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 = 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 = 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 runTest(self):
m = MeshLine(np.linspace(0., 1.)).refined(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):
@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)