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@sgkang
Created September 20, 2014 19:22
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GPR propagation TEz mode 2D with GPML boundary condition
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"from SimPEG import *\n",
"from scipy.constants import mu_0, epsilon_0\n",
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from SimPEG.Utils import mkvc, sdiag, sdInv, speye"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"cs = 1.0*1e-2\n",
"hx = np.ones(200)*cs\n",
"hy = np.ones(200)*cs\n",
"mesh = Mesh.TensorMesh([hx, hy], 'CC')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 212
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"2D Geo Penetrating Radar (GPR) modeling: $TE^z$ mode with Generalized PML (GPML) boundary "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a href=\"http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1429022&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F9769%2F30810%2F01429022.pdf%3Farnumber%3D1429022\"> \n",
"Generalized Perfectly Mached Layer for the Absorption of Propagating and Evanescent Waves in Losless and Lossy Media (Fand and Zhonghua, 1996)\n",
"</a>"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Maxwell's equations in time domain:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$ \\nabla_s \\times \\vec{E} = -\\imath\\omega\\mu^{'}\\vec{H}$\n",
"\n",
"$ \\nabla_s \\times \\vec{H} -\\imath\\omega\\epsilon^{'}\\vec{E} = 0 $\n",
"\n",
"where\n",
"\n",
"$\\mu^{'} = \\mu + \\frac{\\sigma_0^{*}}{\\imath\\omega}$\n",
"\n",
"$\\epsilon^{'} = \\epsilon + \\frac{\\sigma_0}{\\imath\\omega}$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\nabla_s = \\hat{u}_x\\frac{1}{s_x}\\frac{\\partial}{\\partial x}+\\hat{u}_y\\frac{1}{s_y}\\frac{\\partial}{\\partial y}\n",
"+\\hat{u}_z\\frac{1}{s_z}\\frac{\\partial}{\\partial z}$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"where"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$s_x (x) = s_{x0}(x)(1+\\frac{\\sigma_x(x)}{\\imath\\omega\\epsilon})$\n",
"\n",
"$s_y (y) = s_{y0}(y)(1+\\frac{\\sigma_y(y)}{\\imath\\omega\\epsilon})$\n",
"\n",
"$s_z (z) = s_{z0}(z)(1+\\frac{\\sigma_z(z)}{\\imath\\omega\\epsilon})$"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"In time domain assuming $TE^z$ mode ($e_x$, $e_y$, $h_z$):"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$-\\frac{\\partial e_x^{n}}{\\partial y} = -s_{y0}[\\mu\\triangle t^{-1}(h_{zy}^{n+1/2}-h_{zy}^{n-1/2}) \n",
" + (\\sigma^{*}_0+\\sigma^{*}_y)h_{zy}^{n-1/2}\n",
" + \\mu^{-1}\\sigma^{*}_0\\sigma^{*}_yh_{zy}^{I \\ n}\n",
"]$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\frac{\\partial e_y^{n}}{\\partial x} = -s_{x0}[\\mu\\triangle t^{-1}(h_{zx}^{n+1/2}-h_{zx}^{n-1/2}) \n",
" + (\\sigma^{*}_0+\\sigma^{*}_x)h_{zx}^{n-1/2}\n",
" + \\mu^{-1}\\sigma_0^{*}\\sigma^{*}_xh_{zx}^{I \\ n}\n",
"]$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"where $h_{zx}^{I \\ n} = h_{zx}^{I \\ n-1}+\\triangle t h_{zx}^{n-1/2}$ and $h_{zy}^{I \\ n} = h_{zy}^{I \\ n-1}+\\triangle t h_{zy}^{n-1/2}$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$-\\frac{\\partial h_z^{n+1/2}}{\\partial x} = s_{x0}[\\epsilon\\triangle t^{-1}(e_{y}^{n+1}-e_{y}^{n}) \n",
" + (\\sigma_0+\\sigma_x)e_{y}^{n-1/2}\n",
" + \\epsilon^{-1}\\sigma_0\\sigma_xe_{y}^{I \\ n+1/2}\n",
"]$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\frac{\\partial h_z^{n+1/2}}{\\partial y} = s_{y0}[\\epsilon\\triangle t^{-1}(e_{x}^{n+1}-e_{x}^{n}) \n",
" + (\\sigma_0+\\sigma_y)e_{x}^{n-1/2}\n",
" + \\epsilon^{-1}\\sigma_0\\sigma_ye_{x}^{I \\ n+1/2}\n",
"]$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"where $e_y^{I \\ n+1/2} = e_{y}^{I \\ n-1/2}+\\triangle t e_{y}^{n}$ and $e_x^{I \\ n+1/2} = e_{x}^{I \\ n-1/2}+\\triangle t e_{x}^{n}$"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Discretize the system:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\mathbf{Curl}^{vec}\\mathbf{e}^{n} = -\\triangle t^{-1}\\mathbf{S}_{\\mu}(\\mathbf{h}_d^{n+1/2}-\\mathbf{h}_d^{n-1/2})\n",
" -\\mathbf{S}_{\\sigma^{*}}\\mathbf{h}_d^{n-1/2} - \\mathbf{S}_{\\mu^{-1}\\sigma^{*}}\\mathbf{h}_d^{I \\ n}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\mathbf{h}_d^{n+1/2} = \\mathbf{h}_d^{n-1/2} - \\triangle t\\mathbf{S}^{-1}_{\\mu}[\\mathbf{Curl}^{vec}\\mathbf{e}^{n}\n",
" +\\mathbf{S}_{\\sigma^{*}}\\mathbf{h}_d^{n-1/2} + \\mathbf{S}_{\\mu^{-1}\\sigma^{*}}\\mathbf{h}_d^{I \\ n}]\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"where"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\n",
"\\mathbf{h}_d =\n",
"\\begin{bmatrix}\n",
" \\mathbf{h_{zy}} & \\\\[0.3em]\n",
" \\mathbf{h_{zx}}\n",
"\\end{bmatrix}\n",
"$\n",
",\n",
"$\n",
"\\mathbf{S}_{\\mu} =\n",
"\\begin{bmatrix}\n",
" \\mathbf{diag}(\\mu s_{y0}) & 0 \\\\[0.3em]\n",
" 0 & \\mathbf{diag}(\\mu s_{x0})\n",
"\\end{bmatrix}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\n",
"\\mathbf{S}_{\\sigma^{*}} =\n",
"\\begin{bmatrix}\n",
" \\mathbf{diag}((\\sigma_0^{*}+\\sigma_y^{*}) s_{y0}) & 0 \\\\[0.3em]\n",
" 0 & \\mathbf{diag}((\\sigma_0^{*}+\\sigma_x^{*})s_{x0})\n",
"\\end{bmatrix}\n",
"$\n",
", and\n",
"$\n",
"\\mathbf{S}_{\\mu^{-1}\\sigma^{*}} =\n",
"\\begin{bmatrix}\n",
" \\mathbf{diag}(\\mu^{-1}(\\sigma_0^{*}\\sigma_y^{*}s_{y0}) & 0 \\\\[0.3em]\n",
" 0 & \\mathbf{diag}(\\mu^{-1}(\\sigma_0^{*}\\sigma_x^{*}s_{x0})\n",
"\\end{bmatrix}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\mathbf{Curl}^T\\mathbf{h} = \\triangle t^{-1} \\mathbf{M}^e_{s\\epsilon}(\\mathbf{e}^{n+1}-\\mathbf{e}^{n})\n",
" +\\mathbf{M}^e_{s\\sigma}\\mathbf{e}^{n} + \\mathbf{M}^e_{s\\epsilon^{-1}\\sigma} \\mathbf{e}^{I \\ n+1/2}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\n",
"\\mathbf{e}^{n+1} = \\mathbf{e}^{n} + \\triangle t (\\mathbf{M}^e_{s\\epsilon})^{-1}[\\mathbf{Curl}^T\\mathbf{h} \n",
" - \\mathbf{M}^e_{s\\sigma}\\mathbf{e}^{n} - \\mathbf{M}^e_{s\\epsilon^{-1}\\sigma} \\mathbf{e}^{I \\ n+1/2}]\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"where"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\n",
"\\mathbf{M}^e_{s\\epsilon} = \\mathbf{diag}\n",
"(\\mathbf{A}^{e \\ T}_{c \\ vec}\n",
"\\begin{bmatrix}\n",
" \\epsilon s_{y0} \\\\[0.3em]\n",
" \\epsilon s_{x0}\n",
"\\end{bmatrix}\n",
")\n",
"$\n",
",\n",
"$\n",
"\\mathbf{M}^e_{s\\sigma} = \\mathbf{diag}\n",
"(\\mathbf{A}^{e \\ T}_{c \\ vec}\n",
"\\begin{bmatrix}\n",
" (\\sigma_0+\\sigma_y) s_{y0} \\\\[0.3em]\n",
" (\\sigma_0+\\sigma_x) s_{x0}\n",
"\\end{bmatrix}\n",
")\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\n",
"\\mathbf{M}^e_{s\\epsilon^{-1}\\sigma} = \\mathbf{diag}\n",
"(\\mathbf{A}^{e \\ T}_{c \\ vec}\n",
"\\begin{bmatrix}\n",
" \\epsilon^{-1} \\sigma_0\\sigma_y s_{y0} \\\\[0.3em]\n",
" \\epsilon^{-1} \\sigma_0\\sigma_x s_{x0}\n",
"\\end{bmatrix}\n",
")\n",
"$\n",
"and\n",
"$\n",
"\\mathbf{h} = [\\mathbf{I}^{cc}, \\mathbf{I}^{cc}]\n",
"\\begin{bmatrix}\n",
" \\mathbf{h_{zy}} & \\\\[0.3em]\n",
" \\mathbf{h_{zx}}\n",
"\\end{bmatrix} = \\mathbf{h_{zy}}+\\mathbf{h_{zx}}\n",
"$"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Some useful properties:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$s_{x0}(x) = 1+s_m(\\frac{x}{\\delta_x})^2$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\sigma_x(x) = \\sigma_m sin^2(\\frac{\\pi x}{2\\delta_x})$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\sigma_m = \\frac{\\epsilon c \\delta^{-1}}{1+s_m(1/3+2/\\pi^2)}log(R_{th})$"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"First compute:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$ \\mathbf{h}_d^{I \\ n} = \\mathbf{h}_d^{I \\ n-1} + \\triangle t \\mathbf{h}_d^{n-1/2} $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\mathbf{h}_d^{n+1/2} = \\mathbf{h}_d^{n-1/2} - \\triangle t\\mathbf{S}^{-1}_{\\mu}[\\mathbf{Curl}^{vec}\\mathbf{e}^{n}\n",
" +\\mathbf{S}_{\\sigma^{*}}\\mathbf{h}_d^{n-1/2} + \\mathbf{S}_{\\mu^{-1}\\sigma^{*}}\\mathbf{h}_d^{I \\ n}]\n",
"$"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Then we compute:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$ \\mathbf{e}^{I \\ n+1/2} = \\mathbf{e}^{I \\ n-1/2} + \\triangle t \\mathbf{e}^{n} $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\n",
"\\mathbf{e}^{n+1} = \\mathbf{e}^{n} + \\triangle t (\\mathbf{M}^e_{s\\epsilon})^{-1}[\\mathbf{Curl}^T\\mathbf{h} \n",
" - \\mathbf{M}^e_{s\\sigma}\\mathbf{e}^{n} - \\mathbf{M}^e_{s\\epsilon^{-1}\\sigma} \\mathbf{e}^{I \\ n+1/2}]\n",
"$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"npad = 20\n",
"ax = mesh.vectorCCx[-npad]\n",
"ay = mesh.vectorCCy[-npad]\n",
"indy = np.logical_or(mesh.gridCC[:,1]<=-ay, mesh.gridCC[:,1]>=ay)\n",
"indx = np.logical_or(mesh.gridCC[:,0]<=-ax, mesh.gridCC[:,0]>=ax)\n",
"tempx = zeros_like(mesh.gridCC[:,0])\n",
"tempx[indx] = (abs(mesh.gridCC[:,0][indx])-ax)**2\n",
"tempx[indx] = tempx[indx]-tempx[indx].min()\n",
"tempx[indx] = tempx[indx]/tempx[indx].max()\n",
"tempy = zeros_like(mesh.gridCC[:,1])\n",
"tempy[indy] = (abs(mesh.gridCC[:,1][indy])-ay)**2\n",
"tempy[indy] = tempy[indy]-tempy[indy].min()\n",
"tempy[indy] = tempy[indy]/tempy[indy].max()\n",
"tempx[tempx>1.] = 1.\n",
"tempy[tempy>1.] = 1."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 213
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Lx = mesh.hx[-npad:].sum()\n",
"Ly = mesh.hy[-npad:].sum()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 214
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sighalf = 1e-3\n",
"mu = mu_0*np.ones(mesh.nC)\n",
"epsilon = epsilon_0*np.ones(mesh.nC)*1.\n",
"epsilon[mesh.gridCC[:,1]<0.5] = epsilon_0*2.\n",
"sig0 = sighalf*np.ones(mesh.nC)\n",
"sigs = 0.\n",
"c = 1/np.sqrt(mu*epsilon)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 313
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fmain = 200.*1e6\n",
"lamda = c.min()/fmain\n",
"sm = lamda/(2*hx.min())-1\n",
"sm = 3.\n",
"Rth = 1e-8\n",
"sigm = -(epsilon.max()*c.max()/(0.5*(Lx+Ly)))/(1.+sm*(1./3+2./(np.pi**2)))*np.log(Rth)\n",
"print ('>> sm: %5.2e, lamda: %5.2e, sigm: %5.2e') % (sm, lamda, sigm)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
">> sm: 3.00e+00, lamda: 1.06e+00, sigm: 1.87e-01\n"
]
}
],
"prompt_number": 369
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sigx = sigm*np.sin(0.5*np.pi*np.sqrt(tempx))**2\n",
"sigy = sigm*np.sin(0.5*np.pi*np.sqrt(tempy))**2\n",
"sx0 = 1.+sm*tempx\n",
"sy0 = 1.+sm*tempy"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 370
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(mesh.vectorCCx, sigx.reshape((mesh.nCx, mesh.nCy), order='F')[:,0])\n",
"plt.plot(mesh.vectorCCx, sx0.reshape((mesh.nCx, mesh.nCy), order='F')[:,0])\n",
"plt.plot(mesh.vectorCCx, (sigx*sx0).reshape((mesh.nCx, mesh.nCy), order='F')[:,0])\n",
"plt.legend(('$\\sigma_x$', '$s_{x0}$', '$\\sigma_xs_{x0}$'), fontsize = 16)\n",
"plt.xlabel('x')\n",
"plt.grid(True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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X3NxcMjMzAUhOTiYrK6vpllyNB2FML6/PXU9+eT5L31xKSd25L11JQQlA2C4f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\nY2cNxgp0JysAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x17ab169b0>"
]
}
],
"prompt_number": 384
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Smu = sp.block_diag([sdiag(mu*sy0), sdiag(mu*sx0)])\n",
"SmuI = sp.block_diag([sdiag(1./(mu*sy0)), sdiag(1./(mu*sx0))])\n",
"Smuisig = sp.block_diag([sdiag(sigs*sigy*(1./epsilon)*sy0), sdiag(sigs*sigx*(1./epsilon)*sx0)])\n",
"Ssig = sp.block_diag([sdiag((sigy*mu/epsilon+sigs)*sy0), sdiag((sigx*mu/epsilon+sigs)*sx0)])\n",
"Mesepsisig = sdiag(mesh.aveE2CCV.T*np.r_[1./epsilon*sig0*sigy*sy0, 1./epsilon*sig0*sigx*sx0])\n",
"Messig = sdiag(mesh.aveE2CCV.T*np.r_[(sig0+sigy)*sy0, (sig0+sigx)*sx0])\n",
"Meseps = sdiag(mesh.aveE2CCV.T*np.r_[epsilon*sy0, epsilon*sx0])\n",
"MesepsI = sdInv(Meseps)\n",
"Icc = sp.hstack((speye(mesh.nC), speye(mesh.nC)))\n",
"curl = mesh.edgeCurl\n",
"curlvec = sp.block_diag((curl[:,:mesh.nEx], curl[:,mesh.nEx:]))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 372
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = plt.subplots(1,3, figsize = (15, 6))\n",
"dat = mesh.plotImage(sigx, ax = ax[0])\n",
"plt.colorbar(dat[0], ax = ax[0], orientation='horizontal')\n",
"dat = mesh.plotImage(sigy, ax = ax[1])\n",
"plt.colorbar(dat[0], ax = ax[1], orientation='horizontal')\n",
"dat = mesh.plotImage(epsilon, ax = ax[2])\n",
"plt.colorbar(dat[0], ax = ax[2], orientation='horizontal')\n",
"ax[0].set_title(\"$\\sigma_x$\", fontsize = 18)\n",
"ax[1].set_title(\"$\\sigma_y$\", fontsize = 18)\n",
"ax[2].set_title(\"$\\epsilon$\", fontsize = 18)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 373,
"text": [
"<matplotlib.text.Text at 0x138ab6438>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x179468eb8>"
]
}
],
"prompt_number": 373
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def ricker(fpeak, t, tlag):\n",
" \"\"\"\n",
" Generating Ricker Wavelet\n",
" \n",
" .. math ::\n",
" \n",
" \"\"\"\n",
"# return (1-2*np.pi**2*fpeak**2*(t-tlag)**2)*np.exp(-np.pi**2*fpeak**2*(t-tlag)**2)\n",
" return np.exp(-2*fpeak**2*(t-tlag)**2)*np.cos(np.pi*fpeak*(t-tlag))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 374
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"dt = 1e-11\n",
"fmain = 3e9\n",
"time = np.arange(700)*dt\n",
"wave = ricker(fmain, time, 50*dt)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 375
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(time, wave, '.-')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 376,
"text": [
"[<matplotlib.lines.Line2D at 0x177d4d160>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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kyq0rca9I8+iXLIGHH4Z/+7fyv7NjB0yYADt3Vl2tJDVUPebRPw1MB6YAg4BPEh7GdnYc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\nJElSsvx/NFfbA4IYhLIAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x13a39ee80>"
]
}
],
"prompt_number": 376
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Put Jx source\n",
"txind = Utils.closestPoints(mesh, [0., 0.], gridLoc='Ex')\n",
"q = np.zeros(mesh.nE)\n",
"q[txind] = 1.\n",
"q = Utils.sdiag(1/mesh.edge)*q\n",
"# Put Mz source\n",
"# txind = Utils.closestPoints(mesh, [0., 0.], gridLoc='CC')\n",
"# q = np.zeros(mesh.nC)\n",
"# q[txind] = 1.\n",
"Px = mesh.getInterpolationMat(mesh.gridCC, 'Ex')\n",
"Py = mesh.getInterpolationMat(mesh.gridCC, 'Ey')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 377
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"First compute:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$ \\mathbf{h}_d^{I \\ n} = \\mathbf{h}_d^{I \\ n-1} + \\triangle t \\mathbf{h}_d^{n-1/2} $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\mathbf{h}_d^{n+1/2} = \\mathbf{h}_d^{n-1/2} - \\triangle t\\mathbf{S}^{-1}_{\\mu}[\\mathbf{Curl}^{vec}\\mathbf{e}^{n}\n",
" +\\mathbf{S}_{\\sigma^{*}}\\mathbf{h}_d^{n-1/2} + \\mathbf{S}_{\\mu^{-1}\\sigma^{*}}\\mathbf{h}_d^{I \\ n}]\n",
"$"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Then compute:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$ \\mathbf{e}^{I \\ n+1/2} = \\mathbf{e}^{I \\ n-1/2} + \\triangle t \\mathbf{e}^{n} $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\n",
"\\mathbf{e}^{n+1} = \\mathbf{e}^{n} + \\triangle t (\\mathbf{M}^e_{s\\epsilon})^{-1}[\\mathbf{Curl}^T\\mathbf{h} \n",
" - \\mathbf{M}^e_{s\\sigma}\\mathbf{e}^{n} - \\mathbf{M}^e_{s\\epsilon^{-1}\\sigma} \\mathbf{e}^{I \\ n+1/2} + \\mathbf{j}_s]\n",
"$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"hd0 = np.zeros(2*mesh.nC)\n",
"hd1 = np.zeros(2*mesh.nC)\n",
"hId0 = np.zeros(2*mesh.nC)\n",
"hId1 = np.zeros(2*mesh.nC)\n",
"e0 = np.zeros(mesh.nE)\n",
"e1 = np.zeros(mesh.nE)\n",
"eI0 = np.zeros(mesh.nE)\n",
"eI1 = np.zeros(mesh.nE)\n",
"h = np.zeros((mesh.nC, time.size))\n",
"ex = np.zeros((mesh.nC, time.size))\n",
"ey = np.zeros((mesh.nC, time.size))\n",
"\n",
"for i in range (time.size):\n",
" \n",
" js = q*wave[i] \n",
" eI1 = eI0 + dt*e0\n",
" e1 = e0 + MesepsI*dt*(curl.T*(Icc*hd1)-Messig*e0-Mesepsisig*eI1-js)\n",
"# e1 = e0 + MesepsI*dt*(curl.T*(Icc*hd1) - Messig*e0 - Mesepsisig*eI1)\n",
" e0 = e1.copy()\n",
" ex[:,i] = Px*e1\n",
" ey[:,i] = Py*e1\n",
" hId1 = hId0 + dt*hd0\n",
"# hd1 = hd0 - SmuI*dt*(curlvec*e0+Ssig*hd0+Smuisig*hId1+np.r_[js, js]*0.5)\n",
" hd1 = hd0 - SmuI*dt*(curlvec*e0+Ssig*hd0+Smuisig*hId1) \n",
" hd0 = hd1.copy()\n",
" h[:,i] = Icc*hd1 "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 378
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"icount = 600\n",
"extent = [mesh.vectorCCx.min(), mesh.vectorCCx.max(), mesh.vectorCCy.min(), mesh.vectorCCy.max()]\n",
"plt.imshow(np.flipud(h[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent) \n",
"plt.imshow(np.flipud(c.reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'jet', extent=extent, alpha=0.2) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 382,
"text": [
"<matplotlib.image.AxesImage at 0x1793b28d0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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ITY+R86syfTyDJ4a+FUyZ++F4hsiI5SSHiIQgjIFe3B9TQJ3XxXIniMmgt46N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\nZXHwxwrpZMcoDZkpSZC4lOjWciwTppICHE4MsVg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cpRmreUyP1Tg/5nG+3GZsY57ozjXq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\nQIECBQoUKPA84v8B0YpmQ6L3mfsAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x176afd0b8>"
]
}
],
"prompt_number": 382
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from JSAnimation import IPython_display\n",
"from matplotlib import animation\n",
"extent = [mesh.vectorCCx.min(), mesh.vectorCCx.max(), mesh.vectorCCy.min(), mesh.vectorCCy.max()]\n",
"fig, ax = plt.subplots(1,3, figsize = (24, 8))\n",
"for i in range(3):\n",
" ax[i].set_xlabel('x (m)', fontsize = 16)\n",
" ax[i].set_ylabel('y (m)', fontsize = 16)\n",
" ax[i].set_xlim(extent[:2])\n",
" ax[i].set_ylim(extent[2:])\n",
"ax[0].set_title('$h_z$', fontsize = 20)\n",
"ax[1].set_title('$e_x$', fontsize = 20)\n",
"ax[2].set_title('$e_y$', fontsize = 20)\n",
"nskip = 40\n",
"def animate(i_id):\n",
" icount = i_id*nskip\n",
" frame1 = ax[0].imshow(np.flipud(h[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent) \n",
" frame2 = ax[1].imshow(np.flipud(ex[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent, vmin = ex[:,icount].min()*0.05, vmax = ex[:,icount].max()*0.05)\n",
" frame3 = ax[2].imshow(np.flipud(ey[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent, vmin = ey[:,icount].min()*0.05, vmax = ey[:,icount].max()*0.05) \n",
" for i in range(3):\n",
" ax[i].imshow(np.flipud(c.reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'jet', extent=extent, alpha=0.2) \n",
" return frame1, frame2, frame3\n",
"animation.FuncAnimation(fig, animate, frames=16, interval=40, blit=True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"<script language=\"javascript\">\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src = this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" } \n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<div class=\"animation\" align=\"center\">\n",
" <img id=\"_anim_imgAGCNRDHKRIEIIYDV\">\n",
" <br>\n",
" <input id=\"_anim_sliderAGCNRDHKRIEIIYDV\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animAGCNRDHKRIEIIYDV.set_frame(parseInt(this.value));\"></input>\n",
" <br>\n",
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" <button onclick=\"animAGCNRDHKRIEIIYDV.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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" <button onclick=\"animAGCNRDHKRIEIIYDV.last_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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" <button onclick=\"animAGCNRDHKRIEIIYDV.faster()\">+</button>\n",
" <form action=\"#n\" name=\"_anim_loop_selectAGCNRDHKRIEIIYDV\" class=\"anim_control\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" > Reflect </input>\n",
" </form>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_imgAGCNRDHKRIEIIYDV\";\n",
" var slider_id = \"_anim_sliderAGCNRDHKRIEIIYDV\";\n",
" var loop_select_id = \"_anim_loop_selectAGCNRDHKRIEIIYDV\";\n",
" var frames = new Array(0);\n",
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