mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 23:58:09 +08:00
Lars Ruthotto
261 lines
10 KiB
Python
261 lines
10 KiB
Python
import numpy as np
|
|
from scipy import sparse as sp
|
|
from sputils import sdiag, speye, kron3, spzeros
|
|
from utils import mkvc
|
|
|
|
|
|
def ddx(n):
|
|
"""Define 1D derivatives, inner, this means we go from n+1 to n+1"""
|
|
return sp.spdiags((np.ones((n+1, 1))*[-1, 1]).T, [0, 1], n, n+1, format="csr")
|
|
|
|
|
|
def checkBC(bc):
|
|
""" Checks if boundary condition 'bc' is valid. """
|
|
if(type(bc) is str):
|
|
bc = [bc, bc]
|
|
assert type(bc) is list, 'bc must be a list'
|
|
assert len(bc) == 2, 'bc must have two elements'
|
|
|
|
for bc_i in bc:
|
|
assert type(bc_i) is str, "each bc must be a string"
|
|
assert bc_i in ['dirichlet', 'neumann'], "each bc must be either, 'dirichlet' or 'neumann'"
|
|
return bc
|
|
|
|
|
|
def ddxCellGrad(n, bc):
|
|
"""Create 1D derivative operator from cell-centres to nodes this means we go from n to n+1"""
|
|
bc = checkBC(bc)
|
|
|
|
D = sp.spdiags((np.ones((n+1, 1))*[-1, 1]).T, [-1, 0], n+1, n, format="csr")
|
|
# Set the first side
|
|
if(bc[0] == 'dirichlet'):
|
|
D[0, 0] = 2
|
|
elif(bc[0] == 'neumann'):
|
|
D[0, 0] = 0
|
|
# Set the second side
|
|
if(bc[1] == 'dirichlet'):
|
|
D[-1, -1] = -2
|
|
elif(bc[1] == 'neumann'):
|
|
D[-1, -1] = 0
|
|
return D
|
|
|
|
|
|
def av(n):
|
|
"""Define 1D averaging operator from cell-centres to nodes."""
|
|
return sp.spdiags((0.5*np.ones((n+1, 1))*[1, 1]).T, [0, 1], n, n+1, format="csr")
|
|
|
|
|
|
class DiffOperators(object):
|
|
"""
|
|
Class creates the differential operators that you need!
|
|
"""
|
|
def __init__(self):
|
|
raise Exception('DiffOperators is a base class providing differential operators on meshes and cannot run on its own. Inherit to your favorite Mesh class.')
|
|
|
|
def faceDiv():
|
|
doc = "Construct divergence operator (face-stg to cell-centres)."
|
|
|
|
def fget(self):
|
|
if(self._faceDiv is None):
|
|
# The number of cell centers in each direction
|
|
n = self.n
|
|
# Compute faceDivergence operator on faces
|
|
if(self.dim == 1):
|
|
D = ddx(n[0])
|
|
elif(self.dim == 2):
|
|
D1 = sp.kron(speye(n[1]), ddx(n[0]))
|
|
D2 = sp.kron(ddx(n[1]), speye(n[0]))
|
|
D = sp.hstack((D1, D2), format="csr")
|
|
elif(self.dim == 3):
|
|
D1 = kron3(speye(n[2]), speye(n[1]), ddx(n[0]))
|
|
D2 = kron3(speye(n[2]), ddx(n[1]), speye(n[0]))
|
|
D3 = kron3(ddx(n[2]), speye(n[1]), speye(n[0]))
|
|
D = sp.hstack((D1, D2, D3), format="csr")
|
|
# Compute areas of cell faces & volumes
|
|
S = self.area
|
|
V = self.vol
|
|
self._faceDiv = sdiag(1/V)*D*sdiag(S)
|
|
|
|
return self._faceDiv
|
|
return locals()
|
|
_faceDiv = None
|
|
faceDiv = property(**faceDiv())
|
|
|
|
def nodalGrad():
|
|
doc = "Construct gradient operator (nodes to edges)."
|
|
|
|
def fget(self):
|
|
if(self._nodalGrad is None):
|
|
# The number of cell centers in each direction
|
|
n = self.n
|
|
# Compute divergence operator on faces
|
|
if(self.dim == 1):
|
|
G = ddx(n[0])
|
|
elif(self.dim == 2):
|
|
D1 = sp.kron(speye(n[1]+1), ddx(n[0]))
|
|
D2 = sp.kron(ddx(n[1]), speye(n[0]+1))
|
|
G = sp.vstack((D1, D2), format="csr")
|
|
elif(self.dim == 3):
|
|
D1 = kron3(speye(n[2]+1), speye(n[1]+1), ddx(n[0]))
|
|
D2 = kron3(speye(n[2]+1), ddx(n[1]), speye(n[0]+1))
|
|
D3 = kron3(ddx(n[2]), speye(n[1]+1), speye(n[0]+1))
|
|
G = sp.vstack((D1, D2, D3), format="csr")
|
|
# Compute lengths of cell edges
|
|
L = self.edge
|
|
self._nodalGrad = sdiag(1/L)*G
|
|
return self._nodalGrad
|
|
return locals()
|
|
_nodalGrad = None
|
|
nodalGrad = property(**nodalGrad())
|
|
|
|
def setCellGradBC(self, BC):
|
|
"""
|
|
Function that sets the boundary conditions for cell-centred derivative operators.
|
|
|
|
Examples:
|
|
|
|
BC = 'neumann' # Neumann in all directions
|
|
BC = ['neumann', 'dirichlet', 'neumann'] # 3D, Dirichlet in y Neumann else
|
|
BC = [['neumann', 'dirichlet'], 'dirichlet', 'dirichlet'] # 3D, Neumann in x on bottom of domain,
|
|
# Dirichlet else
|
|
|
|
"""
|
|
if(type(BC) is str):
|
|
BC = [BC for _ in self.n] # Repeat the str self.dim times
|
|
elif(type(BC) is list):
|
|
assert len(BC) == self.dim, 'BC list must be the size of your mesh'
|
|
else:
|
|
raise Exception("BC must be a str or a list.")
|
|
|
|
for i, bc_i in enumerate(BC):
|
|
BC[i] = checkBC(bc_i)
|
|
|
|
self._cellGrad = None # ensure we create a new gradient next time we call it
|
|
self._cellGradBC = BC
|
|
return BC
|
|
_cellGradBC = 'neumann'
|
|
|
|
def cellGrad():
|
|
doc = "The cell centered Gradient, takes you to cell faces."
|
|
|
|
def fget(self):
|
|
if(self._cellGrad is None):
|
|
BC = self.setCellGradBC(self._cellGradBC)
|
|
n = self.n
|
|
if(self.dim == 1):
|
|
G = ddxCellGrad(n[0], BC[0])
|
|
elif(self.dim == 2):
|
|
G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC[0]))
|
|
G2 = sp.kron(ddxCellGrad(n[1], BC[1]), speye(n[0]))
|
|
G = sp.vstack((G1, G2), format="csr")
|
|
elif(self.dim == 3):
|
|
G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC[0]))
|
|
G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC[1]), speye(n[0]))
|
|
G3 = kron3(ddxCellGrad(n[2], BC[2]), speye(n[1]), speye(n[0]))
|
|
G = sp.vstack((G1, G2, G3), format="csr")
|
|
# Compute areas of cell faces & volumes
|
|
S = self.area
|
|
V = self.vol
|
|
self._cellGrad = sdiag(S)*G*sdiag(1/V)
|
|
return self._cellGrad
|
|
return locals()
|
|
_cellGrad = None
|
|
cellGrad = property(**cellGrad())
|
|
|
|
def edgeCurl():
|
|
doc = "Construct the 3D curl operator."
|
|
|
|
def fget(self):
|
|
if(self._edgeCurl is None):
|
|
# The number of cell centers in each direction
|
|
n1 = np.size(self.hx)
|
|
n2 = np.size(self.hy)
|
|
n3 = np.size(self.hz)
|
|
|
|
# Compute lengths of cell edges
|
|
L = self.edge
|
|
|
|
# Compute areas of cell faces
|
|
S = self.area
|
|
|
|
# Compute divergence operator on faces
|
|
d1 = ddx(n1)
|
|
d2 = ddx(n2)
|
|
d3 = ddx(n3)
|
|
|
|
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])
|
|
|
|
C = sp.vstack((sp.hstack((O1, -D32, D23)),
|
|
sp.hstack((D31, O2, -D13)),
|
|
sp.hstack((-D21, D12, O3))), format="csr")
|
|
|
|
self._edgeCurl = sdiag(1/S)*(C*sdiag(L))
|
|
return self._edgeCurl
|
|
return locals()
|
|
_edgeCurl = None
|
|
edgeCurl = property(**edgeCurl())
|
|
|
|
def faceAve():
|
|
doc = "Construct the averaging operator on cell faces to cell centers."
|
|
|
|
def fget(self):
|
|
if(self._faceAve is None):
|
|
n = self.n
|
|
if(self.dim == 1):
|
|
self._faceAve = av(n[0])
|
|
elif(self.dim == 2):
|
|
self._faceAve = sp.hstack((sp.kron(speye(n[1]), av(n[0])),
|
|
sp.kron(av(n[1]), speye(n[0]))), format="csr")
|
|
elif(self.dim == 3):
|
|
self._faceAve = sp.hstack((kron3(speye(n[2]), speye(n[1]), av(n[0])),
|
|
kron3(speye(n[2]), av(n[1]), speye(n[0])),
|
|
kron3(av(n[2]), speye(n[1]), speye(n[0]))), format="csr")
|
|
return self._faceAve
|
|
return locals()
|
|
_faceAve = None
|
|
faceAve = property(**faceAve())
|
|
|
|
def edgeAve():
|
|
doc = "Construct the averaging operator on cell edges to cell centers."
|
|
|
|
def fget(self):
|
|
if(self._edgeAve is None):
|
|
# The number of cell centers in each direction
|
|
n = self.n
|
|
if(self.dim == 1):
|
|
raise Exception('Edge Averaging does not make sense in 1D: Use Identity?')
|
|
elif(self.dim == 2):
|
|
self._edgeAve = sp.hstack((sp.kron(av(n[1]), speye(n[0])),
|
|
sp.kron(speye(n[1]), av(n[0]))), format="csr")
|
|
elif(self.dim == 3):
|
|
self._edgeAve = sp.hstack((kron3(av(n[2]), av(n[1]), speye(n[0])),
|
|
kron3(av(n[2]), speye(n[1]), av(n[0])),
|
|
kron3(speye(n[2]), av(n[1]), av(n[0]))), format="csr")
|
|
return self._edgeAve
|
|
return locals()
|
|
_edgeAve = None
|
|
edgeAve = property(**edgeAve())
|
|
|
|
def getEdgeMass(self, materialProp=None):
|
|
"""mass matix for products of edge functions w'*M(materialProp)*e"""
|
|
if(materialProp is None):
|
|
materialProp = np.ones(self.nC)
|
|
Av = self.edgeAve
|
|
return sdiag(Av.T * (self.vol * mkvc(materialProp)))
|
|
|
|
def getFaceMass(self, materialProp=None):
|
|
"""mass matix for products of edge functions w'*M(materialProp)*e"""
|
|
if(materialProp is None):
|
|
materialProp = np.ones(self.nC)
|
|
Av = self.faceAve
|
|
return sdiag(Av.T*(self.vol*mkvc(materialProp)))
|