initial notebook

2026-10-29 13:40:11 +08:00 · 2013-11-06 10:33:46 -08:00
1 parent 059ccd40b3
commit d67df06ec3
@@ -0,0 +1,171 @@
+{
+ "metadata": {
+  "name": "FWI"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import sys\n",
+      "sys.path.append('/Users/haber/dropbox/simpegMaster/')\n",
+      "import SimPEG\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Warning: you may not have the required pubsub installed, use pypubsub. You will not be able to listen to events.\n"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import scipy.sparse as sp"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "n1 = 128; n2 = 128;\n",
+      "h1  = 1.0/n1; h2 = 1.0/n2;\n",
+      "w = 100; m = np.ones(n1*n2)\n",
+      "mbc = 1;\n",
+      "k = np.sqrt(w**2 * mbc)\n",
+      "import numpy as np\n",
+      "import SimPEG.utils as utils\n",
+      "\n",
+      "mesh = SimPEG.mesh.TensorMesh([h1*np.ones(n1),h2*np.ones(n2)])"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 86
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "L1 = (1.0/h1**2) * sp.spdiags((np.ones((n1+1,1))*[1, -2, 1]).T,[-1,0,1],n1+1,n1+1);\n",
+      "L2 = (1.0/h2**2) * sp.spdiags((np.ones((n2+1,1))*[1, -2, 1]).T,[-1,0,1],n2+1,n2+1);\n",
+      "\n",
+      "av1 = sp.spdiags((np.ones((n1+1,1))*[0.5, 0.5]).T,[0,1],n1,n1+1);\n",
+      "av2 = sp.spdiags((np.ones((n2+1,1))*[0.5, 0.5]).T,[0,1],n2,n2+1);\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 87
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "B1 = utils.spzeros(n1+1,n1+1);\n",
+      "B2 = utils.spzeros(n2+1,n2+1);\n",
+      "B1.dtype = complex\n",
+      "B2.dtype = complex\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 88
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "B1[0,0] = 1-2*1j*k*h1; B1[-1,-1] = 1-2*1j*k*h1\n",
+      "B2[0,0] = 1-2*1j*k*h2; B2[-1,-1] = 1-2*1j*k*h2"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 89
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# generate the 2D Laplacian\n",
+      "L = sp.kron(sp.identity(n2+1),L1+B1) + sp.kron(L2+B2,sp.identity(n1+1)) \n",
+      "\n",
+      "# Generate the Mass matrix\n",
+      "Av = sp.kron(av2,av1)\n",
+      "M = utils.sdiag(Av.T*utils.mkvc(m))\n",
+      "A = L + w**2 * M"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 90
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "q = np.zeros((n1+1,n2+1)); q[64,64] = 1; q = utils.mkvc(q);\n",
+      "u = sp.linalg.spsolve(A,q);\n",
+      "u = u.reshape((n1+1,n2+1),order='F')\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 91
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "imshow(u.real)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "pyout",
+       "prompt_number": 92,
+       "text": [
+        "<matplotlib.image.AxesImage at 0x1010851d0>"
+       ]
+      },
+      {
+       "output_type": "display_data",
+       "png": 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truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x10eba9d50>"
+       ]
+      }
+     ],
+     "prompt_number": 92
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}