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Added a nodal laplacian

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This commit is contained in:
Rowan Cockett
2013-11-06 14:48:53 -08:00
parent 3d91fc54cf
commit 291cabe931
2 changed files with 66 additions and 29 deletions
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SimPEG/Examples/FWI/seismic.py
+30 -25
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@@ -1,5 +1,8 @@
import sys
sys.path.append('/Users/haber/dropbox/simpegMaster/')
try:
import sys
sys.path.append('/Users/haber/dropbox/simpegMaster/')
except Exception, e:
pass
import SimPEG
import scipy.sparse as sp
@@ -16,12 +19,12 @@ def HelmholtzSol(model,mesh,w,mbc,q,P):
k = np.sqrt(w**2 * mbc)
D1 = utils.sdiag(1./h1) * utils.ddx(mesh.nCx)
D2 = utils.sdiag(1./h2) * utils.ddx(mesh.nCy)
L1 = D1.T*D1; L2 = D2.T*D2;
print L1.todense()
# D1 = utils.sdiag(1./h1) * utils.ddx(mesh.nCx)
# D2 = utils.sdiag(1./h2) * utils.ddx(mesh.nCy)
# L1 = - D1.T*D1
# L2 = - D2.T*D2
Av = mesh.aveN2CC
B1 = utils.spzeros(n1+1,n1+1);
@@ -33,21 +36,23 @@ def HelmholtzSol(model,mesh,w,mbc,q,P):
B2[0,0] = 2*1j*k*h2[0]; B2[-1,-1] = 2*1j*k*h2[-1]
# generate the 2D Laplacian
L = sp.kron(sp.identity(n2+1),L1+B1) + sp.kron(L2+B2,sp.identity(n1+1))
# L = sp.kron(sp.identity(n2+1),L1) + sp.kron(L2,sp.identity(n1+1))
L = mesh.nodalLaplacian
B = sp.kron(sp.identity(n2+1),B1) + sp.kron(B2,sp.identity(n1+1))
L = L+B
#plt.spy(L)
#plt.show()
# Generate the Mass matrix
M = utils.sdiag(Av.T*utils.mkvc(model))
A = L - w**2 * M
A = - L - w**2 * M
mesh.ForModMat = A
u = sp.linalg.spsolve(A,q);
d = P*u
return u, d
def HelmholtzJmatVec(v,model,u,mesh,w,mbc,P):
Cm = -w**2 * utils.sdiag(u)*mesh.aveN2CC.T
Cu = mesh.ForModMat
Cmv = Cm*v;
@@ -55,20 +60,20 @@ def HelmholtzJmatVec(v,model,u,mesh,w,mbc,P):
return -P*lam
def HelmholtzJTmatVec(v,model,u,mesh,w,mbc,P):
Cm = -w**2 * utils.sdiag(u)*mesh.aveN2CC.T
Cu = mesh.ForModMat
Pv = -P.T*v
z = sp.linalg.spsolve(Cu.T,Pv);
return Cm.T*z
if __name__ == '__main__':
# odel,mesh,w,mbc,q
n1 = 128; n2 = 128
h1 = np.ones(n1); h2 = np.ones(n2);
P = sp.identity((n1+1)*(n2+1))
mesh = TensorMesh([h1,h2])
model = np.ones(mesh.nC)
w = 1
@@ -76,21 +81,21 @@ if __name__ == '__main__':
q = np.zeros((mesh.nNx,mesh.nNy))
q[n1/2,n2/2] = 1.0
q = q.reshape(mesh.nN,order = 'F')
u, d = HelmholtzSol(model,mesh,w,mbc,q,P)
u = u.reshape((mesh.nCx+1,mesh.nCy+1),order = 'F')
plt.imshow(u.real)
plt.show()
dm = np.random.rand(mesh.nC)*1e-1+2
u1, d1 = HelmholtzSol(model+dm,mesh,w,mbc,q,P)
dd = HelmholtzJmatVec(dm,model,u,mesh,w,mbc,P)
print np.linalg.norm(d1-d)
print np.linalg.norm(d1-d-dd)