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made the inner products easy to use to get the derivatives with respect to conductivity/mu

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ehaber99
2013-08-03 10:23:35 -07:00
parent 24773c4f60
commit caaa7dcb41
1 changed files with 31 additions and 14 deletions
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SimPEG/InnerProducts.py
+31 -14
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@@ -81,23 +81,34 @@ def getFaceInnerProduct(mesh, mu):
if mu.size == mesh.nC: # Isotropic! if mu.size == mesh.nC: # Isotropic!
mu = mkvc(mu) # ensure it is a vector. mu = mkvc(mu) # ensure it is a vector.
mu = sdiag(np.r_[mu, mu, mu]) Mu = sdiag(np.r_[mu, mu, mu])
elif mu.shape[1] == 3: # Diagonal tensor elif mu.shape[1] == 3: # Diagonal tensor
mu = sdiag(np.r_[mu[:, 0], mu[:, 1], mu[:, 2]]) Mu = sdiag(np.r_[mu[:, 0], mu[:, 1], mu[:, 2]])
elif mu.shape[1] == 6: # Fully anisotropic elif mu.shape[1] == 6: # Fully anisotropic
row1 = sp.hstack((sdiag(mu[:, 0]), sdiag(mu[:, 3]), sdiag(mu[:, 4]))) row1 = sp.hstack((sdiag(mu[:, 0]), sdiag(mu[:, 3]), sdiag(mu[:, 4])))
row2 = sp.hstack((sdiag(mu[:, 3]), sdiag(mu[:, 1]), sdiag(mu[:, 5]))) row2 = sp.hstack((sdiag(mu[:, 3]), sdiag(mu[:, 1]), sdiag(mu[:, 5])))
row3 = sp.hstack((sdiag(mu[:, 4]), sdiag(mu[:, 5]), sdiag(mu[:, 2]))) row3 = sp.hstack((sdiag(mu[:, 4]), sdiag(mu[:, 5]), sdiag(mu[:, 2])))
mu = sp.vstack((row1, row2, row3)) Mu = sp.vstack((row1, row2, row3))
# Cell volume # Cell volume
v = np.sqrt(mesh.vol) v = np.sqrt(mesh.vol)
v3 = np.r_[v, v, v] v3 = (0.125)**(0.5)*np.r_[v, v, v]
V = sdiag(v3)*mu*sdiag(v3) # to keep symmetry #V = sdiag(v3)*mu*sdiag(v3) # to keep symmetry
#A = P000.T*V*P000 + P001.T*V*P001 + P010.T*V*P010 + P011.T*V*P011 + P100.T*V*P100 + P101.T*V*P101 + P110.T*V*P110 + P111.T*V*P111
#A = 0.125*A
P000 = sdiag(v3)*P000; P001 = sdiag(v3)*P001; P010 = sdiag(v3)*P010; P011 = sdiag(v3)*P011
P100 = sdiag(v3)*P100; P101 = sdiag(v3)*P101; P110 = sdiag(v3)*P110; P111 = sdiag(v3)*P111
A = P000.T*Mu*P000 + P001.T*Mu*P001 + P010.T*Mu*P010 + P011.T*Mu*P011 + P100.T*Mu*P100 + P101.T*Mu*P101 + P110.T*Mu*P110 + P111.T*Mu*P111
#P = sp.vstack((sdiag(v3)*P000,sdiag(v3)*P001,sdiag(v3)*P010,sdiag(v3)*P011,
# sdiag(v3)*P100,sdiag(v3)*P101,sdiag(v3)*P110,sdiag(v3)*P111))
#A = 0.125*(P.T * sp.kron(sp.eye(8),Sigma) * P)
P = [P000,P001,P010,P011,P100,P101,P110,P111]
return A, P
A = P000.T*V*P000 + P001.T*V*P001 + P010.T*V*P010 + P011.T*V*P011 + P100.T*V*P100 + P101.T*V*P101 + P110.T*V*P110 + P111.T*V*P111
A = 0.125*A
return A return A
@@ -168,15 +179,21 @@ def getEdgeInnerProduct(mesh, sigma):
# Cell volume # Cell volume
v = np.sqrt(mesh.vol) v = np.sqrt(mesh.vol)
v3 = np.r_[v, v, v] v3 = (0.125)**(0.5)*np.r_[v, v, v]
V = sdiag(v3)*Sigma*sdiag(v3) # to keep symmetry
P000 = sdiag(v3)*P000; P001 = sdiag(v3)*P001; P010 = sdiag(v3)*P010; P011 = sdiag(v3)*P011
P100 = sdiag(v3)*P100; P101 = sdiag(v3)*P101; P110 = sdiag(v3)*P110; P111 = sdiag(v3)*P111
A = P000.T*V*P000 + P001.T*V*P001 + P010.T*V*P010 + P011.T*V*P011 + P100.T*V*P100 + P101.T*V*P101 + P110.T*V*P110 + P111.T*V*P111
A = 0.125*A #V = sdiag(v3)*Sigma*sdiag(v3) # to keep symmetry
P = sp.vstack((sdiag(v3)*P000,sdiag(v3)*P001,sdiag(v3)*P010,sdiag(v3)*P011,
sdiag(v3)*P100,sdiag(v3)*P101,sdiag(v3)*P110,sdiag(v3)*P111))
A = P000.T*Sigma*P000 + P001.T*Sigma*P001 + P010.T*Sigma*P010 + P011.T*Sigma*P011 + P100.T*Sigma*P100 + P101.T*Sigma*P101 + P110.T*Sigma*P110 + P111.T*Sigma*P111
#P = sp.vstack((sdiag(v3)*P000,sdiag(v3)*P001,sdiag(v3)*P010,sdiag(v3)*P011,
# sdiag(v3)*P100,sdiag(v3)*P101,sdiag(v3)*P110,sdiag(v3)*P111))
#A = 0.125*(P.T * sp.kron(sp.eye(8),Sigma) * P)
P = [P000,P001,P010,P011,P100,P101,P110,P111]
return A, P return A, P
@@ -187,5 +204,5 @@ if __name__ == '__main__':
mesh = TensorMesh(h) mesh = TensorMesh(h)
mu = np.ones((mesh.nC, 6)) mu = np.ones((mesh.nC, 6))
A = getFaceInnerProduct(mesh,mu) A = getFaceInnerProduct(mesh,mu)
B = getEdgeInnerProduct(mesh,mu) B, P = getEdgeInnerProduct(mesh,mu)