mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-27 23:08:55 +08:00
Rowan Cockett
120 lines
3.2 KiB
Python
120 lines
3.2 KiB
Python
#============= Nodal Gradients ===========================
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def getNodalGradient(h1,h2,h3):
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n1 = size(h1)
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n2 = size(h2)
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n3 = size(h3)
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D1 = kron3(speye(n3+1),speye(n2+1),ddx(n1))
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D2 = kron3(speye(n3+1),ddx(n2),speye(n1+1))
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D3 = kron3(ddx(n3),speye(n2+1),speye(n1+1))
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# topological gradient
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GRAD = appendBottom3(D1,D2,D3)
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# scale for non-uniform mesh
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L = blkDiag3(kron3(speye(n3+1),speye(n2+1),sdiag(1/h1)),
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kron3(speye(n3+1),sdiag(1/h2),speye(n1+1)),
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kron3(sdiag(1/h3),speye(n2+1),speye(n1+1)))
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return L*GRAD
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#============= Edge CURL ===========================
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def getCurlMatrix(h1,h2,h3):
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n1 = size(h1)
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n2 = size(h2)
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n3 = size(h3)
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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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# derivatives on x-edge variables
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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(shape(D32)[0],shape(D31)[1])
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O2 = spzeros(shape(D31)[0],shape(D32)[1])
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O3 = spzeros(shape(D21)[0],shape(D13)[1])
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CURL = appendBottom3(
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appendRight3(O1, -D32, D23),
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appendRight3(D31, O2, -D13),
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appendRight3(-D21, D12, O3))
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# scale for non-uniform mesh
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F = blkDiag3(kron3(sdiag(1/h3),sdiag(1/h2),speye(n1+1)),
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kron3(sdiag(1/h3),speye(n2+1),sdiag(1/h1)),
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kron3(speye(n3+1),sdiag(1/h2),sdiag(1/h1)))
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L = blkDiag3(kron3(speye(n3+1),speye(n2+1),sdiag(h1)),
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kron3(speye(n3+1),sdiag(h2),speye(n1+1)),
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kron3(sdiag(h3),speye(n2+1),speye(n1+1)))
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return F*(CURL*L)
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#============= Face DIV ===========================
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def getDivMatrix(h1,h2,h3):
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n1 = size(h1)
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n2 = size(h2)
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n3 = size(h3)
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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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D1 = kron3(speye(n3),speye(n2),d1)
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D2 = kron3(speye(n3),d2,speye(n1))
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D3 = kron3(d3,speye(n2),speye(n1))
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# divergence on faces
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D = appendRight3(D1, D2, D3)
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# scale for non-uniform mesh
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F = blkDiag3(kron3(sdiag(h3),sdiag(h2),speye(n1+1)),
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kron3(sdiag(h3),speye(n2+1),sdiag(h1)),
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kron3(speye(n3+1),sdiag(h2),sdiag(h1)))
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V = kron3(sdiag(1/h3),sdiag(1/h2),sdiag(1/h1))
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return V*(D*F)
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#====== Face Averageing =================
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def getFaceAverage(n1,n2,n3):
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av1 = av(n1)
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av2 = av(n2)
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av3 = av(n3)
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Af = appendRight3(kron3(speye(n3),speye(n2),av1),
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kron3(speye(n3),av2,speye(n1)),
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kron3(av3,speye(n2),speye(n1)))
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return Af
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#====== Edge Averageing =================
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def getEdgeAverage(n1,n2,n3):
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av1 = av(n1)
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av2 = av(n2)
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av3 = av(n3)
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Ae = appendRight3(kron3(av3,av2,speye(n1)),
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kron3(av3,speye(n2),av1),
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kron3(speye(n3),av2,av1))
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return Ae
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#====== Node Averageing =================
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def getNodeAverage(n1,n2,n3):
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av1 = av(n1)
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av2 = av(n2)
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av3 = av(n3)
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return kron3(av3,av2,av1)
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