M.p - m.p)**2) > 0
@pytest.mark.parametrize("m", [
MeshTri(),
MeshTet(),
])
def test_oriented(m):
# integral is over the domain of the first argument
assert_almost_equal((mass.assemble(
mb[0], mb[1]).dot(m1.p[0] * 0. + 1.).dot(m2.p[0] * 0. + 1.)), lenright)
assert_almost_equal((mass.assemble(
mb[1], mb[0]).dot(m2.p[0] * 0. + 1.).dot(m1.p[0] * 0. + 1.)), lenright)
assert_allclose(
mass.assemble(mb[0], mb[1]).toarray(),
mass.assemble(mb[1], mb[0]).T.toarray())
@pytest.mark.parametrize("m, e, fun", [
(MeshTri(), ElementTriP1(), lambda x: x[0]),
(MeshTri(), ElementTriRT0(), lambda x: x),
(MeshQuad(), ElementQuadRT0(), lambda x: x),
])
def test_basis_project(m, e, fun):
basis = CellBasis(m, e)
y = basis.project(fun)
@Functional
def int_y_1(w):
return w.y**2
@Functional
def int_y_2(w):
return fun(w.x)**2
assert_almost_equal(int_y_1.assemble(basis, y=y), int_y_2.assemble(basis))