mirror of
https://github.com/wassname/simpeg.git
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seogi_macbook
295 lines
7.3 KiB
Plaintext
295 lines
7.3 KiB
Plaintext
{
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"metadata": {
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"name": "",
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"signature": "sha256:189621fc59a92a7c23842dcbc46e2decfeef63b14613f47a605c97b622f48fc0"
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"worksheets": [
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{
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"cells": [
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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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"from SimPEG import Mesh, Utils, np, SolverLU\n",
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"import matplotlib.pyplot as plt\n",
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"# %pylab inline"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stderr",
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"text": [
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"Vendor: Continuum Analytics, Inc.\n",
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"Package: mkl\n",
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"Message: trial mode expires in 20 days\n"
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]
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}
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],
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"prompt_number": 1
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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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"import matplotlib\n",
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"from matplotlib.mlab import griddata"
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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": 2
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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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"matplotlib.rcParams.update({'font.size': 16, 'text.usetex': True})"
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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": 3
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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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"sz = [15,15]\n",
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"tM = Mesh.TensorMesh(sz)\n",
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"qM = Mesh.TreeMesh(sz)\n",
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"qM.refine(lambda X: 1 if np.sqrt(((X-0.5)**2).sum()) < 0.45 else 0)\n",
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"rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz,'rotate'))"
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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": 5
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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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"fun = lambda X: 1 if np.sqrt(((X-0.5)**2).sum()) < 0.45 else 0"
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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": 6
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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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"fun(np.ones(30))"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 7,
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"text": [
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"0"
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]
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}
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],
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"prompt_number": 7
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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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"def DCfun(mesh, pts):\n",
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" D = mesh.faceDiv\n",
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" G = D.T\n",
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" sigma = 1e-2*np.ones(mesh.nC)\n",
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" Msigi = mesh.getFaceInnerProduct(1./sigma)\n",
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" MsigI = Utils.sdInv(Msigi)\n",
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" A = D*MsigI*G\n",
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" A[-1,-1] /= mesh.vol[-1] # Remove null space\n",
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" rhs = np.zeros(mesh.nC)\n",
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" txind = Utils.meshutils.closestPoints(mesh, pts)\n",
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" rhs[txind] = np.r_[1,-1]\n",
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" return A, rhs"
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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": 8
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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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"tM.vectorCCy"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 9,
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"text": [
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"array([ 0.03333333, 0.1 , 0.16666667, 0.23333333, 0.3 ,\n",
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" 0.36666667, 0.43333333, 0.5 , 0.56666667, 0.63333333,\n",
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" 0.7 , 0.76666667, 0.83333333, 0.9 , 0.96666667])"
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]
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}
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],
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"prompt_number": 9
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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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"pts = np.vstack((np.r_[0.25, 0.5], np.r_[0.75, 0.5]))"
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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": 10
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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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"AtM, rhstM = DCfun(tM, pts)\n",
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"AinvtM = SolverLU(AtM)\n",
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"phitM = AinvtM*rhstM"
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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": 11
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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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"AqM, rhsqM = DCfun(qM, pts)\n",
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"AinvqM = SolverLU(AqM)\n",
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"phiqM = AinvqM*rhsqM"
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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": 12
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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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"ArM, rhsrM = DCfun(rM, pts)\n",
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"AinvrM = SolverLU(ArM)\n",
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"phirM = AinvrM*rhsrM"
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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": 13
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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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"coreind = (qM.gridCC[:,0]-0.5)**2+(qM.gridCC[:,1]-0.5)**2 >0.43**2\n",
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"phiqM[coreind] = 0."
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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": 14
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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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"Xi = tM.gridCC[:,0].reshape(sz[0], sz[1], order='F')\n",
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"Yi = tM.gridCC[:,1].reshape(sz[0], sz[1], order='F')\n",
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"PHItM = griddata(tM.gridCC[:,0], tM.gridCC[:,1], phitM, Xi, Yi, interp='linear')\n",
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"PHIqM = griddata(qM.gridCC[:,0], qM.gridCC[:,1], phiqM, Xi, Yi, interp='linear')\n",
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"PHIrM = griddata(rM.gridCC[:,0], rM.gridCC[:,1], phirM, Xi, Yi, interp='linear')"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stderr",
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"text": [
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"/Users/sgkang/anaconda/lib/python2.7/site-packages/matplotlib/tri/triangulation.py:110: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.\n",
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" self._neighbors)\n"
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]
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}
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],
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"prompt_number": 15
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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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"fig, axes = plt.subplots(1,3,figsize=(14*1.2,4*1.2))\n",
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"label = [\"(a)\", \"(b)\", \"(c)\"]\n",
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"opts = {}\n",
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"vmin, vmax = PHItM.min(), PHItM.max()\n",
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"dat = axes[0].contourf(Xi, Yi, PHItM, 100)\n",
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"tM.plotGrid(ax=axes[0], **opts)\n",
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"axes[0].set_title('TensorMesh')\n",
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"axes[1].contourf(Xi, Yi, PHIqM, 100)\n",
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"qM.plotGrid(ax=axes[1], **opts)\n",
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"axes[1].set_title('TreeMesh')\n",
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"axes[2].contourf(Xi, Yi, PHIrM, 100)\n",
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"rM.plotGrid(ax=axes[2], **opts)\n",
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"axes[2].set_title('CurvilinearMesh')\n",
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"for i in range(3):\n",
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" axes[i].set_xlim(0.025, 0.975)\n",
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" axes[i].set_ylim(0.025, 0.975)\n",
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" axes[i].text(0., 1.0, label[i], fontsize=24)\n",
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" if i==0: \n",
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" axes[i].set_ylabel(\"y\")\n",
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" else:\n",
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" axes[i].set_ylabel(\" \")\n",
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" axes[i].set_xlabel(\"x\")\n",
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"plt.show()\n",
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"# fig.savefig(\"./ThreeMesh.png\", dpi=100)"
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],
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"language": "python",
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"metadata": {},
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"outputs": []
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},
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"cell_type": "code",
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"input": [],
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},
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"language": "python",
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"outputs": [],
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"prompt_number": 68
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},
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"cell_type": "code",
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"collapsed": false,
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} |