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SEOGI KANG
132 lines
3.9 KiB
Python
132 lines
3.9 KiB
Python
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from SimPEG.Utils.sputils import kron3, speye, sdiag, spzeros
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import numpy as np
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import scipy.sparse as sp
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def ddxFaceDivBC(n, bc):
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ij = (np.array([0, n-1]),np.array([0, 1]))
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vals = np.zeros(2)
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# Set the first side
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if(bc[0] == 'dirichlet'):
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vals[0] = 0
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elif(bc[0] == 'neumann'):
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vals[0] = -1
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# Set the second side
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if(bc[1] == 'dirichlet'):
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vals[1] = 0
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elif(bc[1] == 'neumann'):
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vals[1] = 1
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D = sp.csr_matrix((vals, ij), shape=(n,2))
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return D
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def faceDivBC(mesh, BC, ind):
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"""
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The facd divergence boundary condtion matrix
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"""
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# The number of cell centers in each direction
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n = mesh.vnC
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# Compute faceDivergence operator on faces
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if(mesh.dim == 1):
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D = ddxFaceDivBC(n[0], BC[0])
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elif(mesh.dim == 2):
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D1 = sp.kron(speye(n[1]), ddxFaceDivBC(n[0], BC[0]))
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D2 = sp.kron(ddxFaceDivBC(n[1], BC[1]), speye(n[0]))
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D = sp.hstack((D1, D2), format="csr")
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elif(mesh.dim == 3):
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D1 = kron3(speye(n[2]), speye(n[1]), ddxFaceDivBC(n[0], BC[0]))
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D2 = kron3(speye(n[2]), ddxFaceDivBC(n[1], BC[1]), speye(n[0]))
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D3 = kron3(ddxFaceDivBC(n[2], BC[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 = mesh.area[ind]
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V = mesh.vol
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mesh._faceDiv = sdiag(1/V)*D*sdiag(S)
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return mesh._faceDiv
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def faceBCind(mesh):
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"""
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Find indices of boundary faces in each direction
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"""
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if(mesh.dim==1):
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indxd = (mesh.gridFx==min(mesh.gridFx))
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indxu = (mesh.gridFx==max(mesh.gridFx))
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return indxd, indxu
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elif(mesh.dim==2):
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indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
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indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
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indyd = (mesh.gridFy[:,1]==min(mesh.gridFy[:,1]))
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indyu = (mesh.gridFy[:,1]==max(mesh.gridFy[:,1]))
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return indxd, indxu, indyd, indyu
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elif(mesh.dim==3):
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indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
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indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
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indyd = (mesh.gridFy[:,1]==min(mesh.gridFy[:,1]))
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indyu = (mesh.gridFy[:,1]==max(mesh.gridFy[:,1]))
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indzd = (mesh.gridFz[:,2]==min(mesh.gridFz[:,2]))
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indzu = (mesh.gridFz[:,2]==max(mesh.gridFz[:,2]))
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return indxd, indxu, indyd, indyu, indzd, indzu
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def faceDivProj(mesh, flag):
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""""
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Construct divergence operator (face-stg to cell-centres).
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"""
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# The number of cell centers in each direction
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n = mesh.vnC
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# Compute faceDivergence operator on faces
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if (flag=='in'):
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if(mesh.dim == 1):
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Pin = ddxPin(n[0])
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elif(mesh.dim == 2):
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P1 = sp.kron(speye(n[1]), ddxPin(n[0]))
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P2 = sp.kron(ddxPin(n[1]), speye(n[0]))
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Pin = sp.block_diag((P1, P2), format="csr")
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elif(mesh.dim == 3):
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P1 = kron3(speye(n[2]), speye(n[1]), ddxPin(n[0]))
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P2 = kron3(speye(n[2]), ddxPin(n[1]), speye(n[0]))
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P3 = kron3(ddxPin(n[2]), speye(n[1]), speye(n[0]))
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Pin = sp.block_diag((P1, P2, P3), format="csr")
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# Compute areas of cell faces & volumes
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return Pin
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elif(flag=='out'):
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if(mesh.dim == 1):
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Pout = ddxPout(n[0])
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elif(mesh.dim == 2):
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P1 = sp.kron(speye(n[1]), ddxPout(n[0]))
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P2 = sp.kron(ddxPout(n[1]), speye(n[0]))
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Pout = sp.block_diag((P1, P2), format="csr")
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elif(mesh.dim == 3):
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P1 = kron3(speye(n[2]), speye(n[1]), ddxPout(n[0]))
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P2 = kron3(speye(n[2]), ddxPout(n[1]), speye(n[0]))
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P3 = kron3(ddxPout(n[2]), speye(n[1]), speye(n[0]))
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Pout = sp.block_diag((P1, P2, P3), format="csr")
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# Compute areas of cell faces & volumes
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return Pout
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def ddxPin(n):
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p0 =spzeros(n-1, 1)
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P = sdiag(np.ones(n-1))
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P = sp.hstack((p0, P, p0))
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return P
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def ddxPout(n):
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ij = (np.array([0, 1]),np.array([0, n]))
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vals = np.ones(2)
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P = sp.csr_matrix((vals, ij), shape=(2,n+1))
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return P
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