class ConvergenceLineP1(ConvergenceQ1):
def create_basis(self, m):
e = ElementLineP1()
return InteriorBasis(m, e)
def setUp(self):
self.mesh = MeshLine()
self.mesh.refine(3)
class ConvergenceLineP2(ConvergenceQ1):
rateL2 = 3.0
rateH1 = 2.0
def create_basis(self, m):
e = ElementLineP2()
return InteriorBasis(m, e)
def setUp(self):
self.mesh = MeshLine()
self.mesh.refine(3)
def runTest(self):
m = MeshLine()
for itr in range(10):
prev_t_size = m.t.shape[1]
prev_p_size = m.p.shape[1]
m = m.refined([prev_t_size - 1])
# check that new size is current size + 1
self.assertEqual(prev_t_size, m.t.shape[1] - 1)
self.assertEqual(prev_p_size, m.p.shape[1] - 1)
def runTest(self):
m = MeshLine(np.linspace(0., 1.))
m.refine(2)
ib = InteriorBasis(m, self.e)
fb = FacetBasis(m, self.e)
@LinearForm
def boundary_flux(v, w):
return v * (w.x[0] == 1) - v * (w.x[0] == 0)
L = asm(laplace, ib)
M = asm(mass, ib)
b = asm(boundary_flux, fb)
u = solve(L + 1e-6 * M, b)
np.testing.assert_array_almost_equal(u[ib.nodal_dofs[0]], m.p[0] - .5, -4)
def runTest(self):
m = MeshLine(np.linspace(0., 1.)).refined(2)
ib = InteriorBasis(m, self.e)
fb = FacetBasis(m, self.e)
@LinearForm
def boundary_flux(v, w):
return v * (w.x[0] == 1.)
L = asm(laplace, ib)
b = asm(boundary_flux, fb)
D = m.nodes_satisfying(lambda x: x == 0.0)
I = ib.complement_dofs(D) # noqa E741
u = solve(*condense(L, b, I=I)) # noqa E741
np.testing.assert_array_almost_equal(u[ib.nodal_dofs[0]], m.p[0], -10)
def runTest(self):
m = MeshLine(np.linspace(0., 1.))
m.refine(2)
e = ElementLineP1()
ib = InteriorBasis(m, e)
fb = FacetBasis(m, e)
@linear_form
def boundary_flux(v, dv, w):
return v * (w.x[0] == 1) - v * (w.x[0] == 0)
L = asm(laplace, ib)
M = asm(mass, ib)
b = asm(boundary_flux, fb)
u = solve(L + 1e-6 * M, b)
self.assertTrue(np.sum(np.abs(u - m.p[0, :] + 0.5)) < 1e-4)
def runTest(self):
m = MeshLine(np.linspace(0., 1.))
m.refine(2)
e = ElementLineP1()
ib = InteriorBasis(m, e)
fb = FacetBasis(m, e)
@linear_form
def boundary_flux(v, dv, w):
return -v * (w.x[0] == 1.)
L = asm(laplace, ib)
b = asm(boundary_flux, fb)
D = m.nodes_satisfying(lambda x: x == 0.0)
I = ib.complement_dofs(D) # noqa E741
u = solve(*condense(L, b, I=I)) # noqa E741
self.assertTrue(np.sum(np.abs(u + m.p[0, :])) < 1e-10)
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 = MeshLine(np.linspace(0., 1.))
m.refine(2)
ib = InteriorBasis(m, self.e)
m.define_boundary('left' ,lambda x: x[0] == 0.0)
m.define_boundary('right', lambda x: x[0] == 1.0)
fb = FacetBasis(m, self.e, facets=m.boundaries['right'])
@LinearForm
def boundary_flux(v, w):
return -w.x[0] * v
L = asm(laplace, ib)
b = asm(boundary_flux, fb)
D = ib.find_dofs()['left'].all()
I = ib.complement_dofs(D) # noqa E741
u = solve(*condense(L, b, I=I)) # noqa E741
np.testing.assert_array_almost_equal(u[ib.nodal_dofs[0]], -m.p[0], -10)
def runTest(self):
m = MeshLine(np.linspace(0., 1.)).refined(2).with_boundaries({
'left':
lambda x: x[0] == 0.0,
'right':
lambda x: x[0] == 1.0,
})
ib = Basis(m, self.e)
fb = FacetBasis(m, self.e, facets=m.boundaries['right'])
@LinearForm
def boundary_flux(v, w):
return -w.x[0] * v
L = asm(laplace, ib)
b = asm(boundary_flux, fb)
D = ib.get_dofs('left')
I = ib.complement_dofs(D) # noqa E741
u = solve(*condense(L, b, I=I)) # noqa E741
np.testing.assert_array_almost_equal(u[ib.nodal_dofs[0]], -m.p[0], -10)
MeshQuad().refined(2),
MeshQuad1DG,
ElementQuad1(),
),
(
MeshQuad().refined(2),
MeshQuad1DG,
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 runTest(self):
for itr in range(5):
finder = MeshLine().refined(itr).element_finder()
self.assertEqual(finder(np.array([0.001]))[0], 0)
self.assertEqual(finder(np.array([0.999]))[0], 2**itr - 1)
def setUp(self):
self.mesh = MeshLine().refined(3)
def do_refined(self, m, itr):
return (MeshLine(np.linspace(0, 1, 2**(itr + 2))) *
MeshTri().refined(itr + 2))
def setUp(self):
self.mesh = MeshLine()
self.mesh.refine(3)
assert_array_equal(
tri.find_simplex(query_pts.T),
finder(*query_pts),
)
@pytest.mark.parametrize("m", [
MeshTri(),
MeshQuad(),
MeshTet(),
MeshHex(),
MeshTri2(),
MeshQuad2(),
MeshTet2(),
MeshHex2(),
MeshLine(),
])
def test_meshio_cycle(m):
M = from_meshio(to_meshio(m))
assert_array_equal(M.p, m.p)
assert_array_equal(M.t, m.t)
if m.boundaries is not None:
np.testing.assert_equal(m.boundaries, M.boundaries)
if m.subdomains is not None:
np.testing.assert_equal(m.subdomains, M.subdomains)
_test_lambda = {
'left': lambda x: x[0] < 0.6,
'right': lambda x: x[0] > 0.3,
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)