{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Laplace equation using the relaxation method\n", "\n", "In this notebook you will see how to solve the **Laplace equation** using the **relaxation method** in `Python` programming language." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Importing the libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from pathlib import Path\n", "import matplotlib.pyplot as pl\n", "import matplotlib.animation as animation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The code" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "Path(\"./results\").mkdir(parents=True, exist_ok=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Geometry of the box" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "n_x , n_y = 40 , 40\n", "x = np.arange(n_x)\n", "y = np.arange(n_y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initialize the array" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "field = np.zeros((4, n_x,n_y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Set the boundary conditions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example 0: A line" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def in_cond0(field):\n", " field[15:25,20] = 1\n", " return field" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example 1: A square" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def in_cond1(field):\n", " field[15:26,15] = 1\n", " field[15,15:26] = 1\n", " field[15:26,25] = 1\n", " field[25,15:26] = 1\n", " return field" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example 2: A triangle" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def in_cond2(field):\n", " field[15:25,15] = 1\n", " field[15,15:25] = 1\n", " for ij in range(11):\n", " field[15+ij,25-ij]=1\n", " return field" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example 3: Open triangle" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def in_cond3(field):\n", " field[15:25,15] = 1\n", " field[15,15:25] = 1\n", " for ij in range(8):\n", " field[15+ij,25-ij]=1\n", " return field" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualizing the examples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the initial conditions" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "field = np.zeros((4, n_x,n_y))\n", "field[0] = in_cond0(field[0])\n", "field[1] = in_cond1(field[1])\n", "field[2] = in_cond2(field[2])\n", "field[3] = in_cond3(field[3])" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for i in range(4):\n", " pl.figure(dpi = 100)\n", " pl.imshow(field[i])\n", " pl.title(f'Example {i} - Iteration 0')\n", " pl.savefig(f'results/cond{i}-It_0.pdf')\n", " pl.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plots until iteration 10" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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KbKF6PXqqC+zujC67LbF+qG9vSmo/1F7qX7N/zUd2s2w42M0y4WA3y4SD3SwTTtCNMA3UZJYSiaX+geYTdIdNfTpZnpofvW5KptTgkLszP3sqGdc7Z2Oybl17U5L7oS7RWbd/zUd2s1w42M0y4WA3y4SD3SwTDnazTDgb3wZRMzhC7NhRKVN/Oo3c01ddRt/25t+et0x/JP3EodWiZS/bN1k1NSVTahTYuoEnUl1g67Lute1NSO2H3sT+gvT+Tb0Pde/ZeOYju1kmHOxmmXCwm2XCwW6WiVamf7oQOBMYzMCcHxE/6FRDu1pdF83+aiJrwuZtyaqTNlaTY+vWVa8vrzNvSl9N+dKml9GtNif2w/SNNVNYpfZv4n2ofc/GsWbSvYPTP90raTpwj6Tby+cujYjPdK55ZtYuzQw4uRpYXd7fIGlw+iczG0N26zv7kOmfAM6RtFTSVZJm1rxmoaS7Jd29nfSpppl1XivTP11G0WVjLsWR/7Op13n6J7Pu0FSwp6Z/iog1EdEfEQPAFcAxnWummbWqmWx8cvqnwXneyoenAA90poldJtXNMtJdYKOvmhmesGFLsu60ldVs/Nal1ZFdAQ7h/ZWyKTPTy+2dWO0q2jOhpqtp7ZCtzUmNAls3AEeqC2wq6w7wkqWTKmXTVm5N1k3t34HE+1D3no3neeFamf7pNElzKX6OWw58oAPtM7M2aWX6pzx/Uzcbo9yDziwTDnazTPh69jaIVHdMgG3VxFA8vyFZddKq6pCt+9Ssb/Jz1YTVtml7Jev29yaSZjUf8bsx21RSMr9XkwdLXY9e1wU2lYybtOr5ZN3U/o3U+1D3no1jPrKbZcLBbpYJB7tZJhzsZplwsJtlwtn4dqgbXXZ7YlTTTdURWCHda6l3W2KiNWDis9VupQNTqhl6gOipfp7HhJq0e6sf/YnMe93ca6lRYOsG9kh1ga37VSO1f1Pvw3juFlvHR3azTDjYzTLhYDfLhIPdLBNO0HXSQLVL5kA6B4ViU7WsJkGnDdVkXE9PdZomAO3R4lusRDKvDcmt1JRMyVFgSV+PnuoCCzXJuMT7kCMf2c0y4WA3y4SD3SwTDnazTDQz4ORk4E6gt6x/U0RcIOkQ4Hpgb+Ae4PSIqEk/2QtqkkWxLdH9rCZhFVsT4+/X9IpTKsHWBZLzo9dNyZQYHLL2evQMe8Y1q5kjex9wfEQcRTFG/DxJxwGXUEz/dBiwDjijY600s5btMtijsLF8OLG8BXA8cFNZvgg4uRMNNLP2aHaSiJ5yGOm1wO3AY8D6iBj8UXMFNfO/efons+7QVLCXM7/MBeZQzPzy6mZX4OmfzLrDbmXjI2I9cAfwRmCGpMEE3xxgZXubZmbt1Ew2fl9ge0Ssl7QncAJFcu4O4N0UGfkFwC2dbOi4l8giJ7uUQroLa91ih9uebuIMe1s003F6NrBIUg/FmcCNEXGbpIeA6yVdBPyaYj44M+tSzUz/tJRiTvah5Y/jmVvNxgz3oDPLhIPdLBO+nn0scsLKhsFHdrNMONjNMuFgN8uEg90sEw52s0w42M0y4WA3y4SD3SwTDnazTDjYzTLhYDfLhIPdLBMOdrNMONjNMuFgN8vELoNd0mRJv5J0v6QHJX2qLL9G0u8l3Vfe5na8tWY2bM0MXjE4/dNGSROBn0v6YfncRyPipp281sy6RDMDTgaQmv7JzMaQYU3/FBFLyqculrRU0qWSktO9ePons+4wrOmfJL0G+ATFNFBvAGYBH695rad/MusCw53+aV5ErC5neO0DrsZjyJt1tWay8ftKmlHeH5z+6beSZpdlopiu+YHONdPMWtXK9E8/LeeBE3AfcFbnmmlmrWpl+qfjO9IiM+sI96Azy4SD3SwTDnazTDjYzTLhYDfLhIPdLBMOdrNMONjNMuFgN8uEg90sEw52s0w42M0y4WA3y4SD3SwTDnazTDjYzTLhYDfLhIPdLBMOdrNMqJjwZYRWJj0NPFE+3Ad4ZsRWPnK8XWPPeNq2gyJi39QTIxrsL1qxdHdEHD0qK+8gb9fYM563rZFP480y4WA3y8RoBvvlo7juTvJ2jT3jedteMGrf2c1sZPk03iwTDnazTIx4sEuaJ+kRScsknTfS628nSVdJWivpgYayWZJul/Ro+XfmaLZxOCQdKOkOSQ9JelDSh8vyMb1tkiZL+pWk+8vt+lRZfoikJeX/5A2SJo12WzthRIO9nAn2y8BfAEcAp0k6YiTb0GbXAPOGlJ0HLI6Iw4HF5eOxZgdwbkQcARwHnF2+T2N92/qA4yPiKGAuME/SccAlwKURcRiwDjhj9JrYOSN9ZD8GWBYRj0fENuB64KQRbkPbRMSdwHNDik8CFpX3F1HMXT+mRMTqiLi3vL8BeBg4gDG+bVHYWD6cWN4COB64qSwfc9vVrJEO9gOAJxseryjLxpP9ImJ1ef8pYL/RbEyrJB1MMWX3EsbBtknqkXQfsBa4HXgMWB8RO8oq4/F/EnCCrqOi+F1zzP62KWkacDPwkYh4vvG5sbptEdEfEXOBORRnmq8e3RaNnJEO9pXAgQ2P55Rl48kaSbMByr9rR7k9wyJpIkWgfzMivlMWj4ttA4iI9cAdwBuBGZL2KJ8aj/+TwMgH+13A4WX2cxJwKnDrCLeh024FFpT3FwC3jGJbhkWSgCuBhyPicw1Pjeltk7SvpBnl/T2BEyjyEXcA7y6rjbntataI96CT9A7g80APcFVEXDyiDWgjSdcBb6W4RHINcAHwPeBG4OUUl/POj4ihSbyuJulNwH8BvwEGyuLzKb63j9ltk3QkRQKuh+JAd2NE/KOkV1Aki2cBvwbeExF9o9fSznB3WbNMOEFnlgkHu1kmHOxmmXCwm2XCwW6WCQe7WSYc7GaZ+D9BkC38qio6tQAAAABJRU5ErkJggg==\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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f6mF3r3v38JHdLBMOu1kmHHazTDjsZploZvqni4GzgIHemgsjojpXUMaid2u18NX0NE3jn6vOnPXGhXsm6771hU9UymY+m+50m/pE9Tvmo9a+lKwbr1aHxva9vLFar6/OHOieG72rNdIbPzD90/2SpgD3SbqjXHd5RPxr+5pnZq3SyAUnVwIry+UNkgamfzKzEWSH3rMPmv4J4DxJD0m6RlLya1eSzpa0SNKiraQvnWRm7dfM9E9XAG8G5lAc+b+aepynfzLrDg2FPTX9U0Ssjoi+iOgHrgKObF8zzaxZjfTGJ6d/Gpjnrbx7ErCkPU0cwaI6VLX/lVeSVUet66mUTb0/PdR08jNTKmWje6q95gCxoVrev7E6BBagf0vi04NIXGwjsV/W/ZqZ/uk0SXMoPo5bCnysDe0zsxZpZvonf6ZuNoJ4BJ1ZJhx2s0z4++wdVm+oad/66hDWUa+lxyXoxerQ2v7+9FVrY3P1OeoOd3XH207NR3azTDjsZplw2M0y4bCbZcJhN8uEe+M7rV6Pd1R7yOsNrUWJ/9GpYa3b2p5lx0d2s0w47GaZcNjNMuGwm2XCHXTdbAc688y2x0d2s0w47GaZcNjNMuGwm2Viu2GXNEHS7yQ9KOkRSZeU5ftLWijpSUk3SGp8MnEz67hGjuybgeMi4u0U14ifK+lo4DKK6Z8OANYDZ7atlWbWtO2GPQoD1yMeW94COA74UVk+HzixHQ00s9ZodJKI0eVlpNcAdwBPAT0RMXBh8+XUmf/N0z+ZdYeGwl7O/DIHmEUx88vBjW7A0z+ZdYcd6o2PiB7gTuBdwDRJAyPwZgErWts0M2ulRnrj95Q0rVyeCJwAPEYR+pPLaqcDt7SpjWbWAo2MjZ8JzJc0muKfw40RcZukR4HrJV0KPEAxH5yZdalGpn96iGJO9sHlT+OZW81GDI+gM8uEw26WCYfdLBMOu1kmHHazTDjsZplw2M0y4bCbZcJhN8uEw26WCYfdLBMOu1kmHHazTDjsZplw2M0y4bCbZcJhN8uEw26WiWamf7pW0jOSFpe3OW1vrZkNWSMXnByY/mmjpLHA3ZJ+Vq77dET8aBuPNbMu0cgFJwNITf9kZiPIkKZ/ioiF5aovSXpI0uWSktO9ePons+4wpOmfJB0GfI5iGqh3AtOBz9Z5rKd/MusCQ53+aW5ErCxneN0MfA9fQ96sqw11+qffS5pZloliuuYl7WummTWrmemffiVpT0DAYuCc9jXTzJrVzPRPx7WlRWbWFh5BZ5YJh90sEw67WSYcdrNMOOxmmXDYzTLhsJtlwmE3y4TDbpYJh90sEw67WSYcdrNMOOxmmXDYzTLhsJtlwmE3y4TDbpYJh90sEw67WSZUTPjSoY1JLwDPlnf3ANZ2bOOd4/0aeXamfds3IvZMreho2F+3YWlRRBwxLBtvI+/XyLMz71stn8abZcJhN8vEcIb9ymHcdjt5v0aenXnf/mjY3rObWWf5NN4sEw67WSY6HnZJcyU9LulJSRd0evutJOkaSWskLakpmy7pDklPlD93G842DoWk2ZLulPSopEckfbIsH9H7JmmCpN9JerDcr0vK8v0lLSz/Jm+QNG6429oOHQ17ORPst4H3AYcCp0k6tJNtaLFrgbmDyi4AFkTEgcCC8v5I0wucHxGHAkcD55a/p5G+b5uB4yLi7cAcYK6ko4HLgMsj4gBgPXDm8DWxfTp9ZD8SeDIino6ILcD1wLwOt6FlIuIuYN2g4nnA/HJ5PsXc9SNKRKyMiPvL5Q3AY8DejPB9i8LG8u7Y8hbAccCPyvIRt1+N6nTY9waW1dxfXpbtTGZExMpyeRUwYzgb0yxJ+1FM2b2QnWDfJI2WtBhYA9wBPAX0RERvWWVn/JsE3EHXVlF8rjliP9uUtAtwE/CpiHi5dt1I3beI6IuIOcAsijPNg4e3RZ3T6bCvAGbX3J9Vlu1MVkuaCVD+XDPM7RkSSWMpgv7DiLi5LN4p9g0gInqAO4F3AdMkjSlX7Yx/k0Dnw34vcGDZ+zkOOBW4tcNtaLdbgdPL5dOBW4axLUMiScDVwGMR8bWaVSN63yTtKWlauTwROIGiP+JO4OSy2ojbr0Z1fASdpPcDXwdGA9dExJc62oAWknQdcCzFVyRXAxcBPwFuBPah+DrvKRExuBOvq0k6BvgN8DDQXxZfSPG+fcTum6S3UXTAjaY40N0YEV+Q9CaKzuLpwAPAhyNi8/C1tD08XNYsE+6gM8uEw26WCYfdLBMOu1kmHHazTDjsZplw2M0y8f9ToXVCbDaI1wAAAABJRU5ErkJggg==\n", 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Iterate N times, plot each iteration\n", "for i in range(4):\n", " for nit in range(10):\n", " field[i,1:-1,1:-1] = 0.25 * (field[i,0:-2,1:-1] + field[i,2:,1:-1] + field[i,1:-1,0:-2] + field[i,1:-1,2:])\n", " # Re-inforce initial conditions\n", " field[0] = in_cond0(field[0])\n", " field[1] = in_cond1(field[1])\n", " field[2] = in_cond2(field[2])\n", " field[3] = in_cond3(field[3])\n", "\n", " # plot\n", " pl.imshow(field[i])\n", " pl.title(f'Example {i}, Iteration {nit}')\n", " name = f\"results/example{i}-It_\" + str(nit+1) + \".pdf\"\n", " pl.savefig(name,dpi=100)\n", " pl.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Making a movie (until iteration 100) for each example" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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hq/FJotDYOskr6oTLjsdto5JMURbYKPEEJEJgA9UdYGZDVVb14+KyQ8eu31exHbd2f9j2qPHpim1VM6HcpzJNLGIhkeViNggJnW7Foci7p1dXbE9PxrMi94+vrRoTKXKj8NxmkJ12bDr+pcNXBMr/dOK+i+7RVEh3KovyABl+D4QQA0HOLkQmyNmFyAQ5uxCZMHyBLln+qbv67J4Q6CIxLhLiIC6/FNlSWWCj+eipENhIjDvtxMWp/wrOP/6Riu2UFXFy32OaVTFvhcVCXCMosN4M4k9biXStc8Ek8+mFWKDb06qKcdunjg/b3tU8s2KbnI2VzrH9QZ376ilIl8sKxN5mUFKqWBCJyIm20b2bup9TIl+XaGQXIhPk7EJkgpxdiEyQswuRCZ3koLvZzHaa2f1ttuvN7Akz21a+Xt/fbgohuqUTNf5jwJ8Af7bIfqO7v7/nPTpApEjWmuyfyPIZKffjcduFwN6qln8La69BIgtskHgC4hDYSHUHuOGEbaF9+bM9tL5pqqq8f3tXEEILLKwMfm0JfhDwZiIZxFiQyTbRto5qHiWq8AGH0C61/JMQYpnRzUfL283svvIx/9ie9UgI0ReW6uwfBM4CNgI7gA+kGprZVWZ2r5ndO8fMEncnhOiWJTm7uz/p7i13XwA+DLz8EG1V602IEWBJ4bJmdlJbFdc3Avcfqn3PSAkadcIWg9DHKEQSYCEIqYzCLFOllyJ7KgtsNB89FQJ7pHLr5DGhfd9c54NEVJkqykTrQSbd5PopYTiiTtsBc1hnL8s/vQp4npk9DlwHvMrMNlIk7n0EeGv/uiiE6AVLLf/0kT70RQjRRxRBJ0QmyNmFyAQ5uxCZMPzkFTVqvSUn+9cKlw2U2SBEEiBIlspCcMYiG8DCiqriG9VegzgLbJR44khhy1T15G6dOCtsu2t/kHV2Pr6+UV4OWwhq2NWokWYeK/fLDY3sQmSCnF2ITJCzC5EJcnYhMmH4Al0N6hSvT4U4RvYonBISYl4g2gVJVUt7INCNxcpQVJIplQV2OfF30/Hxbt33oortwb0nhm0nJqulohpT8TjVmAtsgSYaiXZF28CeaEsk3NUR87yGStgDNLILkQlydiEyQc4uRCbI2YXIBDm7EJkwump8KjS2W8LkBHHTzhMhJPYV2BuJpAljjaryHtVeG2XunqlK4Vv3V1V3gPsmTq7YntgTJ6+Ym6im9B2fii9aM8h8Fiv08XUIQ2tbietQQ433EQi51cguRCbI2YXIBDm7EJnQSfmnU83sTjP7npk9YGbvKO0bzOwOM3uo/Kvc8UKMMJ0IdPPA1e7+LTM7Cvimmd0BXAFscff3mdk1wDXA7/Svq4cgnM8++G4sxi0QewJbiibDF3UiIiEOYOv+F1Zs2yZOCds+smdDxTaxtxoWC9CYrMYoj+1LCHTVtAA0Z6rnsTGbEOjmqmKctRLXYT4IZ06JeVHIbSoMd6E/wmwn5Z92uPu3yvcTwIPAycBFwOay2Wbg4r70UAjRE2qNf2Z2BvAyYCtwQlvu+J8AJ/S2a0KIXtKxs5vZOuCzwG+5+972ZV78iBg+k6j8kxCjQUfObmbjFI7+CXf/XGl+0sxOKpefBOyM1lX5JyFGg04qwhhFUYgH3f0P2xbdDlwOvK/8e1tPe5YSLyKi6KR+BZ9F3Up01YIQvIWFRHLLIAyvFYX7DZg4Kq4qxAFsmzi1YvvhnueFbXftXlc17g0KqQPjk9XzMF6tlgXA2FT1YjQDMa45E98gjflAoJuL8wqEkXWpSLlg7nqdqDqv4w8JOlHj/zXwFuC7ZrattF1L4eS3mtmVwKPAJV33RgjRNzop//R1wohyAF7d2+4IIfrFCPwaLYQYBHJ2ITJBzi5EJozufPaAlHoZCQrJkj2BOZVpNJpOHs93TkgaUTRlK/58nQ1qTc2l0tb2iU6V90h1B/j+7udXbE89e1TYtrUnmKO+Nz43kRo/ti++ZuOBGj82Vb2QjdlYjbeZ4KJFYbEArfACJ9oG+0uExfZr7rtGdiEyQc4uRCbI2YXIBDm7EJkwfIGuB2GAdRL/RSGOqfnKjcDemK+KRUGuyMI+V207Px/UjwKmW9VQ0emFOHy0W5IlmYLkkNF89FQIbCTGze2J50OM76meh/GJWOgcmwzW359I3BmIcc3geBszQU0oEqGxNUQ3TyanrBFa2wufCNDILkQmyNmFyAQ5uxCZIGcXIhPk7EJkwvDV+ARRyGAqrDUMRUyoopEanyoFFNnDUkKzcbcaM1V1eW46PuW7p6uZVfe01sQbrsGWqarqvXVf5yWZoiywYeIJEiGwgepe2KvnZsVE2JTxIDQ2pcZHyntzuqq8N2YTCSlmqxfY5mLlnvnAvhBvN1Tp+5RFNoVGdiEyQc4uRCbI2YXIhG7KP11vZk+Y2bby9fr+d1cIsVS6Kf8EcKO7v78vPYvEiyjkEBLZZRMCXZQ9NLBBXCIozFQ6nQjzDGqIz++LBaunJ6ti3Pap48O2sL1iuXUyrm2+deKsiu3BvSeGbaP66GFJplQW2GA+eioENhLjxidj0W3Fvur1GdsfX7OxfYEYF4TG2mwiXDaau56Yzx6KbqnQ2uB+TM5bD0NruxfzOkk4uQPYUb6fMLMD5Z+EEMuIbso/AbzdzO4zs5tVxVWI0aab8k8fBM4CNlKM/B9IrKfyT0KMAEsu/+TuT7p7y90XgA8DL4/WVfknIUaDTtT4sPzTgTpvJW8E7u9994QQvaKb8k+XmdlGinytjwBvXVIP6qiMqcQAgQIaqqoAgfKeCp1szlSV87GZ6udjVF8MoLUvqFG2J/583T++tmK7q3lm2PZNU0dXbPvm4qemXfurKv/EZKCwA3MT1XDXxmSQZCLI9pqyR4knIA6BjVR3gLFIjZ+K1fRmkB22EYTLEoTFpuwehcVCGC6bTF4RqfR9SlKRopvyT1/qfXeEEP1CEXRCZIKcXYhMkLMLkQkjO589zhibKJcThCJaaq5wMDfZ5uLT0AjEnuZUEBI6HgtWUfUmbyRKRXlVCJucrQpxAN/eVRXzksxX+9sIjgFgPAjvHYtExv3xrqKSTKl555E9GQIbiHHN/Ylw16lAeOt2jnpKoKtR/ikMjU3ez8ouK4ToAjm7EJkgZxciE+TsQmSCnF2ITBhdNT5S05PZZTtPOGDNIJwykciAsepnoQe25EemBYkqEocQ1YUb2x8nulhYWbV7QuS34DREGXIBmsGkxOZ01ZYKDx4P7FHttWK7QQhskHii6FcQDh2p7oDNVFP9RhljU+GyYWhsSmEPQ2ATvwINODQ2QiO7EJkgZxciE+TsQmSCnF2ITBi6QJcMDYzCCxNCibUCwSoR4miN4POtGX/mWbOqegWmeAJwAmvF+2oG8+Rb++JtLATJXVNhuFHJrEZCj4yEu+ZMZxl2IRbjIiGusHeWBRbqzUfvVIzzuYRKWWeOenCP1skYm773o+yy3Qt8GtmFyAQ5uxCZIGcXIhPk7EJkwmEFOjNbBdwFrCzbf8bdrzOzFwC3AMcB3wTe4u6JSuVLIBIvUiJFOK848TkWCDA2mwo/q9rrfDpG4pjNx1FxY9PVtq0ViXnygUrojfjcWKD1pOrch/Xoo3JXM6lyWUEyz5ToFiT5TJVkqjUfvVMxLiG61SnpFEfQDT9SLkUn9+4McKG7n0NREGKTmb0CuIGi1tsLgWeBK/vWSyFE1xzW2b3gQELg8fLlwIXAZ0r7ZuDifnRQCNEbOq0I0yxzxu8E7gB+COx29wPPUo+TKPao8k9CjAYdOXtZ5mkjcApFmacXd7oDlX8SYjSopca7+27gTuCVwHozOyDwnQI80duuCSF6SSdq/PHAnLvvNrPVwGsoxLk7gV+iUOQvB25bUg9S5Z+iCdqJucKRKmrzCSU7sKWiXS1Q4yMaiUOwQNm12fiU+4rq5+5CIozXxwI1vkbIbqS6Q+LXg7lAYQ9KaAFYNO98LhHiHCnsqZJdUQhsIhw6DJPuskxTqLpD4hejGhlj65Q+6wGdxMafBGw2sybFk8Ct7v5FM/secIuZ/T7wbYrij0KIEaWTWm/3AS8L7NtJlGkWQoweiqATIhPk7EJkwtDns9chJapEc9STbYP4UY+yMgJGkLwwCtlNCIfWqp7elGDl09Uw2maU3JJEuGxCTIz7mxDoIkGxFYl2CcEqEthSOQiicNeEQNep6JbaX99CYLudo56iB3PXIzSyC5EJcnYhMkHOLkQmyNmFyAQ5uxCZMLJqfKRqRtWUIBEum9puYEu2DRTUSN2OVGwgVpfn4oOok/WWqG0dkhlQA3twDMnjDZOIpM5NjRDWbksyRVlgRyEEtk+qewqN7EJkgpxdiEyQswuRCXJ2ITJh+AJdUqSISuAkpLSFIFyWVAhssNlED8yD7YZlqRLhsvPV9a2ZUBnrCHThzmpMaK8j0EXHViPLb1J0W+g8tLZOuGsUuhxes0GHwI4AGtmFyAQ5uxCZIGcXIhPk7EJkwmGd3cxWmdndZvYdM3vAzN5d2j9mZj8ys23la2PfeyuEWDKdqPEHyj9Nmtk48HUz+3K57Lfd/TOHWLenpFRRi9K7Bgo9xCq9pbLWLgTKeZTgoZlQkaP1U0kXLOhvI5GQoo7yXoOOVeuUCh0q9zVqqiWuQ6jyp34R6DKEtW9ZYAccGhvRScJJB6LyT0KIZcSSyj+5+9Zy0XvM7D4zu9HMwnIvKv8kxGiwpPJPZvZS4F0UZaDOAzYAv5NYV+WfhBgBllr+aZO77ygrvM4AH0U55IUYaZZc/snMTnL3HVaoRRcD9/e3qxxiXnEQlpqqyRRNd47EMQhFlUgcC4U4iMW8OuJaQqBL9rdT6ghOgWCVFsdqhNZ2Gtaa6EPXolu6cY22y0u66qb80/8tPwgM2Ab8ev+6KYTolm7KP13Ylx4JIfqCIuiEyAQ5uxCZIGcXIhOGn7wiRaR0ppTsKOFAIrdBFJbatXJfR5WtpcaPwGdxKoQ1oFaSiHADI6Cwh+svL9U9xQjcTUKIQSBnFyIT5OxCZIKcXYhMGF2BLqInQkkNMS/CogysNdZPhMAuJ2qJY/U23KftHhkCW7doZBciE+TsQmSCnF2ITJCzC5EJcnYhMmF5qfG9oFtltpZ0H6y+vMqDiSMIjexCZIKcXYhMkLMLkQlydiEywZIZPfuxM7OngEfLf58H7BrYzgeHjmv5cSQd2+nufny0YKDOftCOze5193OHsvM+ouNafhzJx9aOHuOFyAQ5uxCZMExnv2mI++4nOq7lx5F8bP/E0L6zCyEGix7jhciEgTu7mW0ys++b2cNmds2g999LzOxmM9tpZve32TaY2R1m9lD599hh9nEpmNmpZnanmX3PzB4ws3eU9mV9bGa2yszuNrPvlMf17tL+AjPbWt6TnzazFcPuaz8YqLOXxSH/J/A64CXAZWb2kkH2ocd8DNi0yHYNsMXdzwa2lP8vN+aBq939JcArgLeV12m5H9sMcKG7nwNsBDaZ2SuAG4Ab3f2FwLPAlcPrYv8Y9Mj+cuBhd9/u7rPALcBFA+5Dz3D3u4BnFpkvAjaX7zdTlLNeVrj7Dnf/Vvl+AngQOJllfmxeMFn+O16+HLgQ+ExpX3bH1SmDdvaTgcfa/n+8tB1JnODuO8r3PwFOGGZnusXMzqCo4ruVI+DYzKxpZtuAncAdwA+B3e4+XzY5Eu9JQAJdX/Hip45l+3OHma0DPgv8lrvvbV+2XI/N3VvuvhE4heJJ88XD7dHgGLSzPwGc2vb/KaXtSOJJMzsJoPy7c8j9WRJmNk7h6J9w98+V5iPi2ADcfTdwJ/BKYL2ZHUjkciTek8Dgnf0e4OxS/VwBXArcPuA+9JvbgcvL95cDtw2xL0vCzAz4CPCgu/9h26JlfWxmdryZrS/frwZeQ6FH3An8Utls2R1Xpww8qMbMXg/8EdAEbnb39wy0Az3EzD4FvIpi1tSTwHXA/wFuBU6jmOF3ibsvFvFGGjO7APga8F2eq6pxLcX39mV7bGb2zykEuCbFQHeru/+emZ1JIRZvAL4N/Kq7zwyvp/1BEXRCZIIEOiEyQc4uRCbI2YXIBDm7EJkgZxciE+TsQmSCnF2ITJCzC5EJ/x9hpzkIigsD3AAAAABJRU5ErkJggg==\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Iterate N times, plot each iteration\n", "for i in range(4):\n", " fig, ax = pl.subplots()\n", " ims = []\n", " for nit in range(100):\n", " field[i,1:-1,1:-1] = 0.25 * (field[i,0:-2,1:-1] + field[i,2:,1:-1] + field[i,1:-1,0:-2] + field[i,1:-1,2:])\n", " # Re-inforce initial conditions\n", " field[0] = in_cond0(field[0])\n", " field[1] = in_cond1(field[1])\n", " field[2] = in_cond2(field[2])\n", " field[3] = in_cond3(field[3])\n", "\n", " # plot\n", " im = pl.imshow(field[i], animated=True)\n", " title = ax.text(0.5,1.09,f\"Example {i}, iteration {nit}\", size=pl.rcParams[\"axes.titlesize\"], ha=\"center\", transform=ax.transAxes, )\n", " ims.append([im, title])\n", " ani = animation.ArtistAnimation(fig, ims, interval=100, blit=False)\n", " ani.save(f\"results/example{i}-movie_from_figs.mp4\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }