Eldad's initial code for logically orthogonal mesh simulation.

2026-07-01 21:32:22 +08:00 · 2013-06-01 14:18:31 -07:00
commit 2554318427
15 changed files with 1370 additions and 0 deletions
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+from scipy.sparse import linalg
+from scipy import sparse
+from sputils import *
+from utils import *
+from numpy import *
+from getEdgeTangent import *
+from getCellVolume import getCellVolume
+from getFaceNormals import getFaceNormals
+
+
+#============= Face DIV ===========================	
+def getDivMatrix(X,Y,Z):
+
+    n = array(shape(X))-1
+    n1 = n[0]; n2 = n[1]; n3 = n[2]
+    
+    n1x,n1y,n1z,n2x,n2y,n2z,n3x,n3y,n3z,area1,area2,area3 = getFaceNormals(X,Y,Z)
+    
+    area = hstack((hstack((mkvc(area1),mkvc(area2))),mkvc(area3)))
+    S  = sdiag(area)
+    V   = getCellVolume(X,Y,Z)
+    
+    d1 = ddx(n1)
+    d2 = ddx(n2)
+    d3 = ddx(n3)
+    D1  = kron3(speye(n3),speye(n2),d1)
+    D2  = kron3(speye(n3),d2,speye(n1))
+    D3  = kron3(d3,speye(n2),speye(n1))
+    
+    # divergence on faces
+    D = appendRight3(D1, D2, D3)
+    
+    return sdiag(1/V)*D*S
+ 
+ #============= Edge CURL ===========================	
+  
+def getCurlMatrix(X,Y,Z):
+    
+    n = array(shape(X))-1
+    n1 = n[0]; n2 = n[1]; n3 = n[2]
+
+    d1 = ddx(n1); d2 = ddx(n2); d3 = ddx(n3)
+    # derivatives on x-edge variables
+    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(shape(D32)[0],shape(D31)[1])
+    O2 = spzeros(shape(D31)[0],shape(D32)[1])
+    O3 = spzeros(shape(D21)[0],shape(D13)[1])
+
+    CURL = appendBottom3(
+        appendRight3(O1,    -D32,  D23),
+        appendRight3(D31,    O2,  -D13),
+        appendRight3(-D21,  D12,   O3))
+        
+    # scale for non-uniform mesh     
+    e1x,e1y,e1z,e2x,e2y,e2z,e3x,e3y,e3z,norme1,norme2,norme3 = getEdgeTangent(X,Y,Z)
+    n1x,n1y,n1z,n2x,n2y,n2z,n3x,n3y,n3z,area1,area2,area3    = getFaceNormals(X,Y,Z)
+ 
+    area = hstack((hstack((mkvc(area1),mkvc(area2))),mkvc(area3)))
+    S  = sdiag(1/area)
+    lngth = hstack((hstack((mkvc(norme1),mkvc(norme2))),mkvc(norme3)))
+    L = sdiag(lngth)                 
+    
+    return S*(CURL*L)	
+
+#============= Nodal Gradients ===========================	
+def getNodalGradient(X,Y,Z):
+    
+    n = array(shape(X))-1
+    n1 = n[0]; n2 = n[1]; n3 = n[2]
+
+    D1  = kron3(speye(n3+1),speye(n2+1),ddx(n1))
+    D2  = kron3(speye(n3+1),ddx(n2),speye(n1+1))
+    D3  = kron3(ddx(n3),speye(n2+1),speye(n1+1))
+    
+    # topological gradient
+    GRAD = appendBottom3(D1,D2,D3)
+    
+    # scale for non-uniform mesh
+    e1x,e1y,e1z,e2x,e2y,e2z,e3x,e3y,e3z,norme1,norme2,norme3 = getEdgeTangent(X,Y,Z)
+    lngth = hstack((hstack((mkvc(norme1),mkvc(norme2))),mkvc(norme3)))
+    L = sdiag(1/lngth)                 
+
+    return L*GRAD	
+   
+       
+if __name__ == '__main__':    
+               
+    X,Y,Z = ndgrid(linspace(0,2,3),linspace(0,2,3),linspace(0,2,3))
+    Z[2,2,2] = 2.5;   Z[0,0,0] = -0.5
+    X[2,2,2] = 2.5; X[0,0,0] = -0.5
+    sig = ones([2,2,2])
+    C = getCurlMatrix(X,Y,Z)    
+
+    G = getNodalGradient(X,Y,Z)
+    
+    tt = C*G
+    print(tt)