def compute_hybrid_matrices(
self,
cell: Cell,
faces: List[Face],
cell_basis_l: Basis,
cell_basis_k: Basis,
cell_basis_k1: Basis,
face_basis_k: Basis,
unknown: Unknown,
):
"""
================================================================================================================
Method :
================================================================================================================
================================================================================================================
Parameters :
================================================================================================================
-
================================================================================================================
Returns :
================================================================================================================
-
"""
# ==============================================================================================================
# GRADIENT OPERATOR / STABILIZATION OPERATOR
# ==============================================================================================================
mat_F_phi_k_phi_l_list = []
mat_F_phi_k_psi_k_list = []
for mface in mfaces:
mat_F_phi_k_phi_l = Integration.get_cell_mass_matrix_in_face(
mcell.cell, mface.face, cell_basis_k, cell_basis_l)
mat_F_phi_k_phi_l_list.append(mat_F_phi_k_phi_l_list)
# ----------------------------------------------------------------------------------------------------------
mat_F_phi_k_psi_k = Integration.get_hybrid_mass_matrix_in_face(
mcell.cell, mface.face, cell_basis_k, face_basis_k,
mface.face.reference_frame_transformation_matrix)
mat_F_phi_k_psi_k_list.append(mat_F_phi_k_psi_k)
# ==============================================================================================================
# RECONSTRUCTION OPERATOR
# ==============================================================================================================
mat_F_grad_phi_k1_psi_k_list = []
mat_F_grad_phi_k1_phi_l_list = []
for mface in mfaces:
mat_F_grad_phi_k1_psi_k_j_list = []
mat_F_grad_phi_k1_phi_l_j_list = []
for j in range(len(unknown.problem_dimension)):
# ------------------------------------------------------------------------------------------------------
mat_F_grad_phi_k1_psi_k_j = Integration.get_hybrid_advection_matrix_in_face(
mcell.cell,
mface.face,
cell_basis_k1,
face_basis_k,
mface.face.reference_frame_transformation_matrix,
j,
)
mat_F_grad_phi_k1_psi_k_j_list.append(
mat_F_grad_phi_k1_psi_k_j)
# ------------------------------------------------------------------------------------------------------
mat_F_phi_l_grad_phi_k1_j = Integration.get_cell_advection_matrix_in_face(
mcell.cell, mface.face, cell_basis_l, cell_basis_k1, j)
# ------------------------------------------------------------------------------------------------------
mat_F_grad_phi_k1_phi_l_j = mat_F_phi_l_grad_phi_k1_j.T
mat_F_grad_phi_k1_phi_l_j_list.append(
mat_F_grad_phi_k1_phi_l_j)
# ----------------------------------------------------------------------------------------------------------
mat_F_grad_phi_k1_psi_k_list.append(mat_F_grad_phi_k1_psi_k_j_list)
mat_F_grad_phi_k1_phi_l_list.append(mat_F_grad_phi_k1_phi_l_j_list)
# ==============================================================================================================
# STABILIZATION OPERATOR
# ==============================================================================================================
mat_F_psi_k_phi_k1_list = []
for mface in mfaces:
mat_F_phi_k1_psi_k = Integration.get_hybrid_mass_matrix_in_face(
mcell.cell, mface.face, cell_basis_k1, face_basis_k,
mface.face.reference_frame_transformation_matrix)
mat_F_psi_k_phi_k1_list.append(mat_F_phi_k1_psi_k)
return (
mat_F_phi_k_phi_l_list,
mat_F_phi_k_psi_k_list,
mat_F_grad_phi_k1_psi_k_list,
mat_F_grad_phi_k1_phi_l_list,
mat_F_psi_k_phi_k1_list,
)
def get_stabilization_operator(
self,
cell: Cell,
faces: List[Face],
cell_basis_l: Basis,
cell_basis_k: Basis,
cell_basis_k1: Basis,
face_basis_k: Basis,
unknown: Unknown,
) -> Mat:
"""
================================================================================================================
Method :
================================================================================================================
================================================================================================================
Parameters :
================================================================================================================
-
================================================================================================================
Returns :
================================================================================================================
-
"""
# --------------------------------------------------------------------------------------------------------------
# rec
# --------------------------------------------------------------------------------------------------------------
local_reconstruction_operator = self.get_local_reconstruction_operator(
cell, faces, cell_basis_l, cell_basis_k, cell_basis_k1,
face_basis_k, unknown)
# --------------------------------------------------------------------------------------------------------------
# Initializing the local stabilization form matrix
# --------------------------------------------------------------------------------------------------------------
local_problem_size = self.get_local_problem_size(
faces, cell_basis_l, face_basis_k, unknown)
local_stabilization_operator = np.zeros(
(local_problem_size, local_problem_size))
derivative_directions = range(unknown.problem_dimension)
directions = range(unknown.field_dimension)
for i in directions:
# # ------------------------------------------------------------------------------------------------------
# r0_r = i * cell_basis_k1.basis_dimension
# r1_r = (i + 1) * cell_basis_k1.basis_dimension
# ------------------------------------------------------------------------------------------------------
c0_c = i * cell_basis_l.basis_dimension
c1_c = (i + 1) * cell_basis_l.basis_dimension
for f, face in enumerate(faces):
passmat = Operator.get_face_passmat(cell, face)
# normal_vector_component = passmat[-1, j]
# --------------------------------------------------------------------------------------------------
# Getting the indices corresponding to the face_indexth face for the field on the ith axis
# --------------------------------------------------------------------------------------------------
c0_f = (
unknown.field_dimension * cell_basis_l.basis_dimension +
f * unknown.field_dimension * face_basis_k.basis_dimension
+ i * face_basis_k.basis_dimension)
c1_f = (
unknown.field_dimension * cell_basis_l.basis_dimension +
f * unknown.field_dimension * face_basis_k.basis_dimension
+ (i + 1) * face_basis_k.basis_dimension)
# ------------------------------------------------------------------------------------------------------
# Compting matrices 1
# ------------------------------------------------------------------------------------------------------
m_face_id = np.eye(face_basis_k.basis_dimension)
m_face_psi_k_psi_k = Integration.get_face_mass_matrix_in_face(
face, face_basis_k, face_basis_k, passmat)
m_face_psi_k_psi_k_inv = np.linalg.inv(m_face_psi_k_psi_k)
# ------------------------------------------------------------------------------------------------------
m_cell_phi_k_phi_k = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_k, cell_basis_k)
m_cell_phi_k_phi_k_inv = np.linalg.inv(m_cell_phi_k_phi_k)
m_cell_phi_l_phi_l = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_l, cell_basis_l)
m_cell_phi_l_phi_l_inv = np.linalg.inv(m_cell_phi_l_phi_l)
# ------------------------------------------------------------------------------------------------------
# proj T -> F, l -> k
# ------------------------------------------------------------------------------------------------------
m_face_phi_l_psi_k = Integration.get_hybrid_mass_matrix_in_face(
cell, face, cell_basis_l, face_basis_k, passmat)
m_face_psi_k_phi_l = m_face_phi_l_psi_k.T
pi_c_f_l_k = m_face_psi_k_psi_k_inv @ m_face_psi_k_phi_l
# ------------------------------------------------------------------------------------------------------
# proj T -> F, k -> k
# ------------------------------------------------------------------------------------------------------
m_face_phi_k_psi_k = Integration.get_hybrid_mass_matrix_in_face(
cell, face, cell_basis_k, face_basis_k, passmat)
m_face_psi_k_phi_k = m_face_phi_k_psi_k.T
pi_c_f_k_k = m_face_psi_k_psi_k_inv @ m_face_psi_k_phi_k
# ------------------------------------------------------------------------------------------------------
# proj T -> F, k1 -> k
# ------------------------------------------------------------------------------------------------------
m_face_phi_k1_psi_k = Integration.get_hybrid_mass_matrix_in_face(
cell, face, cell_basis_k1, face_basis_k, passmat)
m_face_psi_k_phi_k1 = m_face_phi_k1_psi_k.T
pi_c_f_k1_k = m_face_psi_k_psi_k_inv @ m_face_psi_k_phi_k1
# ------------------------------------------------------------------------------------------------------
# proj T -> T, k1 -> l
# ------------------------------------------------------------------------------------------------------
m_cell_phi_l_phi_k1 = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_l, cell_basis_k1)
pi_c_c_k1_l = m_cell_phi_l_phi_l_inv @ m_cell_phi_l_phi_k1
# ------------------------------------------------------------------------------------------------------
m_stab_face_jump = np.zeros(
(face_basis_k.basis_dimension, local_problem_size))
m_stab_face_jump[:, c0_c:c1_c] -= pi_c_f_l_k
m_stab_face_jump[:, c0_f:c1_f] += m_face_id
# ------------------------------------------------------------------------------------------------------
c0_r = i * cell_basis_k1.basis_dimension
c1_r = (i + 1) * cell_basis_k1.basis_dimension
m_stab_face_jump -= pi_c_f_k1_k @ local_reconstruction_operator[
c0_r:c1_r, :]
m_stab_face_jump += pi_c_f_l_k @ (
pi_c_c_k1_l @ local_reconstruction_operator[c0_r:c1_r, :])
h_f = 1.0 / face.diameter
local_stabilization_operator += h_f * m_stab_face_jump.T @ m_face_psi_k_psi_k_inv @ m_stab_face_jump
return local_stabilization_operator
def get_local_gradient_operator(
self,
cell: Cell,
faces: List[Face],
cell_basis_l: Basis,
cell_basis_k: Basis,
cell_basis_k1: Basis,
face_basis_k: Basis,
unknown: Unknown,
) -> Mat:
"""
================================================================================================================
Method :
================================================================================================================
================================================================================================================
Parameters :
================================================================================================================
-
================================================================================================================
Returns :
================================================================================================================
-
"""
# --------------------------------------------------------------------------------------------------------------
# Getting the local problem size depending on the problem dimension and the field dimension
# --------------------------------------------------------------------------------------------------------------
local_problem_size = self.get_local_problem_size(
faces, cell_basis_l, face_basis_k, unknown)
# --------------------------------------------------------------------------------------------------------------
# Initializing the local gradient operator matrix
# --------------------------------------------------------------------------------------------------------------
local_gradient_operator = np.zeros(
(len(unknown.indices) * cell_basis_k.basis_dimension,
local_problem_size))
# --------------------------------------------------------------------------------------------------------------
m_cell_phi_k_phi_k = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_k, cell_basis_k)
m_cell_phi_k_phi_k_inv = np.linalg.inv(m_cell_phi_k_phi_k)
# --------------------------------------------------------------------------------------------------------------
derivative_directions = range(unknown.problem_dimension)
directions = range(unknown.field_dimension)
for j in derivative_directions:
# ----------------------------------------------------------------------------------------------------------
# Compting matrices 1
# ----------------------------------------------------------------------------------------------------------
m_cell_phi_k_grad_phi_l = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_k, cell_basis_l, j)
for f, face in enumerate(faces):
passmat = Operator.get_face_passmat(cell, face)
normal_vector_component = passmat[-1, j]
# m_face_phi_l_psi_k = Integration.get_hybrid_mass_matrix_in_face(
# cell, face, cell_basis_l, face_basis_k, passmat
# )
m_face_phi_k_psi_k = Integration.get_hybrid_mass_matrix_in_face(
cell, face, cell_basis_k, face_basis_k, passmat)
m_face_phi_k_phi_l = Integration.get_cell_mass_matrix_in_face(
cell, face, cell_basis_k, cell_basis_l)
for i in directions:
# --------------------------------------------------------------------------------------------------
# bkbjkj
# --------------------------------------------------------------------------------------------------
line = self.get_line_from_indices(i, j, unknown)
r0 = line * cell_basis_k.basis_dimension
r1 = (line + 1) * cell_basis_k.basis_dimension
# --------------------------------------------------------------------------------------------------
c0_T = i * cell_basis_l.basis_dimension
c1_T = (i + 1) * cell_basis_l.basis_dimension
# --------------------------------------------------------------------------------------------------
# Getting the indices corresponding to the face_index-th face for the field on the ith axis
# --------------------------------------------------------------------------------------------------
c0_F = (unknown.field_dimension *
cell_basis_l.basis_dimension +
f * unknown.field_dimension *
face_basis_k.basis_dimension +
i * face_basis_k.basis_dimension)
c1_F = (unknown.field_dimension *
cell_basis_l.basis_dimension +
f * unknown.field_dimension *
face_basis_k.basis_dimension +
(i + 1) * face_basis_k.basis_dimension)
# --------------------------------------------------------------------------------------------------
# grad
# --------------------------------------------------------------------------------------------------
# local_gradient_operator[r0:r1, c0_T:c1_T] += m_cell_phi_k_grad_phi_l
local_gradient_operator[
r0:r1, c0_F:
c1_F] += m_face_phi_k_psi_k * normal_vector_component
local_gradient_operator[
r0:r1, c0_T:
c1_T] -= m_face_phi_k_phi_l * normal_vector_component
for i in directions:
line = self.get_line_from_indices(i, j, unknown)
r0 = line * cell_basis_k.basis_dimension
r1 = (line + 1) * cell_basis_k.basis_dimension
# ------------------------------------------------------------------------------------------------------
c0_T = i * cell_basis_l.basis_dimension
c1_T = (i + 1) * cell_basis_l.basis_dimension
local_gradient_operator[r0:r1,
c0_T:c1_T] += m_cell_phi_k_grad_phi_l
local_gradient_operator[
r0:
r1, :] = m_cell_phi_k_phi_k_inv @ local_gradient_operator[
r0:r1, :]
return local_gradient_operator
def __init__(
self,
cell_faces_connectivity_matrix: Mat,
mcell: Mcell,
mfaces: List[Mface],
cell_basis_l: Basis,
cell_basis_k: Basis,
cell_basis_k1: Basis,
unknown: Unknown,
):
"""
================================================================================================================
Class :
================================================================================================================
The Mbox class
================================================================================================================
Parameters :
================================================================================================================
-
================================================================================================================
Attributes :
================================================================================================================
-
"""
# ==============================================================================================================
# GRADIENT OPERATOR / STABILIZATION OPERATOR
# ==============================================================================================================
self.mat_F_phi_k_phi_l_list = []
self.mat_F_phi_k_psi_k_list = []
for mface in mfaces:
mat_F_phi_k_phi_l = Integration.get_cell_mass_matrix_in_face(
mcell.cell, mface.face, cell_basis_k, cell_basis_l)
self.mat_F_phi_k_phi_l_list.append(mat_F_phi_k_phi_l_list)
# ----------------------------------------------------------------------------------------------------------
mat_F_phi_k_psi_k = Integration.get_hybrid_mass_matrix_in_face(
mcell.cell, mface.face, cell_basis_k, face_basis_k,
mface.face.reference_frame_transformation_matrix)
self.mat_F_phi_k_psi_k_list.append(mat_F_phi_k_psi_k)
# ==============================================================================================================
# RECONSTRUCTION OPERATOR
# ==============================================================================================================
self.mat_F_grad_phi_k1_psi_k_list = []
self.mat_F_grad_phi_k1_phi_l_list = []
for mface in mfaces:
mat_F_grad_phi_k1_psi_k_j_list = []
mat_F_grad_phi_k1_phi_l_j_list = []
for j in range(len(unknown.problem_dimension)):
# ------------------------------------------------------------------------------------------------------
mat_F_grad_phi_k1_psi_k_j = Integration.get_hybrid_advection_matrix_in_face(
mcell.cell,
mface.face,
cell_basis_k1,
face_basis_k,
mface.face.reference_frame_transformation_matrix,
j,
)
mat_F_grad_phi_k1_psi_k_j_list.append(
mat_F_grad_phi_k1_psi_k_j)
# ------------------------------------------------------------------------------------------------------
mat_F_phi_l_grad_phi_k1_j = Integration.get_cell_advection_matrix_in_face(
mcell.cell, mface.face, cell_basis_l, cell_basis_k1, j)
# ------------------------------------------------------------------------------------------------------
mat_F_grad_phi_k1_phi_l_j = mat_F_phi_l_grad_phi_k1_j.T
mat_F_grad_phi_k1_phi_l_j_list.append(
mat_F_grad_phi_k1_phi_l_j)
# ----------------------------------------------------------------------------------------------------------
self.mat_F_grad_phi_k1_psi_k_list.append(
mat_F_grad_phi_k1_psi_k_j_list)
self.mat_F_grad_phi_k1_phi_l_list.append(
mat_F_grad_phi_k1_phi_l_j_list)
# ==============================================================================================================
# STABILIZATION OPERATOR
# ==============================================================================================================
self.mat_F_psi_k_phi_k1_list = []
for mface in mfaces:
mat_F_phi_k1_psi_k = Integration.get_hybrid_mass_matrix_in_face(
mcell.cell, mface.face, cell_basis_k1, face_basis_k,
mface.face.reference_frame_transformation_matrix)
self.mat_F_psi_k_phi_k1_list.append(mat_F_phi_k1_psi_k)
