def set_numQuadPts_for_bilinear(self, numQuadPts):
self.numQuadPts = np.asarray(numQuadPts)
self.points, self.weights = quad.Quadrature.get_gauss_quad(numQuadPts)
if self.problemType == 1 or self.problemType == 2:
self.basisAtQuadPts = np.empty(self.grid.order + 1, np)
for I in itertools.product(
*[range(n) for n in (self.grid.order + 1)]):
self.basisAtQuadPts[I] = np.zeros(numQuadPts)
basis = self.grid.referenceElement.nodal_basis
for I in itertools.product(
*[range(n) for n in (self.grid.order + 1)]):
for J in itertools.product(*[range(n) for n in (numQuadPts)]):
self.basisAtQuadPts[I][J] = basis[I].value(self.points[J])
if self.problemType == 2:
self.basisGradAtQuadPts = np.empty(self.grid.order + 1, np)
for I in itertools.product(
*[range(n) for n in (self.grid.order + 1)]):
self.basisGradAtQuadPts[I] = np.zeros(
np.hstack((numQuadPts, self.grid.domain.dimension)))
basisGrad = self.grid.referenceElement.nodal_basis_gradient
for I in itertools.product(
*[range(n) for n in (self.grid.order + 1)]):
for J in itertools.product(*[range(n) for n in (numQuadPts)]):
self.basisGradAtQuadPts[I][J] = np.asarray(
polyNd.get_value_for_polyNdarray(
basisGrad[I], self.points[J]))
def build_interpolation_operators(self):
order_double_grid = self.grid.referenceElement.order_double_grid
order = self.grid.referenceElement.order
RefElement = RectReferenceElement(1, [order[0]])
RefElement.set_order_double_grid([order_double_grid[0]])
RefElement.set_nodal_coord()
RefElement.set_nodal_coord_double_grid()
RefElement.set_nodal_basis()
RefElement.set_nodal_basis_double_grid()
RefElement.set_first_order_derivatives()
basis = RefElement.nodal_basis
basisGrad = RefElement.nodal_basis_gradient
if self.problemType == 1 or self.problemType == 2:
B = np.zeros((order_double_grid[0] + 1, order[0] + 1))
i = 0
for I in itertools.product(
*[range(n) for n in RefElement.numNodes]):
S = tuple(I[::-1])
j = 0
for J in itertools.product(
*[range(n) for n in RefElement.numNodes_double_grid]):
T = tuple(J[::-1])
B[j, i] = basis[S].value(RefElement.coord_double_grid[T])
j += 1
i += 1
self.grid.referenceElement.B = scsp.csr_matrix(B)
self.grid.referenceElement.B_adj = scsp.csr_matrix(B.T)
if self.problemType == 2:
self.grid.referenceElement.B_1 = self.grid.referenceElement.B
self.grid.referenceElement.B_1_adj = scsp.csr_matrix(B.T)
B_2 = scsp.lil_matrix((order_double_grid[0] + 1, order[0] + 1))
for i in range(np.prod(RefElement.numNodes)):
S = RefElement.get_local_nodeID(i)
for j in range(np.prod(RefElement.numNodes_double_grid)):
T = RefElement.get_local_nodeID(i)
B_2[j, i] = polyNd.get_value_for_polyNdarray(
basisGrad[i], RefElement.coord_double_grid[j])
self.grid.referenceElement.B_2 = B_2.tocsr()
self.grid.referenceElement.B_2_adj = B_2.transpose().tocsr()
def build_interpolation_operators(self):
numNodes_double_grid = self.grid.referenceElement.numNodes_double_grid
numNodes = self.grid.referenceElement.numNodes
basis = self.grid.referenceElement.nodal_basis
if self.problemType == 1:
B = np.zeros((np.prod(numNodes_double_grid), np.prod(numNodes)))
i = 0
for I in itertools.product(*[range(n) for n in numNodes]):
S = tuple(I[::-1])
j = 0
for J in itertools.product(
*[range(n) for n in numNodes_double_grid]):
T = tuple(J[::-1])
B[j, i] = basis[S].value(
self.grid.referenceElement.coord_double_grid[T])
j += 1
i += 1
self.grid.referenceElement.B = scsp.csr_matrix(B)
self.grid.referenceElement.B_adj = scsp.csr_matrix(B.T)
elif self.problemType == 2:
basisGrad = self.grid.referenceElement.nodal_basis_gradient
B = np.zeros((self.grid.domain.dimension,
np.prod(numNodes_double_grid), np.prod(numNodes)))
i = 0
for I in itertools.product(*[range(n) for n in numNodes]):
S = tuple(I[::-1])
j = 0
for J in itertools.product(
*[range(n) for n in numNodes_double_grid]):
T = tuple(J[::-1])
B[:, j, i] = polyNd.get_value_for_polyNdarray(
basisGrad[S],
self.grid.referenceElement.coord_double_grid[T])
j += 1
i += 1
for dim in range(self.grid.domain.dimension):
self.grid.referenceElement.B.append(
scsp.csr_matrix(B[dim, :, :]))
for k in range(np.prod(numNodes)):
self.grid.referenceElement.B_adj.append(
scsp.csr_matrix(B[:, :, k]))