def runTest(self):
m = self.init_mesh()
basis = InteriorBasis(m, self.element_type())
A = laplace.assemble(basis)
b = unit_load.assemble(basis)
x = solve(*condense(A, b, D=basis.get_dofs()))
self.assertAlmostEqual(np.max(x), self.maxval, places=3)
def runTest(self):
path = Path(__file__).parents[1] / 'docs' / 'examples' / 'meshes'
m = self.mesh_type.load(path / self.filename)
basis = InteriorBasis(m, self.element_type())
A = laplace.assemble(basis)
b = unit_load.assemble(basis)
x = solve(*condense(A, b, D=basis.get_dofs()))
self.assertAlmostEqual(np.max(x), 0.06261690318912218, places=3)
def test_periodic_mesh_assembly(m, mdgtype, etype, check1, check2):
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(check1)),
_sort(m.nodes_satisfying(check2)))
basis = Basis(mp, etype())
A = laplace.assemble(basis)
f = unit_load.assemble(basis)
D = basis.get_dofs()
x = solve(*condense(A, f, D=D))
if m.dim() == 2:
assert_almost_equal(x.max(), 0.125)
else:
assert_almost_equal(x.max(), 0.07389930610869411, decimal=3)
assert not np.isnan(x).any()
def laplace(m, **params):
"""Solve the Laplace equation using the FEM.
Parameters
----------
m
A Mesh object.
"""
e = ElementTriP1()
basis = CellBasis(m, e)
A = laplacian.assemble(basis)
b = unit_load.assemble(basis)
u = solve(*condense(A, b, I=m.interior_nodes()))
# evaluate the error estimators
fbasis = [InteriorFacetBasis(m, e, side=i) for i in [0, 1]]
w = {"u" + str(i + 1): fbasis[i].interpolate(u) for i in [0, 1]}
@Functional
def interior_residual(w):
h = w.h
return h**2
eta_K = interior_residual.elemental(basis)
@Functional
def edge_jump(w):
h = w.h
n = w.n
dw1 = grad(w["u1"])
dw2 = grad(w["u2"])
return h * ((dw1[0] - dw2[0]) * n[0] + (dw1[1] - dw2[1]) * n[1])**2
eta_E = edge_jump.elemental(fbasis[0], **w)
tmp = np.zeros(m.facets.shape[1])
np.add.at(tmp, fbasis[0].find, eta_E)
eta_E = np.sum(0.5 * tmp[m.t2f], axis=0)
return eta_E + eta_K
def assembler(m):
basis = Basis(m, ElementTetP1())
return (
laplace.assemble(basis),
unit_load.assemble(basis),
)