def test_assemblePatchBoundaryMatrix1d(self):
NPatch = np.array([4])
CLocGetter = fem.localBoundaryNormalDerivativeMatrixGetter(NPatch)
CComputed = fem.assemblePatchBoundaryMatrix(NPatch, CLocGetter)
CCorrect = np.array([[4, -4, 0, 0, 0], [0, 0, 0, 0,
0], [0, 0, 0, 0, 0],
[0, 0, 0, 0, 0], [0, 0, 0, -4, 4]])
self.assertTrue(np.allclose(CComputed.todense(), CCorrect))
NPatch = np.array([4])
aPatch = np.array([2, 10, 10, 3])
CLocGetter = fem.localBoundaryNormalDerivativeMatrixGetter(NPatch)
CComputed = fem.assemblePatchBoundaryMatrix(NPatch, CLocGetter, aPatch)
CCorrect = np.array([[8, -8, 0, 0, 0], [0, 0, 0, 0, 0],
[0, 0, 0, 0, 0], [0, 0, 0, 0, 0],
[0, 0, 0, -12, 12]])
self.assertTrue(np.allclose(CComputed.todense(), CCorrect))
def test_boundaryNormalDerivativeMatrixProperties(self):
# BoundaryNormalDerivative bilinear form should map constants to 0
NPatch = np.array([3, 4, 5])
CLocGetter = fem.localBoundaryNormalDerivativeMatrixGetter(NPatch)
C = fem.assemblePatchBoundaryMatrix(NPatch, CLocGetter)
constant = np.ones(np.prod(NPatch + 1))
self.assertTrue(np.isclose(np.linalg.norm(C * constant), 0))
# BoundaryNormalDerivative bilinear form (a=constant) should map planes to 0
NPatch = np.array([3, 4, 5, 6])
CLocGetter = fem.localBoundaryNormalDerivativeMatrixGetter(NPatch)
C = fem.assemblePatchBoundaryMatrix(NPatch, CLocGetter)
p = util.pCoordinates(NPatch)
pSum = np.sum(p, axis=1)
ones = np.ones(np.prod(NPatch + 1))
self.assertTrue(np.isclose(np.linalg.norm(np.dot(ones, C * pSum)), 0))
# A function f with df/dx_k = 1 at x_k = 0 and df/dx_k = 0 at
# x_k = 1 should give 1'*C*f = -d
NPatch = np.array([5, 4, 3, 7])
CLocGetter = fem.localBoundaryNormalDerivativeMatrixGetter(NPatch)
C = fem.assemblePatchBoundaryMatrix(NPatch, CLocGetter)
p = util.pCoordinates(NPatch)
p = np.minimum(p, 0.5)
pSum = np.sum(p, axis=1)
ones = np.ones(np.prod(NPatch + 1))
self.assertTrue(np.isclose(np.dot(ones, C * pSum), -4))
# Same test as above, but with a coefficient a
NPatch = np.array([5, 4, 3, 7])
CLocGetter = fem.localBoundaryNormalDerivativeMatrixGetter(NPatch)
p = util.pCoordinates(NPatch)
p0 = p[:, 0]
pElement = util.pCoordinates(NPatch, NPatch=NPatch - 1)
pElement0 = pElement[:, 0]
aPatch = 1. * (pElement0 < 0.5) + 10. * (pElement0 >= 0.5)
C = fem.assemblePatchBoundaryMatrix(NPatch, CLocGetter, aPatch)
ones = np.ones(np.prod(NPatch + 1))
self.assertTrue(np.isclose(np.dot(ones, C * p0), 10 - 1))
def test_assemblePatchBoundaryNormalDerivativeMatrix2d(self):
NPatch = np.array([1, 2])
CLocGetter = fem.localBoundaryNormalDerivativeMatrixGetter(NPatch)
CComputed = fem.assemblePatchBoundaryMatrix(NPatch, CLocGetter)
CCorrect = 1. / 12 * np.array(
[[10, 2, 1, -1, 0, 0], [2, 10, -1, 1, 0, 0],
[-7, -5, 4, -4, -7, -5], [-5, -7, -4, 4, -5, -7],
[0, 0, 1, -1, 10, 2], [0, 0, -1, 1, 2, 10]]).T
self.assertTrue(np.allclose(CComputed.todense(), CCorrect))
NPatch = np.array([1, 2])
aPatch = np.array([1, 10])
CLocGetter = fem.localBoundaryNormalDerivativeMatrixGetter(NPatch)
CComputed = fem.assemblePatchBoundaryMatrix(NPatch, CLocGetter, aPatch)
CCorrect = 1. / 12 * np.array(
[[10, 2, 1, -1, 0, 0], [2, 10, -1, 1, 0, 0],
[-7, -5, 22, -22, -70, -50], [-5, -7, -22, 22, -50, -70],
[0, 0, 10, -10, 100, 20], [0, 0, -10, 10, 20, 100]]).T
self.assertTrue(np.allclose(CComputed.todense(), CCorrect))