{ "metadata": { "name": "", "signature": "sha256:3ca35ee2ce462eb6186befc052829c0acef4986990a711f49eacd0ce26abb48f" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Multipole and Local Expansions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import numpy.linalg as la\n", "import matplotlib.pyplot as pt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's consider a potential. This one could look slightly familiar from a homework assignment." ] }, { "cell_type": "code", "collapsed": false, "input": [ "nsources = 15\n", "nxtgts = 400\n", "nytgts = 400\n", "\n", "angles = np.linspace(0, 2*np.pi, nsources, endpoint=False)\n", "r = 1 + 0.3 * np.sin(3*angles)\n", "sources = np.array([\n", " r*np.cos(angles),\n", " r*np.sin(angles),\n", " ])\n", "\n", "charges = 0.5+2*np.sin(3*angles)\n", "\n", "left, right, bottom, top = extent = (-2, 4, -4, 2)\n", "targets = np.mgrid[left:right:nxtgts*1j, bottom:top:nytgts*1j]\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "cell_type": "code", "collapsed": false, "input": [ "pt.plot(sources[0], sources[1], \"x\")\n", "\n", "dist_vecs = sources.reshape(2, -1, 1, 1) - targets.reshape(2, 1, targets.shape[-1], -1)\n", "dists = np.sqrt(np.sum(dist_vecs**2, axis=0))\n", "\n", "potentials = np.sum(charges.reshape(-1, 1, 1) * np.log(dists), axis=0)\n", "pt.imshow(potentials.T[::-1], extent=extent)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 32, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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S4ydft28cvMkjBIrzrgCDjo4CYdmem1AEgPyu4Qyu0agFoLN7T+EQZ3CNqhlz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\n9jWwxCBL9/EzOG9N69D31YC8IS2D343v1eergEW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czv+HmHqVwKmdrxMG6jk6QKjzDtB9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"text": [ "" ] } ], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's create a stash of derivatives, all about a center of 0, to make things easier:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def f(arg):\n", " return np.log(np.sqrt(np.sum(arg**2, axis=0)))\n", "\n", "def fdx(arg):\n", " x, y = arg\n", " r2 = np.sum(arg**2, axis=0)\n", " return x/r2\n", "\n", "def fdy(arg):\n", " x, y = arg\n", " r2 = np.sum(arg**2, axis=0)\n", " return y/r2\n", "\n", "def fdxx(arg):\n", " x, y = arg\n", " r2 = np.sum(arg**2, axis=0)\n", " return 1/r2 - 2*x**2/r2**2\n", "\n", "def fdyy(arg):\n", " x, y = arg\n", " r2 = np.sum(arg**2, axis=0)\n", " return 1/r2 - 2*y**2/r2**2\n", "\n", "def fdxy(arg):\n", " x, y = arg\n", " r2 = np.sum(arg**2, axis=0)\n", " return - 2*x*y/r2**2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 33 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Local expansions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "center = np.array([1.5, -1])\n", "#center = np.array([2, -2])\n", "#center = np.array([3, -3])\n", "#center = np.array([0, 0])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 71 }, { "cell_type": "code", "collapsed": false, "input": [ "expn = 0\n", "for isrc in range(nsources):\n", " a = sources[:, isrc] - center\n", " hx, hy = center.reshape(-1, 1, 1) - targets\n", " expn += charges[isrc]*(\n", " f(a)\n", " + fdx(a)*hx + fdy(a)*hy\n", " + fdxx(a)*hx**2/2\n", " + fdxy(a)*hx*hy\n", " + fdxy(a)*hy**2/2\n", " )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 72 }, { "cell_type": "code", "collapsed": false, "input": [ "err = expn - potentials\n", "pt.plot(center[0], center[1], \"o\")\n", "pt.plot(sources[0], sources[1], \"x\")\n", "pt.imshow(np.log10(1e-2 + np.abs(err.T[::-1])), extent=extent)\n", "pt.colorbar()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 75, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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cyYfT1/G3f/xGvua7/xtvCt/HjXyWHZyhQQ+LYZk2s0xzhp2c3P9xXviFg/wD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\nXUrYSRcDMBOWNmKXMbu+jd1u2wFqocfYpPdA25OzTGiKpN9SUJ+LIY9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WWzpg0lPh/wvr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W48I1UAFpaZ1lrPQZKibQsVImt3oRx175bvHChdInnKTMWQtZpSXLm2n8CMZWyVdBXAN4Bn7oTz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\nNlTmnQGeheLqe3uaZ3apbQ+KDXkI+zJLr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"text": [ "" ] } ], "prompt_number": 75 }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Move the center around, see how the errors change\n", "* Reduce to linears, see how the errors change" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multipole expansions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "center = np.array([0, 0])\n", "# center = np.array([1, 0])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 90 }, { "cell_type": "code", "collapsed": false, "input": [ "expn = 0\n", "for isrc in range(nsources):\n", " a = targets - center.reshape(-1, 1, 1)\n", " hx, hy = center - sources[:, isrc]\n", " expn += charges[isrc]*(\n", " f(a)\n", " + fdx(a)*hx + fdy(a)*hy\n", " + fdxx(a)*hx**2/2\n", " + fdxy(a)*hx*hy\n", " + fdxy(a)*hy**2/2\n", " )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 101 }, { "cell_type": "code", "collapsed": false, "input": [ "err = expn - potentials\n", "pt.plot(center[0], center[1], \"o\")\n", "pt.plot(sources[0], sources[1], \"x\")\n", "pt.imshow(np.log10(1e-2 + np.abs(err.T[::-1])), extent=extent)\n", "pt.colorbar()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 99, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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0rc6QfNjC9k2pqWmqExUboGVL2obKvFY59IDWp82w4r+rE+2vKSMnCxDDosha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I+UCSrLXUA3i/lpNbOYpLIT2gDLrmuQs79njGCwAKX7tIFYrE3OD03teOJ/qMFLs09tLNgMsudT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\nwdT99HE1a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O7w3v/Kbo8HwDl31Dl3uFpeJlStSU+GuQPivf9J7/1V3vsvAb4D+IvnC6DB\nzvnU/h2hHMdNFcX873fovElJTdG10+K9HwHvAv6MwFT9J+/9nbsxFi3Oud8H/ga4vpp78Qd3e0zA\nW4HvITCMt1Wf3WZoLwf+ovKp3Qr8iff+5l0ek5XnlYtjL/h2T/ZkT55Tshvs557syZ7sybbJHqjt\nyZ7syXNK9kBtT/ZkT55Tsgdqe7Ine/Kckj1Q25M92ZPnlOyB2p7syZ48p2QP1PZkT/bkOSV7oLYn\ne7Inzyn5/wFNufgGf7MrQQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 99 }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Move the center around, observe convergence behavior\n", "* Reduce to linears, observe convergence behavior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Look at individual basis functions:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "pt.imshow(\n", " fdx(targets).T[::-1],\n", " extent=extent, vmin=-1, vmax=1)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 115, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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yoA4YDBRipSYFr+UQAIAdMJnEVCYwrbkFLEuUvl5nOhvRizuzkFbugKmyz4FC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\nVV9H98lj/odYgIjI04KilmYsY7Pjku+yNLSa3qMqDx75IftPE39SxyP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"text": [ "" ] } ], "prompt_number": 115 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Why is this thing called a 'multipole' expansion?" ] } ], "metadata": {} } ] }