mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 03:35:09 +08:00
Rowan Cockett
103 lines
3.0 KiB
Python
103 lines
3.0 KiB
Python
from scipy.sparse import linalg
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from scipy import sparse
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from sputils import *
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from utils import *
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from numpy import *
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from getEdgeTangent import *
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from getCellVolume import getCellVolume
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from getFaceNormals import getFaceNormals
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#============= Face DIV ===========================
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def getDivMatrix(X,Y,Z):
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n = array(shape(X))-1
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n1 = n[0]; n2 = n[1]; n3 = n[2]
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n1x,n1y,n1z,n2x,n2y,n2z,n3x,n3y,n3z,area1,area2,area3 = getFaceNormals(X,Y,Z)
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area = hstack((hstack((mkvc(area1),mkvc(area2))),mkvc(area3)))
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S = sdiag(area)
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V = getCellVolume(X,Y,Z)
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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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return sdiag(1/V)*D*S
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#============= Edge CURL ===========================
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def getCurlMatrix(X,Y,Z):
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n = array(shape(X))-1
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n1 = n[0]; n2 = n[1]; n3 = n[2]
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d1 = ddx(n1); d2 = ddx(n2); 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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e1x,e1y,e1z,e2x,e2y,e2z,e3x,e3y,e3z,norme1,norme2,norme3 = getEdgeTangent(X,Y,Z)
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n1x,n1y,n1z,n2x,n2y,n2z,n3x,n3y,n3z,area1,area2,area3 = getFaceNormals(X,Y,Z)
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area = hstack((hstack((mkvc(area1),mkvc(area2))),mkvc(area3)))
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S = sdiag(1/area)
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lngth = hstack((hstack((mkvc(norme1),mkvc(norme2))),mkvc(norme3)))
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L = sdiag(lngth)
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return S*(CURL*L)
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#============= Nodal Gradients ===========================
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def getNodalGradient(X,Y,Z):
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n = array(shape(X))-1
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n1 = n[0]; n2 = n[1]; n3 = n[2]
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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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e1x,e1y,e1z,e2x,e2y,e2z,e3x,e3y,e3z,norme1,norme2,norme3 = getEdgeTangent(X,Y,Z)
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lngth = hstack((hstack((mkvc(norme1),mkvc(norme2))),mkvc(norme3)))
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L = sdiag(1/lngth)
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return L*GRAD
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if __name__ == '__main__':
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X,Y,Z = ndgrid(linspace(0,2,3),linspace(0,2,3),linspace(0,2,3))
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Z[2,2,2] = 2.5; Z[0,0,0] = -0.5
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X[2,2,2] = 2.5; X[0,0,0] = -0.5
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sig = ones([2,2,2])
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C = getCurlMatrix(X,Y,Z)
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G = getNodalGradient(X,Y,Z)
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tt = C*G
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print(tt) |