def __init__(self, cell: Cell, cell_basis_l: Basis, cell_basis_k: Basis, cell_basis_k1: Basis, unknown: Unknown):
"""
================================================================================================================
Class :
================================================================================================================
================================================================================================================
Parameters :
================================================================================================================
================================================================================================================
Attributes :
================================================================================================================
"""
# --------------------------------------------------------------------------------------------------------------
# Building the cell
# --------------------------------------------------------------------------------------------------------------
centroid = cell.centroid
volume = cell.volume
quadrature_points = cell.quadrature_points
quadrature_weights = cell.quadrature_weights
# --------------------------------------------------------------------------------------------------------------
super().__init__(centroid, volume, diameter, quadrature_points, quadrature_weights)
m_phi_k_phi_k = Integration.get_cell_mass_matrix_in_cell(cell, cell_basis_k, cell_basis_k)
m_phi_k_phi_k_inv = np.linalg.inv(m_phi_k_phi_k)
m_grad_phi_k1_grad_phi_k1_list = []
m_phi_k_grad_phi_l_list = []
m_grad_phi_k1_phi_l_list = []
for j in range(unknown.problem_dimension):
# ----------------------------------------------------------------------------------------------------------
m_grad_phi_k1_grad_phi_k1_j = Integration.get_cell_stiffness_matrix_in_cell(
cell, cell_basis_k1, cell_basis_k1, j
)
m_grad_phi_k1_grad_phi_k1_list.append(m_grad_phi_k1_grad_phi_k1_j)
# ----------------------------------------------------------------------------------------------------------
m_phi_k_grad_phi_l_j = Integration.get_cell_advection_matrix_in_cell(cell, cell_basis_k, cell_basis_l, j)
m_phi_k_grad_phi_l_list.append(m_phi_k_grad_phi_l_j)
# ----------------------------------------------------------------------------------------------------------
m_phi_l_grad_phi_k1_j = Integration.get_cell_advection_matrix_in_cell(cell, cell_basis_l, cell_basis_k1, j)
m_grad_phi_k1_phi_l_j = m_phi_l_grad_phi_k1_j.T
m_grad_phi_k1_phi_l_list.append(m_grad_phi_k1_phi_l_j)
def compute_cell_matrices(self, cell: Cell, cell_basis_l: Basis,
cell_basis_k: Basis, cell_basis_k1: Basis,
unknown: Unknown):
"""
================================================================================================================
Method :
================================================================================================================
================================================================================================================
Parameters :
================================================================================================================
-
================================================================================================================
Returns :
================================================================================================================
-
"""
# ==============================================================================================================
# GRADIENT OPERATOR
# ==============================================================================================================
# left-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_phi_k_phi_k = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_k, cell_basis_k)
mat_T_phi_k_phi_k_inv = np.linalg.inv(mat_T_phi_k_phi_k)
# --------------------------------------------------------------------------------------------------------------
# right-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_phi_k_grad_phi_l_list = []
for j in range(unknown.problem_dimension):
mat_T_phi_k_grad_phi_l = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_k, cell_basis_l, j)
mat_T_phi_k_grad_phi_l_list.append(mat_T_phi_k_grad_phi_l)
# ==============================================================================================================
# RECONSTRUCTION OPERATOR
# ==============================================================================================================
# left-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_grad_phi_k1_grad_phi_k1_inv_list = []
for j in range(unknown.problem_dimension):
mat_T_grad_phi_k1_grad_phi_k1_j = Integration.get_cell_stiffness_matrix_in_cell(
cell, cell_basis_k1, cell_basis_k1, j)
mat_T_grad_phi_k1_grad_phi_k1_inv_list.append(
mat_T_grad_phi_k1_grad_phi_k1_j)
# --------------------------------------------------------------------------------------------------------------
# right-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_grad_phi_k1_phi_l_list = []
for j in range(unknown.problem_dimension):
mat_T_phi_l_grad_phi_k1_j = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_l, cell_basis_k1, j)
mat_T_grad_phi_k1_phi_l_j = mat_T_phi_l_grad_phi_k1_j.T
mat_T_grad_phi_k1_phi_l_list.append(mat_T_grad_phi_k1_phi_l_j)
# ==============================================================================================================
# STABILIZATION OPERATOR
# ==============================================================================================================
mat_T_phi_k_phi_k1 = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_k, cell_basis_k1)
proj_T_T_k1_k = mat_T_phi_k_phi_k_inv @ mat_T_phi_k_phi_k1
# ==============================================================================================================
# PROJECTION OPERATOR
# ==============================================================================================================
mat_T_phi_l_phi_l = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_l, cell_basis_l)
mat_T_phi_l_phi_l_inv = np.linalg.inv(mat_T_phi_l_phi_l)
return (
mat_T_phi_k_phi_k_inv,
mat_T_phi_k_grad_phi_l_list,
mat_T_grad_phi_k1_grad_phi_k1_inv_list,
mat_T_grad_phi_k1_phi_l_list,
proj_T_T_k1_k,
)
def __init__(
self,
cell_vertices_connectivity_matrix: Mat,
cell: Cell,
cell_basis_l: Basis,
cell_basis_k: Basis,
cell_basis_k1: Basis,
):
"""
================================================================================================================
Class :
================================================================================================================
The Mcell class
================================================================================================================
Parameters :
================================================================================================================
-
================================================================================================================
Attributes :
================================================================================================================
-
"""
# ==============================================================================================================
# GRADIENT OPERATOR
# ==============================================================================================================
# left-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_phi_k_phi_k = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_k, cell_basis_k)
mat_T_phi_k_phi_k_inv = np.linalg.inv(mat_T_phi_k_phi_k)
# --------------------------------------------------------------------------------------------------------------
# right-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_phi_k_grad_phi_l_x = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_k, cell_basis_l, 0)
mat_T_phi_k_grad_phi_l_y = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_k, cell_basis_l, 1)
mat_T_phi_k_grad_phi_l_list = [
mat_T_phi_k_grad_phi_l_x, mat_T_phi_k_grad_phi_l_y
]
# ==============================================================================================================
# RECONSTRUCTION OPERATOR
# ==============================================================================================================
# left-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_grad_phi_k1_grad_phi_k1_x = Integration.get_cell_stiffness_matrix_in_cell(
cell, cell_basis_k1, cell_basis_k1, 0)
mat_T_grad_phi_k1_grad_phi_k1_y = Integration.get_cell_stiffness_matrix_in_cell(
cell, cell_basis_k1, cell_basis_k1, 1)
mat_T_grad_phi_k1_grad_phi_k1_inv_list = [
mat_T_grad_phi_k1_grad_phi_k1_x, mat_T_grad_phi_k1_grad_phi_k1_y
]
# --------------------------------------------------------------------------------------------------------------
# right-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_phi_l_grad_phi_k1_x = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_l, cell_basis_k1, 0)
mat_T_phi_l_grad_phi_k1_y = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_l, cell_basis_k1, 1)
mat_T_grad_phi_k1_phi_l_list = [
mat_T_phi_l_grad_phi_k1_x, mat_T_phi_l_grad_phi_k1_y
]
# ==============================================================================================================
# STABILIZATION OPERATOR
# ==============================================================================================================
mat_T_phi_k_phi_k1 = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_k, cell_basis_k1)
proj_T_T_k1_k = mat_T_phi_k_phi_k_inv @ mat_T_phi_k_phi_k1
# ==============================================================================================================
# PROJECTION OPERATOR
# ==============================================================================================================
mat_T_phi_l_phi_l = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_l, cell_basis_l)
mat_T_phi_l_phi_l_inv = np.linalg.inv(mat_T_phi_l_phi_l)
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_vertices_connectivity_matrix: Mat,
cell: Cell,
cell_basis_l: Basis,
cell_basis_k: Basis,
cell_basis_k1: Basis,
unknown: Unknown,
):
"""
================================================================================================================
Class :
================================================================================================================
The Mcell class
================================================================================================================
Parameters :
================================================================================================================
-
================================================================================================================
Attributes :
================================================================================================================
-
"""
# ==============================================================================================================
# GRADIENT OPERATOR
# ==============================================================================================================
# left-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_phi_k_phi_k = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_k, cell_basis_k)
self.mat_T_phi_k_phi_k_inv = np.linalg.inv(mat_T_phi_k_phi_k)
# --------------------------------------------------------------------------------------------------------------
# right-hand side
# --------------------------------------------------------------------------------------------------------------
self.mat_T_phi_k_grad_phi_l_list = []
for j in range(unknown.problem_dimension):
mat_T_phi_k_grad_phi_l = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_k, cell_basis_l, j)
self.mat_T_phi_k_grad_phi_l_list.append(mat_T_phi_k_grad_phi_l)
# ==============================================================================================================
# RECONSTRUCTION OPERATOR
# ==============================================================================================================
# left-hand side
# --------------------------------------------------------------------------------------------------------------
self.mat_T_grad_phi_k1_grad_phi_k1_inv_list = []
for j in range(unknown.problem_dimension):
mat_T_grad_phi_k1_grad_phi_k1_j = Integration.get_cell_stiffness_matrix_in_cell(
cell, cell_basis_k1, cell_basis_k1, j)
self.mat_T_grad_phi_k1_grad_phi_k1_inv_list.append(
mat_T_grad_phi_k1_grad_phi_k1_j)
# --------------------------------------------------------------------------------------------------------------
# right-hand side
# --------------------------------------------------------------------------------------------------------------
self.mat_T_grad_phi_k1_phi_l_list = []
for j in range(unknown.problem_dimension):
mat_T_phi_l_grad_phi_k1_j = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_l, cell_basis_k1, j)
mat_T_grad_phi_k1_phi_l_j = mat_T_phi_l_grad_phi_k1_j.T
self.mat_T_grad_phi_k1_phi_l_list.append(mat_T_grad_phi_k1_phi_l_j)
# ==============================================================================================================
# STABILIZATION OPERATOR
# ==============================================================================================================
mat_T_phi_k_phi_k1 = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_k, cell_basis_k1)
self.proj_T_T_k1_k = mat_T_phi_k_phi_k_inv @ mat_T_phi_k_phi_k1
# ==============================================================================================================
# PROJECTION OPERATOR
# ==============================================================================================================
mat_T_phi_l_phi_l = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_l, cell_basis_l)
self.mat_T_phi_l_phi_l_inv = np.linalg.inv(mat_T_phi_l_phi_l)
def compute_cell_matrices(self, cell: Cell, cell_basis_l: Basis,
cell_basis_k: Basis, cell_basis_k1: Basis):
"""
================================================================================================================
Method :
================================================================================================================
================================================================================================================
Parameters :
================================================================================================================
-
================================================================================================================
Returns :
================================================================================================================
-
"""
# ==============================================================================================================
# GRADIENT OPERATOR
# ==============================================================================================================
# left-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_phi_k_phi_k = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_k, cell_basis_k)
mat_T_phi_k_phi_k_inv = np.linalg.inv(mat_T_phi_k_phi_k)
# --------------------------------------------------------------------------------------------------------------
# right-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_phi_k_grad_phi_l_x = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_k, cell_basis_l, 0)
mat_T_phi_k_grad_phi_l_list = [mat_T_phi_k_grad_phi_l_x]
# ==============================================================================================================
# RECONSTRUCTION OPERATOR
# ==============================================================================================================
# left-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_grad_phi_k1_grad_phi_k1_x = Integration.get_cell_stiffness_matrix_in_cell(
cell, cell_basis_k1, cell_basis_k1, 0)
mat_T_grad_phi_k1_grad_phi_k1_inv_list = [
mat_T_grad_phi_k1_grad_phi_k1_x
]
# --------------------------------------------------------------------------------------------------------------
# right-hand side
# --------------------------------------------------------------------------------------------------------------
mat_T_phi_l_grad_phi_k1_x = Integration.get_cell_advection_matrix_in_cell(
cell, cell_basis_l, cell_basis_k1, 0)
mat_T_grad_phi_k1_phi_l_x = mat_T_phi_l_grad_phi_k1_x.T
mat_T_grad_phi_k1_phi_l_list = [mat_T_grad_phi_k1_phi_l_x]
# ==============================================================================================================
# STABILIZATION OPERATOR
# ==============================================================================================================
mat_T_phi_k_phi_k1 = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_k, cell_basis_k1)
proj_T_T_k1_k = mat_T_phi_k_phi_k_inv @ mat_T_phi_k_phi_k1
# ==============================================================================================================
# PROJECTION OPERATOR
# ==============================================================================================================
mat_T_phi_l_phi_l = Integration.get_cell_mass_matrix_in_cell(
cell, cell_basis_l, cell_basis_l)
mat_T_phi_l_phi_l_inv = np.linalg.inv(mat_T_phi_l_phi_l)
return (
mat_T_phi_k_phi_k_inv,
mat_T_phi_k_grad_phi_l_list,
mat_T_grad_phi_k1_grad_phi_k1_inv_list,
mat_T_grad_phi_k1_phi_l_list,
proj_T_T_k1_k,
)
