mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 10:49:37 +08:00
ehaber99
207 lines
5.3 KiB
Python
207 lines
5.3 KiB
Python
import numpy as np
|
|
from scipy import sparse
|
|
from utils import mkvc
|
|
from sputils import *
|
|
#from sputils import ddx, sdiag, speye, kron3, spzeros, appendBottom3,
|
|
|
|
def getVol(h):
|
|
|
|
# Cell sizes in each direction
|
|
h1 = h[0]
|
|
h2 = h[1]
|
|
h3 = h[2]
|
|
|
|
# Compute cell volumes
|
|
V = mkvc(np.outer(mkvc(np.outer(h1,h2)),h3))
|
|
|
|
return V
|
|
|
|
def getArea(h):
|
|
|
|
# Cell sizes in each direction
|
|
h1 = h[0]
|
|
h2 = h[1]
|
|
h3 = h[2]
|
|
|
|
# The number of cell centers in each direction
|
|
n1 = np.size(h1)
|
|
n2 = np.size(h2)
|
|
n3 = np.size(h3)
|
|
# Compute areas of cell faces
|
|
area1 = mkvc(np.outer(np.ones(n1+1),np.outer(h2,h3)))
|
|
area2 = mkvc(np.outer(h1,mkvc(np.outer(np.ones(n2+1),h3))))
|
|
area3 = mkvc(np.outer(h1,mkvc(np.outer(h2,np.ones(n3+1)))))
|
|
area = np.hstack((np.hstack((area1, area2)), area3))
|
|
|
|
return area
|
|
|
|
def getLength(h):
|
|
|
|
h1 = h[0]
|
|
h2 = h[1]
|
|
h3 = h[2]
|
|
|
|
# The number of cell centers in each direction
|
|
n1 = np.size(h1)
|
|
n2 = np.size(h2)
|
|
n3 = np.size(h3)
|
|
|
|
# compute the length of each edge
|
|
Length1 = mkvc(np.outer(h1,mkvc(np.outer(np.ones(n2+1),np.ones(n3+1)))))
|
|
Length2 = mkvc(np.outer(np.ones(n1+1),mkvc(np.outer(h2,np.ones(n3+1)))))
|
|
Length3 = mkvc(np.outer(np.ones(n1+1),mkvc(np.outer(np.ones(n2+1),h3))))
|
|
|
|
Length = np.hstack((np.hstack((Length1, Length2)), Length3))
|
|
|
|
return Length
|
|
|
|
|
|
def getDivMatrix(h):
|
|
"""Consturct the 3D divergence operator on Faces."""
|
|
|
|
# Cell sizes in each direction
|
|
h1 = h[0]
|
|
h2 = h[1]
|
|
h3 = h[2]
|
|
|
|
# The number of cell centers in each direction
|
|
n1 = np.size(h1)
|
|
n2 = np.size(h2)
|
|
n3 = np.size(h3)
|
|
|
|
area = getArea(h)
|
|
S = sdiag(area)
|
|
|
|
# Compute cell volumes
|
|
V = getVol(h)
|
|
|
|
# Compute divergence operator on faces
|
|
d1 = ddx(n1)
|
|
d2 = ddx(n2)
|
|
d3 = ddx(n3)
|
|
D1 = kron3(speye(n3), speye(n2), d1)
|
|
D2 = kron3(speye(n3), d2, speye(n1))
|
|
D3 = kron3(d3, speye(n2), speye(n1))
|
|
|
|
D = sparse.hstack((sparse.hstack((D1, D2)), D3))
|
|
return sdiag(1/V)*D*S
|
|
|
|
|
|
def getCurlMatrix(h):
|
|
"""Edge CURL """
|
|
|
|
# Cell sizes in each direction
|
|
h1 = h[0]; h2 = h[1]; h3 = h[2]
|
|
|
|
# The number of cell centers in each direction
|
|
n1 = np.size(h1); n2 = np.size(h2); n3 = np.size(h3)
|
|
|
|
d1 = ddx(n1); d2 = ddx(n2); d3 = ddx(n3)
|
|
# derivatives on x-edge variables
|
|
D32 = kron3(d3, speye(n2), speye(n1+1))
|
|
D23 = kron3(speye(n3), d2, speye(n1+1))
|
|
D31 = kron3(d3, speye(n2+1), speye(n1))
|
|
D13 = kron3(speye(n3), speye(n2+1), d1)
|
|
D21 = kron3(speye(n3+1), d2, speye(n1))
|
|
D12 = kron3(speye(n3+1), speye(n2), d1)
|
|
|
|
O1 = spzeros(np.shape(D32)[0], np.shape(D31)[1])
|
|
O2 = spzeros(np.shape(D31)[0], np.shape(D32)[1])
|
|
O3 = spzeros(np.shape(D21)[0], np.shape(D13)[1])
|
|
|
|
CURL = appendBottom3(
|
|
appendRight3(O1, -D32, D23),
|
|
appendRight3(D31, O2, -D13),
|
|
appendRight3(-D21, D12, O3))
|
|
|
|
|
|
area = getArea(h)
|
|
S = sdiag(1/area)
|
|
|
|
# Compute edge length
|
|
lngth = getLength(h)
|
|
L = sdiag(lngth)
|
|
|
|
return S*(CURL*L)
|
|
|
|
|
|
def getNodalGradient(h):
|
|
"""Nodal Gradients"""
|
|
|
|
# Cell sizes in each direction
|
|
h1 = h[0]; h2 = h[1]; h3 = h[2]
|
|
|
|
# The number of cell centers in each direction
|
|
n1 = np.size(h1); n2 = np.size(h2); n3 = np.size(h3)
|
|
|
|
|
|
D1 = kron3(speye(n3+1), speye(n2+1), ddx(n1))
|
|
D2 = kron3(speye(n3+1), ddx(n2), speye(n1+1))
|
|
D3 = kron3(ddx(n3), speye(n2+1), speye(n1+1))
|
|
|
|
# topological gradient
|
|
GRAD = appendBottom3(D1, D2, D3)
|
|
|
|
# scale for non-uniform mesh
|
|
# Compute edge length
|
|
lngth = getLength(h)
|
|
L = sdiag(1/lngth)
|
|
|
|
return L*GRAD
|
|
|
|
|
|
def getEdgeToCellAverge(h):
|
|
|
|
"""Average from Edge to Cell center """
|
|
|
|
# Cell sizes in each direction
|
|
h1 = h[0]; h2 = h[1]; h3 = h[2]
|
|
|
|
# The number of cell centers in each direction
|
|
n1 = np.size(h1); n2 = np.size(h2); n3 = np.size(h3)
|
|
|
|
a1 = av(n1); a2 = av(n2); a3 = av(n3)
|
|
# derivatives on x-edge variables
|
|
A1 = kron3(a3, a2, speye(n1))
|
|
A2 = kron3(a3, speye(n2), a1)
|
|
A3 = kron3(speye(n3), a2, a1)
|
|
|
|
return appendRight3(A1, A2, A3)
|
|
|
|
|
|
def getFaceToCellAverge(h):
|
|
|
|
"""Average from Edge to Cell center """
|
|
|
|
# Cell sizes in each direction
|
|
h1 = h[0]; h2 = h[1]; h3 = h[2]
|
|
|
|
# The number of cell centers in each direction
|
|
n1 = np.size(h1); n2 = np.size(h2); n3 = np.size(h3)
|
|
|
|
a1 = av(n1); a2 = av(n2); a3 = av(n3)
|
|
# derivatives on x-edge variables
|
|
A1 = kron3(speye(n3), speye(n2), a1)
|
|
A2 = kron3(speye(n3), a2, speye(n1))
|
|
A3 = kron3(a3, speye(n2), speye(n1))
|
|
|
|
return appendRight3(A1, A2, A3)
|
|
|
|
|
|
def getEdgeMassMatrix(h,sigma):
|
|
# mass matix for products of edge functions w'*M(sigma)*e
|
|
|
|
Av = getEdgeToCellAverge(h)
|
|
v = getVol(h)
|
|
sigma = mkvc(sigma)
|
|
|
|
return sdiag(Av.T*(v*sigma))
|
|
|
|
def getFaceMassMatrix(h,sigma):
|
|
# mass matix for products of edge functions w'*M(sigma)*e
|
|
|
|
Av = getFaceToCellAverge(h)
|
|
v = getVol(h)
|
|
sigma = mkvc(sigma)
|
|
|
|
return sdiag(Av.T*(v*sigma)) |