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ehaber99 committed
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@@ -47,7 +47,7 @@
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"h1 = 1.0/n1; h2 = 1.0/n2;\n",
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"w = 100; m = np.ones(n1*n2)\n",
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"mbc = 1;\n",
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"k = np.sqrt(w**2 * mbc)\n",
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"k = w*np.sqrt(w**2 * mbc)\n",
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"import numpy as np\n",
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"import SimPEG.utils as utils\n",
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"\n",
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@@ -85,19 +85,19 @@
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 88
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"prompt_number": 93
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"B1[0,0] = 1-2*1j*k*h1; B1[-1,-1] = 1-2*1j*k*h1\n",
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"B2[0,0] = 1-2*1j*k*h2; B2[-1,-1] = 1-2*1j*k*h2"
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"B1[0,0] = 1+2*1j*k*h1; B1[-1,-1] = 1+2*1j*k*h1\n",
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"B2[0,0] = 1+2*1j*k*h2; B2[-1,-1] = 1+2*1j*k*h2"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 89
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"prompt_number": 94
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},
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{
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"cell_type": "code",
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@@ -114,7 +114,7 @@
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 90
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"prompt_number": 95
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},
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{
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"cell_type": "code",
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@@ -128,7 +128,7 @@
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 91
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"prompt_number": 96
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},
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{
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"cell_type": "code",
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@@ -141,20 +141,29 @@
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"outputs": [
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{
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"output_type": "pyout",
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"prompt_number": 92,
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"prompt_number": 97,
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"text": [
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"<matplotlib.image.AxesImage at 0x1010851d0>"
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"<matplotlib.image.AxesImage at 0x113625ed0>"
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]
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},
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{
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"output_type": "display_data",
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"png": "iVBORw0KGgoAAAANSUhEUgAAAQIAAAD8CAYAAACcoKqNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
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"text": [
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"<matplotlib.figure.Figure at 0x10eba9d50>"
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"<matplotlib.figure.Figure at 0x10109a5d0>"
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]
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}
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],
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"prompt_number": 92
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"prompt_number": 97
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 97
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},
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{
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"cell_type": "code",
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@@ -0,0 +1,96 @@
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import sys
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sys.path.append('/Users/haber/dropbox/simpegMaster/')
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import SimPEG
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import scipy.sparse as sp
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import numpy as np
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import SimPEG.utils as utils
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import matplotlib.pylab as plt
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from SimPEG.mesh import TensorMesh
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def HelmholtzSol(model,mesh,w,mbc,q,P):
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n1 = mesh.nCx; n2 = mesh.nCy;
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h1 = mesh.hx; h2 = mesh.hy;
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k = np.sqrt(w**2 * mbc)
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D1 = utils.sdiag(1./h1) * utils.ddx(mesh.nCx)
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D2 = utils.sdiag(1./h2) * utils.ddx(mesh.nCy)
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L1 = D1.T*D1; L2 = D2.T*D2;
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print L1.todense()
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Av = mesh.aveN2CC
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B1 = utils.spzeros(n1+1,n1+1);
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B2 = utils.spzeros(n2+1,n2+1);
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B1.dtype = complex
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B2.dtype = complex
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B1[0,0] = 2*1j*k*h1[0]; B1[-1,-1] = 2*1j*k*h1[-1]
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B2[0,0] = 2*1j*k*h2[0]; B2[-1,-1] = 2*1j*k*h2[-1]
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# generate the 2D Laplacian
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L = sp.kron(sp.identity(n2+1),L1+B1) + sp.kron(L2+B2,sp.identity(n1+1))
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#plt.spy(L)
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#plt.show()
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# Generate the Mass matrix
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M = utils.sdiag(Av.T*utils.mkvc(model))
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A = L - w**2 * M
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mesh.ForModMat = A
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u = sp.linalg.spsolve(A,q);
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d = P*u
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return u, d
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def HelmholtzJmatVec(v,model,u,mesh,w,mbc,P):
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Cm = -w**2 * utils.sdiag(u)*mesh.aveN2CC.T
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Cu = mesh.ForModMat
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Cmv = Cm*v;
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lam = sp.linalg.spsolve(Cu,Cmv);
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return -P*lam
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def HelmholtzJTmatVec(v,model,u,mesh,w,mbc,P):
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Cm = -w**2 * utils.sdiag(u)*mesh.aveN2CC.T
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Cu = mesh.ForModMat
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Pv = -P.T*v
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z = sp.linalg.spsolve(Cu.T,Pv);
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return Cm.T*z
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if __name__ == '__main__':
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# odel,mesh,w,mbc,q
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n1 = 128; n2 = 128
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h1 = np.ones(n1); h2 = np.ones(n2);
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P = sp.identity((n1+1)*(n2+1))
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mesh = TensorMesh([h1,h2])
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model = np.ones(mesh.nC)
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w = 1
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mbc = 1
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q = np.zeros((mesh.nNx,mesh.nNy))
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q[n1/2,n2/2] = 1.0
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q = q.reshape(mesh.nN,order = 'F')
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u, d = HelmholtzSol(model,mesh,w,mbc,q,P)
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u = u.reshape((mesh.nCx+1,mesh.nCy+1),order = 'F')
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plt.imshow(u.real)
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plt.show()
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dm = np.random.rand(mesh.nC)*1e-1+2
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u1, d1 = HelmholtzSol(model+dm,mesh,w,mbc,q,P)
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dd = HelmholtzJmatVec(dm,model,u,mesh,w,mbc,P)
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print np.linalg.norm(d1-d)
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print np.linalg.norm(d1-d-dd)
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