def runTest(self):
m = self.mesh().refined(4)
basis = InteriorBasis(m, self.elem)
boundary_basis = FacetBasis(m, self.elem)
boundary_dofs = boundary_basis.get_dofs().flatten()
def dirichlet(x):
"""return a harmonic function"""
return ((x[0] + 1.j * x[1])**2).real
u = basis.zeros()
A = laplace.assemble(basis)
u[boundary_dofs] = projection(dirichlet,
boundary_basis,
I=boundary_dofs)
u = solve(*enforce(A, x=u, D=boundary_dofs))
@Functional
def gradu(w):
gradu = w['sol'].grad
return dot(gradu, gradu)
self.assertAlmostEqual(
gradu.assemble(basis, sol=basis.interpolate(u)),
8 / 3,
delta=1e-10,
)
def test_solving_inhomogeneous_laplace(mesh_elem, impose):
"""Adapted from example 14."""
mesh, elem = mesh_elem
m = mesh().refined(4)
basis = Basis(m, elem)
boundary_basis = FacetBasis(m, elem)
boundary_dofs = boundary_basis.get_dofs().flatten()
def dirichlet(x):
"""return a harmonic function"""
return ((x[0] + 1.j * x[1])**2).real
u = basis.zeros()
A = laplace.assemble(basis)
u[boundary_dofs] = projection(dirichlet, boundary_basis, I=boundary_dofs)
u = solve(*impose(A, x=u, D=boundary_dofs))
@Functional
def gradu(w):
gradu = w['sol'].grad
return dot(gradu, gradu)
np.testing.assert_almost_equal(gradu.assemble(basis,
sol=basis.interpolate(u)),
8 / 3,
decimal=9)
def runTest(self):
m = self.prepare_mesh()
basis = CellBasis(m, self.element_type())
x = projection(lambda x: x[0] ** 2, basis)
fun = basis.interpolator(x)
X = np.linspace(0, 1, 10)
dim = m.dim()
if dim == 3:
y = fun(np.array([X, [0.31] * 10, [0.62] * 10]))
elif dim == 2:
y = fun(np.array([X, [0.31] * 10]))
else:
y = fun(np.array([X]))
assert_allclose(y, X ** 2, atol=1e-10)
def test_trace(mtype, e1, e2, flat):
m = mtype().refined(3)
# use the boundary where last coordinate is zero
basis = FacetBasis(m, e1, facets=m.facets_satisfying(lambda x: x[-1] == 0.0))
xfun = projection(lambda x: x[0], CellBasis(m, e1))
nbasis, y = basis.trace(xfun, lambda p: p[0] if flat else p[:-1], target_elem=e2)
@Functional
def integ(w):
return w.y
# integrate f(x) = x_1 over trace mesh
assert_almost_equal(integ.assemble(nbasis, y=nbasis.interpolate(y)), .5)
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)
assert_allclose(basis.probes(X) @ y, basis.interpolator(y)(X))
assert_allclose(basis.probes(X) @ y, X[0] + X[1])