mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 04:07:25 +08:00
Rowan Cockett
337 lines
13 KiB
Python
337 lines
13 KiB
Python
import numpy as np
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from scipy import sparse as sp
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from SimPEG.utils import mkvc, sdiag, speye, kron3, spzeros
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def ddx(n):
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"""Define 1D derivatives, inner, this means we go from n+1 to n+1"""
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return sp.spdiags((np.ones((n+1, 1))*[-1, 1]).T, [0, 1], n, n+1, format="csr")
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def checkBC(bc):
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""" Checks if boundary condition 'bc' is valid. """
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if(type(bc) is str):
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bc = [bc, bc]
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assert type(bc) is list, 'bc must be a list'
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assert len(bc) == 2, 'bc must have two elements'
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for bc_i in bc:
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assert type(bc_i) is str, "each bc must be a string"
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assert bc_i in ['dirichlet', 'neumann'], "each bc must be either, 'dirichlet' or 'neumann'"
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return bc
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def ddxCellGrad(n, bc):
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"""Create 1D derivative operator from cell-centres to nodes this means we go from n to n+1"""
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bc = checkBC(bc)
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D = sp.spdiags((np.ones((n+1, 1))*[-1, 1]).T, [-1, 0], n+1, n, format="csr")
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# Set the first side
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if(bc[0] == 'dirichlet'):
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D[0, 0] = 2
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elif(bc[0] == 'neumann'):
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D[0, 0] = 0
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# Set the second side
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if(bc[1] == 'dirichlet'):
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D[-1, -1] = -2
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elif(bc[1] == 'neumann'):
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D[-1, -1] = 0
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return D
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def av(n):
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"""Define 1D averaging operator from cell-centres to nodes."""
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return sp.spdiags((0.5*np.ones((n+1, 1))*[1, 1]).T, [0, 1], n, n+1, format="csr")
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class DiffOperators(object):
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"""
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Class creates the differential operators that you need!
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"""
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def __init__(self):
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raise Exception('DiffOperators is a base class providing differential operators on meshes and cannot run on its own. Inherit to your favorite Mesh class.')
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def faceDiv():
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doc = "Construct divergence operator (face-stg to cell-centres)."
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def fget(self):
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if(self._faceDiv is None):
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# The number of cell centers in each direction
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n = self.n
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# Compute faceDivergence operator on faces
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if(self.dim == 1):
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D = ddx(n[0])
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elif(self.dim == 2):
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D1 = sp.kron(speye(n[1]), ddx(n[0]))
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D2 = sp.kron(ddx(n[1]), speye(n[0]))
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D = sp.hstack((D1, D2), format="csr")
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elif(self.dim == 3):
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D1 = kron3(speye(n[2]), speye(n[1]), ddx(n[0]))
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D2 = kron3(speye(n[2]), ddx(n[1]), speye(n[0]))
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D3 = kron3(ddx(n[2]), speye(n[1]), speye(n[0]))
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D = sp.hstack((D1, D2, D3), format="csr")
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# Compute areas of cell faces & volumes
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S = self.area
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V = self.vol
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self._faceDiv = sdiag(1/V)*D*sdiag(S)
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return self._faceDiv
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return locals()
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_faceDiv = None
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faceDiv = property(**faceDiv())
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def nodalGrad():
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doc = "Construct gradient operator (nodes to edges)."
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def fget(self):
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if(self._nodalGrad is None):
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# The number of cell centers in each direction
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n = self.n
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# Compute divergence operator on faces
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if(self.dim == 1):
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G = ddx(n[0])
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elif(self.dim == 2):
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D1 = sp.kron(speye(n[1]+1), ddx(n[0]))
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D2 = sp.kron(ddx(n[1]), speye(n[0]+1))
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G = sp.vstack((D1, D2), format="csr")
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elif(self.dim == 3):
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D1 = kron3(speye(n[2]+1), speye(n[1]+1), ddx(n[0]))
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D2 = kron3(speye(n[2]+1), ddx(n[1]), speye(n[0]+1))
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D3 = kron3(ddx(n[2]), speye(n[1]+1), speye(n[0]+1))
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G = sp.vstack((D1, D2, D3), format="csr")
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# Compute lengths of cell edges
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L = self.edge
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self._nodalGrad = sdiag(1/L)*G
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return self._nodalGrad
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return locals()
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_nodalGrad = None
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nodalGrad = property(**nodalGrad())
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def setCellGradBC(self, BC):
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"""
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Function that sets the boundary conditions for cell-centred derivative operators.
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Examples::
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BC = 'neumann' # Neumann in all directions
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BC = ['neumann', 'dirichlet', 'neumann'] # 3D, Dirichlet in y Neumann else
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BC = [['neumann', 'dirichlet'], 'dirichlet', 'dirichlet'] # 3D, Neumann in x on bottom of domain,
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# Dirichlet else
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"""
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if(type(BC) is str):
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BC = [BC for _ in self.n] # Repeat the str self.dim times
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elif(type(BC) is list):
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assert len(BC) == self.dim, 'BC list must be the size of your mesh'
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else:
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raise Exception("BC must be a str or a list.")
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for i, bc_i in enumerate(BC):
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BC[i] = checkBC(bc_i)
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self._cellGrad = None # ensure we create a new gradient next time we call it
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self._cellGradBC = BC
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return BC
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_cellGradBC = 'neumann'
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def cellGrad():
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doc = "The cell centered Gradient, takes you to cell faces."
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def fget(self):
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if(self._cellGrad is None):
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BC = self.setCellGradBC(self._cellGradBC)
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n = self.n
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if(self.dim == 1):
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G = ddxCellGrad(n[0], BC[0])
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elif(self.dim == 2):
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G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC[0]))
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G2 = sp.kron(ddxCellGrad(n[1], BC[1]), speye(n[0]))
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G = sp.vstack((G1, G2), format="csr")
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elif(self.dim == 3):
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G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC[0]))
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G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC[1]), speye(n[0]))
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G3 = kron3(ddxCellGrad(n[2], BC[2]), speye(n[1]), speye(n[0]))
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G = sp.vstack((G1, G2, G3), format="csr")
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# Compute areas of cell faces & volumes
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S = self.area
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V = self.vol
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self._cellGrad = sdiag(S)*G*sdiag(1/V)
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return self._cellGrad
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return locals()
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_cellGrad = None
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cellGrad = property(**cellGrad())
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def edgeCurl():
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doc = "Construct the 3D curl operator."
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def fget(self):
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if(self._edgeCurl is None):
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# The number of cell centers in each direction
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n1 = self.nCx
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n2 = self.nCy
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n3 = self.nCz
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# Compute lengths of cell edges
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L = self.edge
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# Compute areas of cell faces
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S = self.area
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# Compute divergence operator on faces
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d1 = ddx(n1)
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d2 = ddx(n2)
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d3 = ddx(n3)
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D32 = kron3(d3, speye(n2), speye(n1+1))
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D23 = kron3(speye(n3), d2, speye(n1+1))
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D31 = kron3(d3, speye(n2+1), speye(n1))
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D13 = kron3(speye(n3), speye(n2+1), d1)
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D21 = kron3(speye(n3+1), d2, speye(n1))
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D12 = kron3(speye(n3+1), speye(n2), d1)
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O1 = spzeros(np.shape(D32)[0], np.shape(D31)[1])
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O2 = spzeros(np.shape(D31)[0], np.shape(D32)[1])
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O3 = spzeros(np.shape(D21)[0], np.shape(D13)[1])
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C = sp.vstack((sp.hstack((O1, -D32, D23)),
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sp.hstack((D31, O2, -D13)),
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sp.hstack((-D21, D12, O3))), format="csr")
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self._edgeCurl = sdiag(1/S)*(C*sdiag(L))
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return self._edgeCurl
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return locals()
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_edgeCurl = None
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edgeCurl = property(**edgeCurl())
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def aveF2CC():
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doc = "Construct the averaging operator on cell faces to cell centers."
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def fget(self):
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if(self._aveF2CC is None):
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n = self.n
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if(self.dim == 1):
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self._aveF2CC = av(n[0])
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elif(self.dim == 2):
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self._aveF2CC = sp.hstack((sp.kron(speye(n[1]), av(n[0])),
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sp.kron(av(n[1]), speye(n[0]))), format="csr")
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elif(self.dim == 3):
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self._aveF2CC = sp.hstack((kron3(speye(n[2]), speye(n[1]), av(n[0])),
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kron3(speye(n[2]), av(n[1]), speye(n[0])),
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kron3(av(n[2]), speye(n[1]), speye(n[0]))), format="csr")
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return self._aveF2CC
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return locals()
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_aveF2CC = None
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aveF2CC = property(**aveF2CC())
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def aveE2CC():
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doc = "Construct the averaging operator on cell edges to cell centers."
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def fget(self):
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if(self._aveE2CC is None):
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# The number of cell centers in each direction
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n = self.n
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if(self.dim == 1):
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raise Exception('Edge Averaging does not make sense in 1D: Use Identity?')
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elif(self.dim == 2):
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self._aveE2CC = sp.hstack((sp.kron(av(n[1]), speye(n[0])),
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sp.kron(speye(n[1]), av(n[0]))), format="csr")
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elif(self.dim == 3):
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self._aveE2CC = sp.hstack((kron3(av(n[2]), av(n[1]), speye(n[0])),
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kron3(av(n[2]), speye(n[1]), av(n[0])),
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kron3(speye(n[2]), av(n[1]), av(n[0]))), format="csr")
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return self._aveE2CC
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return locals()
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_aveE2CC = None
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aveE2CC = property(**aveE2CC())
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def aveN2CC():
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doc = "Construct the averaging operator on cell nodes to cell centers."
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def fget(self):
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if(self._aveN2CC is None):
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# The number of cell centers in each direction
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n = self.n
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if(self.dim == 1):
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self._aveN2CC = av(n[0])
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elif(self.dim == 2):
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self._aveN2CC = sp.hstack((sp.kron(av(n[1]), av(n[0])),
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sp.kron(av(n[1]), av(n[0]))), format="csr")
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elif(self.dim == 3):
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self._aveN2CC = sp.hstack((kron3(av(n[2]), av(n[1]), av(n[0])),
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kron3(av(n[2]), av(n[1]), av(n[0])),
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kron3(av(n[2]), av(n[1]), av(n[0]))), format="csr")
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return self._aveN2CC
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return locals()
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_aveN2CC = None
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aveN2CC = property(**aveN2CC())
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def aveN2CCv():
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doc = "Construct the averaging operator on cell nodes to cell centers, keeping each dimension separate."
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def fget(self):
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if(self._aveN2CCv is None):
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# The number of cell centers in each direction
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n = self.n
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if(self.dim == 1):
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self._aveN2CCv = av(n[0])
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elif(self.dim == 2):
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self._aveN2CCv = sp.block_diag((sp.kron(av(n[1]), av(n[0])),
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sp.kron(av(n[1]), av(n[0]))), format="csr")
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elif(self.dim == 3):
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self._aveN2CCv = sp.block_diag((kron3(av(n[2]), av(n[1]), av(n[0])),
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kron3(av(n[2]), av(n[1]), av(n[0])),
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kron3(av(n[2]), av(n[1]), av(n[0]))), format="csr")
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return self._aveN2CCv
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return locals()
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_aveN2CCv = None
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aveN2CCv = property(**aveN2CCv())
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def getMass(self, materialProp=None, loc='e'):
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""" Produces mass matricies.
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:param str loc: Average to location: 'e'-edges, 'f'-faces
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:param None,float,numpy.ndarray materialProp: property to be averaged (see below)
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:rtype: scipy.sparse.csr.csr_matrix
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:return: M, the mass matrix
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materialProp can be::
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None -> takes materialProp = 1 (default)
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float -> a constant value for entire domain
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numpy.ndarray -> if materialProp.size == self.nC
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3D property model
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if materialProp.size = self.nCz
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1D (layered eath) property model
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"""
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if materialProp is None:
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materialProp = np.ones(self.nC)
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elif type(materialProp) is float:
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materialProp = np.ones(self.nC)*materialProp
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elif materialProp.shape == (self.nCz,):
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materialProp = materialProp.repeat(self.nCx*self.nCy)
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materialProp = mkvc(materialProp)
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assert materialProp.shape == (self.nC,), "materialProp incorrect shape"
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if loc=='e':
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Av = self.aveE2CC
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elif loc=='f':
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Av = self.aveF2CC
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else:
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raise ValueError('Invalid loc')
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diag = Av.T * (self.vol * mkvc(materialProp))
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return sdiag(diag)
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def getEdgeMass(self, materialProp=None):
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"""mass matrix for products of edge functions w'*M(materialProp)*e"""
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return self.getMass(loc='e', materialProp=materialProp)
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def getFaceMass(self, materialProp=None):
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"""mass matrix for products of face functions w'*M(materialProp)*f"""
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return self.getMass(loc='f', materialProp=materialProp)
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def getFaceMassDeriv(self):
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Av = self.aveF2CC
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return Av.T * sdiag(self.vol)
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