def runTest(self):
m = MeshTri()
basis = InteriorBasis(m, ElementTriP2())
D1 = basis.get_dofs(lambda x: x[0] == 0)
D2 = basis.get_dofs(lambda x: x[0] == 1)
D3 = basis.get_dofs(lambda x: x[1] == 1)
D4 = basis.get_dofs(lambda x: x[1] == 0)
assert_allclose(D1 | D2 | D3 | D4, basis.get_dofs())
assert_allclose(D1 + D2 + D3 + D4, basis.get_dofs())
def runTest(self):
m = MeshTri()
basis = InteriorBasis(m, ElementTriP2())
dofs = basis.get_dofs()
self.assertEqual(len(dofs.nodal['u']), 4)
self.assertEqual(len(dofs.facet['u']), 4)
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 runTest(self):
"""Solve Stokes problem, try splitting and other small things."""
m = MeshTri()
m.refine()
m.define_boundary('centreline',
lambda x: x[0] == .5,
boundaries_only=False)
m.refine(3)
e = ElementVectorH1(ElementTriP2()) * ElementTriP1()
m.define_boundary('up', lambda x: x[1] == 1.)
m.define_boundary('rest', lambda x: x[1] != 1.)
basis = InteriorBasis(m, e)
self.assertEqual(
basis.get_dofs(m.boundaries['centreline']).all().size,
(2 + 1) * (2**(1 + 3) + 1) + 2 * 2**(1 + 3))
self.assertEqual(basis.find_dofs()['centreline'].all().size,
(2 + 1) * (2**(1 + 3) + 1) + 2 * 2**(1 + 3))
@BilinearForm
def bilinf(u, p, v, q, w):
from skfem.helpers import grad, ddot, div
return (ddot(grad(u), grad(v)) - div(u) * q - div(v) * p -
1e-2 * p * q)
S = asm(bilinf, basis)
D = basis.find_dofs(skip=['u^2'])
x = basis.zeros()
x[D['up'].all('u^1^1')] = .1
x = solve(*condense(S, basis.zeros(), x=x, D=D))
(u, u_basis), (p, p_basis) = basis.split(x)
self.assertEqual(len(u), m.p.shape[1] * 2 + m.facets.shape[1] * 2)
self.assertEqual(len(p), m.p.shape[1])
self.assertTrue(np.sum(p - x[basis.nodal_dofs[2]]) < 1e-8)
U, P = basis.interpolate(x)
self.assertTrue(isinstance(U.value, np.ndarray))
self.assertTrue(isinstance(P.value, np.ndarray))
self.assertTrue((basis.doflocs[:, D['up'].all()][1] == 1.).all())
def runTest(self):
m = self.mesh().refined(3)
ib = InteriorBasis(m, self.elem())
A = asm(laplace, ib)
D = ib.get_dofs().all()
I = ib.complement_dofs(D)
for X in self.funs:
x = self.set_bc(X, ib)
Xh = x.copy()
x = solve(*condense(A, x=x, I=I))
self.assertLessEqual(np.sum(x - Xh), 1e-10)
def runTest(self):
m = MeshTri()
e = ElementTriArgyris()
basis = InteriorBasis(m, e)
all_dofs = basis.get_dofs()
self.assertEqual(len(all_dofs.keep('u').nodal), 1)
self.assertTrue('u' in all_dofs.keep('u').nodal)
self.assertEqual(len(all_dofs.keep('u_n').facet), 1)
self.assertEqual(len(all_dofs.drop('u').facet), 1)
all_dofs = basis.dofs.get_facet_dofs(m.facets_satisfying(lambda x: 1))
self.assertEqual(len(all_dofs.keep('u_n').facet), 1)
self.assertEqual(len(all_dofs.drop('u').facet), 1)
def runTest(self):
m = self.case[0]()
m.refine(self.prerefs)
hs = []
L2s = []
for itr in range(3):
e = self.case[1]()
ib = InteriorBasis(m, e)
@BilinearForm
def bilinf(u, v, w):
return ddot(dd(u), dd(v))
@LinearForm
def linf(v, w):
return 1. * v
K = asm(bilinf, ib)
f = asm(linf, ib)
x = solve(*condense(K, f, D=ib.get_dofs().all()))
X = ib.interpolate(x)
def exact(x):
return (x ** 2 - 2. * x ** 3 + x ** 4) / 24.
@Functional
def error(w):
return (w.w - exact(w.x)) ** 2
L2 = np.sqrt(error.assemble(ib, w=X))
L2s.append(L2)
hs.append(m.param())
m.refine()
hs = np.array(hs)
L2s = np.array(L2s)
pfit = np.polyfit(np.log10(hs), np.log10(L2s), 1)
self.assertGreater(pfit[0], self.limits[0])
self.assertLess(pfit[0], self.limits[1])
self.assertLess(L2s[-1], self.abs_limit)
def runTest(self):
m = MeshTri()
e = ElementTriArgyris()
basis = InteriorBasis(m, e)
all_dofs = basis.get_dofs()
assert_allclose(
all_dofs.keep(['u', 'u_n']).keep('u'), all_dofs.keep('u'))
assert_allclose(
all_dofs.drop(['u_x', 'u_y', 'u_xx', 'u_xy', 'u_yy', 'u_n']),
all_dofs.keep('u'))
assert_allclose(all_dofs, all_dofs.drop('does_not_exist'))
assert_allclose(np.empty((0, ), dtype=np.int64),
all_dofs.keep('does_not_exist'))
def runTest(self):
@bilinear_form
def dudv(u, du, v, dv, w):
return sum(du * dv)
m = self.mesh()
m.refine(4)
ib = InteriorBasis(m, self.elem())
A = asm(dudv, ib)
D = ib.get_dofs().all()
I = ib.complement_dofs(D)
for X in self.funs:
x = self.set_bc(X, ib)
Xh = x.copy()
x = solve(*condense(A, 0 * x, x=x, I=I))
self.assertLessEqual(np.sum(x - Xh), 1e-10)
mesh, element, elements=mesh.subdomains['inner_conductor'])
outer_conductor_basis = InteriorBasis(
mesh, element, elements=mesh.subdomains['outer_conductor'])
inner_insulator_basis = InteriorBasis(
mesh, element, elements=mesh.subdomains['inner_insulator'])
outer_insulator_basis = InteriorBasis(
mesh, element, elements=mesh.subdomains['outer_insulator'])
inner_conductor_outer_surface_basis = FacetBasis(
mesh, element, facets=mesh.boundaries['inner_conductor_outer_surface'])
outer_conductor_inner_surface_basis = FacetBasis(
mesh, element, facets=mesh.boundaries['outer_conductor_inner_surface'])
dofs = {
'boundary':
global_basis.get_dofs(mesh.boundaries['boundary']),
'inner_conductor_outer_surface':
global_basis.get_dofs(mesh.boundaries['inner_conductor_outer_surface']),
'outer_conductor_inner_surface':
global_basis.get_dofs(mesh.boundaries['outer_conductor_inner_surface'])
}
# functional to compute the integral of a load vector over the domain
load_integral = solve(asm(mass, global_basis), asm(unit_load, global_basis))
# all materials have a relative permeability of effectively 1
K_mag = asm(laplace, global_basis) * (1 / mu0)
# pass 1A through the conductors
current = 1
def runTest(self):
m = self.case[0]().refined(self.prerefs)
hs = []
L2s = []
for itr in range(3):
e = self.case[1]()
ib = InteriorBasis(m, e)
t = 1.
E = 1.
nu = 0.3
D = E * t ** 3 / (12. * (1. - nu ** 2))
@BilinearForm
def bilinf(u, v, w):
def C(T):
trT = T[0, 0] + T[1, 1]
return E / (1. + nu) * \
np.array([[T[0, 0] + nu / (1. - nu) * trT, T[0, 1]],
[T[1, 0], T[1, 1] + nu / (1. - nu) * trT]])
return t ** 3 / 12.0 * ddot(C(dd(u)), dd(v))
def load(x):
return np.sin(np.pi * x[0]) * np.sin(np.pi * x[1])
@LinearForm
def linf(v, w):
return load(w.x) * v
K = asm(bilinf, ib)
f = asm(linf, ib)
# TODO fix boundary conditions
# u_x should be zero on top/bottom
# u_y should be zero on left/right
x = solve(*condense(K, f, D=ib.get_dofs().all('u')))
X = ib.interpolate(x)
def exact(x):
return 1. / (4. * D * np.pi ** 4) * load(x)
@Functional
def error(w):
return (w.w - exact(w.x)) ** 2
L2 = np.sqrt(error.assemble(ib, w=X))
L2s.append(L2)
hs.append(m.param())
m = m.refined()
hs = np.array(hs)
L2s = np.array(L2s)
pfit = np.polyfit(np.log10(hs), np.log10(L2s), 1)
self.assertGreater(pfit[0], self.limits[0])
self.assertLess(pfit[0], self.limits[1])
self.assertLess(L2s[-1], self.abs_limit)