{ "nbformat": 4, "nbformat_minor": 0, "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": "3.7.9" }, "colab": { "name": "903_Poisson Equation-Boundary.ipynb", "provenance": [], "include_colab_link": true } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "view-in-github", "colab_type": "text" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "id": "RnvogrHiDmS0" }, "source": [ "# Finite Difference Methods for the Poisson Equation\n", "This notebook will focus on numerically approximating a inhomogenous second order Poisson Equation.\n", "## The Differential Equation\n", "The general two dimensional Poisson Equation is of the form:\n", "\\begin{equation}\\frac{\\partial^2 u}{\\partial y^2} + \\frac{\\partial^2 u}{\\partial x^2}=f(x,y), \\ \\ \\ (x,y) \\in \\Omega=(0,1)\\times (0,1),\\end{equation}\n", "with boundary conditions\n", "\\begin{equation}U(x,y) = g(x,y), \\ \\ \\ (x,y)\\in\\delta\\Omega\\text{ - boundary}. \\end{equation}\n", "## Homogenous Poisson Equation\n", "This notebook will implement a finite difference scheme to approximate the inhomogenous form of the Poisson Equation $f(x,y)=100(x^2+y^2)$:\n", "\\begin{equation} \\frac{\\partial^2 u}{\\partial y^2} + \\frac{\\partial^2 u}{\\partial x^2}=100(x^2+y^2).\\end{equation}\n", "with the Boundary Conditions:\n", "\\begin{equation} u(x,0)=\\sin(2\\pi x), \\ \\ \\ \\ \\ 0 \\leq x \\leq 1, \\text{ lower},\\end{equation}\n", "\\begin{equation} u(x,1)=\\sin(2\\pi x), \\ \\ \\ \\ \\ 0 \\leq x \\leq 1, \\text{ upper},\\end{equation}\n", "\\begin{equation} u(0,y)=2\\sin(2\\pi y), \\ \\ \\ \\ \\ 0 \\leq y \\leq 1, \\text{ left},\\end{equation}\n", "\\begin{equation} u(1,y)=2\\sin(2\\pi y), \\ \\ \\ \\ \\ 0 \\leq y \\leq 1, \\text{ right}.\\end{equation}\n" ] }, { "cell_type": "code", "metadata": { "id": "sxYM5SxYDmS5" }, "source": [ "# LIBRARY\n", "# vector manipulation\n", "import numpy as np\n", "# math functions\n", "import math \n", "\n", "# THIS IS FOR PLOTTING\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt # side-stepping mpl backend\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "from IPython.display import HTML\n", "from mpl_toolkits.mplot3d import axes3d\n", "import matplotlib.pyplot as plt\n" ], "execution_count": 1, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "k35HYKx4DmS6" }, "source": [ "## Discete Grid\n", "The region $\\Omega=(0,1)\\times(0,1)$ is discretised into a uniform mesh $\\Omega_h$. In the $x$ and $y$ directions into $N$ steps giving a stepsize of\n", "\\begin{equation} h=\\frac{1-0}{N},\\end{equation}\n", "resulting in \n", "\\begin{equation}x[i]=0+ih, \\ \\ \\ i=0,1,...,N,\\end{equation}\n", "and \n", "\\begin{equation}x[j]=0+jh, \\ \\ \\ j=0,1,...,N,\\end{equation}\n", "The Figure below shows the discrete grid points for $N=10$, the known boundary conditions (green), and the unknown values (red) of the Poisson Equation." ] }, { "cell_type": "code", "metadata": { "id": "a-J2ZW-eDmS7", "outputId": "a11a1c07-efe2-437b-b2d1-276065c70418", "colab": { "base_uri": "https://localhost:8080/", "height": 324 } }, "source": [ "N=10\n", "h=1/N\n", "x=np.arange(0,1.0001,h)\n", "y=np.arange(0,1.0001,h)\n", "X, Y = np.meshgrid(x, y)\n", "fig = plt.figure()\n", "plt.plot(x[1],y[1],'ro',label='unknown');\n", "plt.plot(X,Y,'ro');\n", "plt.plot(np.ones(N+1),y,'go',label='Boundary Condition');\n", "plt.plot(np.zeros(N+1),y,'go');\n", "plt.plot(x,np.zeros(N+1),'go');\n", "plt.plot(x, np.ones(N+1),'go');\n", "plt.xlim((-0.1,1.1))\n", "plt.ylim((-0.1,1.1))\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.gca().set_aspect('equal', adjustable='box')\n", "plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n", "plt.title(r'Discrete Grid $\\Omega_h,$ h= %s'%(h),fontsize=24,y=1.08)\n", "plt.show();" ], "execution_count": 2, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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gnyaY+MTIuOIsnj0R+ff7kTZdkH+/H4tnT2QcD8fxYk5uxXFrmSZyW6LWbJ4FMKqB268EUGBPpQBmm05o4hMjMfvA26hLAyBAXRow+8DbMf9zLp49EaU7ZqOiTR1UgIo2dSjdMTvmDwvGSUwcL+bkVhy3lmkiE0RVE/NAIvkA3lTVfmFumwtgmaq+YF/fAGCEqlY2FLOkpETj7WfjnybWP2UIXwCofTD61yT/fj8q2tSdNj+vxoctj9UyjsfieDEnt+K4tUw7ichKVS2J685EDl7ZZ5MLYJvj+nZ73mlEpFREykWkvLq6Ou4HrJPY5keytfXpHxINzWec5MbxYk5uxXFrmSYywSvFJmqqOk9VS1S1JDs7/m61vghf9CLNj6T7IV9M8xknuXG8mJNbcdxapolM8Eqx2QGgm+N6V3ueMaXtLgNC/wnVnh+Dh3qWIvNE/XmZJ6z5jOO9OF7Mya04bi3TRCZ4pdgsATDePiptKID9je2vaapZ9/4FZW0vgy8AQK3t2mVtL8Ose/8SU5ybymZhXm4Z8mp8ELW2s8/LLcNNZbMYx4NxvJiTW3HcWqaJTEjIAQIi8gKAEQA6AvgawDQALQBAVeeIiAD4X1hHrB0GcKuqNrrnvykHCBBR43iAALnFn4gHUdUbG7ldAfx7InIhIqLE88pmNCIiasZYbIiIyDgWGyIiMo7FhoiIjGOxISIi41hsiIjIOBYbIiIyjsWGiIiMY7EhIiLjWGyIiMi4lC42rrUZXrwYyM8H0tKsy8WLGcfLcbyYk0tx3GydTeQqVT1jp8GDB2u8Fs0q08wpUEw/NWVOgS6aVRZjoEWqmZmqwKkpM9Oazzjei+PFnFyK49oy7QCgXD3wv87pzJ8S1hbahKac9dm1NsP5+UBFxenz8/KALVsYx2txvJiTS3HcbJ0dxLM+k1tSttikTRdomHa5okBgegyvSVqa9V30tEACBAKM47U4XszJpTiuLdP1UmCxIXek7D4b19oMd+8e23zGSW4cN2N5LI6brbOJ3Jayxca1NsMPPQRkZoYEyrTmM4734ngxJ5fiuNk6m8h1yd5p1JSpKQcIqFo7VPPu86lMg+bd54t/R+qiRap5eaoi1mU8O60ZJ3FxvJiTS3FcW6Zt4AECnFyaUnafDRE1jvtsyC0puxmNiIgSh8WGiIiMY7EhIiLjWGyIiMg4FhsiIjKOxYaIiIxjsSEiIuNYbIiIyDgWGyIiMi4hxUZERonIBhHZJCKTw9zeXUT+JiKrRORTEbkqEXkREVFiGC82IuID8DSAKwEUAbhRRIpChv0EwMuqOhDAWACzTOcFsFNnysbxYk7s1EnNnemTrwEYBmCp4/oDAB4IGTMXwH85xn8YTWx26mQcdup0hGGnTk4enoyfiFNErgMwSlUn2NfHARiiqnc5xuQA+DOA9gBaAxipqisbi81OnYzDTp2OMOzUSR7mlQMEbgTwrKp2BXAVgOdEJGxuIlIqIuUiUl5dXR33A25tffo/ZUPzIwfaGtt8xkluHDdjeSyOa8s0kQGJKDY7AHRzXO9qz3P6AYCXAUBV/w4gA0DHcMFUdZ6qlqhqSXZ2dtxJsVNnisZxM5bH4rBTJ3lZIorNCgAFItJDRNJhHQCwJGTMVgCXAYCI9IVVbOJfbYkCO3WmaBwv5sROnZQKErFjCNamsY0ANgOYYs+bAWC0/XcRgA8ArAbwCYAroonLTp2MEzev5cROnZya+cROnUQUEQ8QILd45QABIiJqxlhsiIjIOBYbIiIyjsWGiIiMY7EhIiLjWGyIiMg4FhsiIjKOxYaIiIxjsSEiIuNYbIiIyLiULjbs1JmicbyYEzt1UnOX7JOzNWVip07GYadORxh26uTk4SllT8TJTp0pGseLObFTJ6WAlC02adMFKqfPFwUC02N4TdLSrO+ipwUSIBBgHK/F8WJOLsVxbZmulwKLDbkjZffZsFNnisZxM5bH4rBTJ3lZyhYbdupM0ThezImdOikVJHunUVMmdupknLh5LSd26uTUzKeU3WdDRI3jPhtyS8puRiMiosRhsSEiIuNYbIiIyDgWGyIiMo7FhoiIjGOxISIi41hsiIjIOBYbIiIyjsWGiIiMS0ixEZFRIrJBRDaJyOQIY24QkXUislZEnk9EXkRElBjGi42I+AA8DeBKAEUAbhSRopAxBQAeADBcVYsB/IfpvAB26kzZOF7MiZ06qbkzffI1AMMALHVcfwDAAyFjHgUwIdbY7NTJOOzU6QjDTp2cPDwZPxGniFwHYJSqTrCvjwMwRFXvcox5HcBGAMMB+ABMV9U/NRabnToZh506HWHYqZM8zJ/sBGx+AAUARgDoCuBdEemvqvtCB4pIKYBSAOgeT+Ms29bWp/9TNjQ/cqCtsc1nnOTGcTOWx+K4tkwTGZCIAwR2AOjmuN7Vnue0HcASVT2hql/BWsspCBdMVeepaomqlmRnZ8edFDt1pmgcN2N5LA47dZKXJWLNZgWAAhHpAavIjAXw/ZAxrwO4EcCvRaQjgEIAX5pM6qGepSjdMRuHW5yaF3enztJS4PBhR6A4uzUyjvk4XszJpTiuLdONWLly5Tl+v/8ZAP3An0+QJQBgTW1t7YTBgwd/E26A8WKjqrUicheApbD2xyxQ1bUiMgPWzscl9m1XiMg6AHUA7lfV3SbzuqlsFjAbmPLlPGxtXYfuh3x4qGepNT+mQDdZl1OmWJs9une3PiSC8xnHW3G8mJNLcVxbphvh9/uf6dy5c9/s7Oy9aWlpZ273RXJNIBCQ6urqoqqqqmcAjA43hp06iSiicAcIrF69+sv+/fuz0FA9gUBAPvvss/YDBgzoGe52rgITUazSWGgolL1MRKwpLDZE1OzNnDnz7PHjx8d/+Co1GYsNEZk1Z04HdOnSH2lpg9GlS3/MmdMh2SlR4rHYEJE5c+Z0wKRJeaisTIcqUFmZjkmT8ppacDZs2JBeUFBQHLw+derUTvfee2+XCy64oHdZWVlu//79++bn5/f705/+1Cb0vi+++GK78847r09lZaX/2muvzb/lllu6DRw4sE/Xrl37//rXv24PAIFAAHfccUfXgoKC4sLCwqL58+e3B4Bx48Z1X7x4cTsAuPzyy8+9/vrr8wHgqaeeOvvuu+/O3bBhQ3rPnj2Lx44dm9erV6/i4cOHF9TU1EhTnmtzwWJDRObMmJGLo0frf84cPZqGGTNyTT1kbW2tfPbZZ58/8sgj22bMmNHFedvChQvPeuyxxzq/9dZbX+Tk5NQCwNdff92ivLx8/e9///svpk2blhsc99lnn7X6/PPP17799tsbp06d2rWioqLFRRdddPDdd9/NAoCqqqr0jRs3ZgDA+++/nzVixIiDALB169aMH/7wh99s2rRpbbt27eoWLlzY3tRzPZOw2BCROVVV6THNd8H111+/FwAuvPDCQ9u3bz/5OB988EHW448/3vmtt976Ijs7++RpFUaPHr3P5/Nh8ODBR3fv3t0CAN57772sG264YY/f70e3bt1qhwwZUvP+++9nXn755TXLly9vs3LlyozCwsIjHTt2PFFRUdFi5cqVrb/1rW/VAEBubu6xCy+88AgADBw48PCWLVtamnquZxIWGyIyp3Pn4zHNj5Lf79dAIHDy+lHH2lNGRobaY1BXV3dyE1ZeXt6xQ4cO+dasWZPhjBUcD1gnJm5Ijx49Thw4cMD3xhtvtLvooosODh8+vGbhwoXtW7duHWjfvn0AANLT008G8fl8Wltby81oYLEhIpOmTt2BjIxAvXkZGQFMnRp6yqqYdO3atXbPnj3+qqoq35EjR2Tp0qXtorjP8VdeeWXzrbfe2qO8vDyjobEXX3zxwVdffbVDbW0tdu7c6f/HP/7R5qKLLjoEAIMGDTo0d+7cc0aOHFkzYsSImqeffrrzkCFDapryfFKBV07ESUTN0Z137gFg7bupqkpH587HMXXqjpPz49SyZUv90Y9+VHn++ef37dSp04levXodjeZ+AwcOPLpw4cIvx4wZc+6SJUs2RRo3bty4fR9++GGbvn37FouIPvjgg9u7d+9eCwD//M//XPPee++17dev37Fjx44d379/v+/iiy8+2JTnkwp4BgEiiijCGQS2DBgwYFeyciLvWr16dccBAwbkh7stpTejsVNnisbxYk7s1EnNXEyb0UTkbgCLVHWvoXwSZvHsidYZcu2j8Cva1KF0x2xgNmI7ceHixfXP2FtRYV0HYjuRIuMkJo4Xc3IpjmvLNJEBMW1GE5H/htUi4GMAC2C1e07adjh26mQcdup0hElQp05uRqNIXNuMpqo/gdXU7FcAbgHwhYj8TETObWqSicZOnSkax81YHovDTp3kZTHvs7HXZKrsqRZAewCvisijLudmFDt1pmgcN2N5LA47dZKXxVRsROQeEVkJ4FEAHwDor6plAAYDuNZAfsY81LMUmSfqz4u7U2dmZkigOLs1Mo75OF7MyaU4ri3TRAbEumbTAcD3VPXbqvqKqp4AAFUNAPgX17Mz6KayWZiXW4a8Gh9Ere3a83LL4uvUOW+etX1dxLqcNy++bo2MYz6OF3NyKY5ry/QZwOfzDe7Tp09R7969i4qKivq+9dZbrU0/Zm5ubv/KykrXf5t47NgxmThxYm5eXl6/oqKivuedd16fl19+ua0bsTMzMwcCwJYtW1qMGjWqJwB8+OGHrV566aWTP4JdvHhxux//+Med3Xi8hvB3NkQUkRsHCMxZMafDjHdn5FbVVKV3btP5+NSLp+648/ym/agzMzNz4OHDh1cBwG9/+9u2Dz/8cM6KFSs2NCVmY3Jzc/uXl5d/HjyBZ2Nqa2vh9zdemyZOnJhbVVXVYvHixRWtWrXSbdu2+ZcuXZo1YcKEJh/163ydgmbOnHl2eXl564ULF8axw7Nh/J0NESXFnBVzOkz686S8yprKdIWisqYyfdKfJ+XNWeFeT5v9+/f72rVrVwtEbg3w5ptvZl166aW9gvcZP35895kzZ54NWEVk0qRJXYqKivoWFhYWrVq1KgMAqqqqfMOHDy/o1atX8ZgxY/KcX8xHjhx5bnFxcd9evXoV/+IXv+gYnJ+ZmTnw9ttv79q7d++iyZMn54wcOfLkwVOvvfZa28svv7zewVQHDx5Me/7557OfeeaZra1atVIA6NatW22w0MydO7dDYWFhUUFBQXFZWVmu83Huvvvu3N69excNGDCgz7Zt2/wAsH79+vTzzjuvT2FhYdEPf/jDk2e8DrZkOHr0qPz85z/v8sYbb7Tv06dP0fz589s7G8tt2LAhfejQoYWFhYVFw4YNK/ziiy/SASBSK4ZYsNgQkTEz3p2Re7S2fouBo7VH02a827QWA8eOHUvr06dPUY8ePYrvueeevGnTplUCkVsDNBavY8eOtevWrfv8tttuq3744Yc7AcDkyZO7DBs2rGbTpk1rv/vd7+6rrKw8eQbpxYsXb1m7du3nn3zyybq5c+d2qqqq8gHAkSNH0oYMGXJow4YN6x599NHKzZs3Z+zcudMPAAsWLDj71ltvrbdGuG7dupY5OTnHO3ToUP/8cbA2fU2fPj132bJlG9etW7d21apVrZ977rmzgo8zbNiwmg0bNqwbNmxYzS9/+ctsAJg4cWL3CRMmVG/cuHFdTk7OidCYGRkZ+sADD+y8+uqr965fv37d7bffXm/tqaysrPtNN920e+PGjevGjBmzu6ysrFvwtnCtGGLBYkNExlTVhG8lEGl+tFq2bBlYv379uq+++mrta6+99sWtt97aIxAIRGwN0Fi873//+3sB4IILLji8bdu2lgCwfPnyrNtuu203AIwdO3Z/27ZtTx5D/sgjj3Tq3bt30eDBg/tWVVW1WLt2bQYA+Hw+3HLLLXsBIC0tDTfccMPu+fPnd9i1a5fv448/bnP99dfvj/Y5vv/++62HDh16sEuXLrUtWrTAmDFj9rzzzjttAKBFixY6duzY/QAwePDgQxUVFekA8PHHH7e5/fbb9wDAHXfcsTvaxwpatWpV69LS0j0AUFZWtmflypUnm8+Fa8UQC56Ik4iM6dym8/HKmsrTCkvnNk1rMeA0cuTIQ3v37vU3tPO+RYsW9VoSHDt2rN5p/x1tCRptCfDmm29mvfPOOyA+hakAAA9ySURBVFnl5eXrs7KyAhdccEHvI0eOpAFAenp6wLmfpqysbPd3vvOdXhkZGXr11VfvbdGi/md0UVHRscrKyvQ9e/akhVu7icTv92taWlrwbzhzTktLM7IjPpZWDOFwzYaIjJl68dQdGf76LQYy/BmBqRc3rcWA06pVqzICgQA6depUG6k1wLnnnnts06ZNrY4cOSK7du3yvf/++40e7TV06NCDzz777NkA8PLLL7c9cOCADwD27dvna9euXV1WVlZg1apVGatXr454JFx+fv6JTp06nXj88cdzSktLTzuoIisrKzB27NhdpaWl3Y8ePSoAsHPnTv+CBQvaX3TRRYc++uijrMrKSn9tbS1eeeWVDiNGjGiwlcGgQYNq5s+f3wEA5s+ff3a4MW3btq2rqakJ+9k/cODAQ88880x7wNpfVFJS4lrrBBYbIjLmzvPv3PPkFU9W5LTJOS4Q5LTJOf7kFU9WNPVotOA+mz59+hSNHTu25+zZs7f4/X6MGzduX3Fx8ZG+ffsWjxgxojDYGqBXr14nrr766r19+vQpvuaaa3oWFxcfbuwxHn744Z0ffPBBm169ehX/7ne/a5+Tk3McAK699tr9tbW10rNnz+L7778/d8CAAYcaijN27NjdOTk5xwcNGhS2DcJTTz21o2PHjrWFhYXFBQUFxaNGjerVrl27ury8vBPTpk3bcckllxT27du3eMCAAYduvvnmfQ091qxZs7bOmzfvnMLCwqIdO3aE3dR15ZVXHty4cWOr4AECztvmzJmz9bnnnutYWFhY9MILL5w9a9asbQ2/StHjoc9EFBHPjdZ048eP7z5w4MDDkyZNavavWUOHPnOfDRGRIcXFxX1btWoVmDt3rmtrCGcqFhsiIkPWrl37ebJz8IqE7LMRkVEiskFENonI5AbGXSsiKiIlkcYQEdGZx3ixEREfgKcBXAmgCMCNIlIUZlwWgHsAfGQ6pyB26kzROF7M6czq1BkIBAINHh5MqcdeJiIevp2INZsLAGxS1S9V9TiAFwFcE2bcTwE8AiDsERtuC3Y1rGhTB5VTXQ1j/ucMdlmsqABUT3VZjPXDgnESE8eLObkUx7VlunFrqqur27HgUFAgEJDq6up2ANZEGmP8aDQRuQ7AKFWdYF8fB2CIqt7lGDMIwBRVvVZElgG4T1UbPcyMnToZh506HWES1Klz5cqV5/j9/mcA9AN/PkGWAIA1tbW1EwYPHvxNuAFJP0BARNIAPAGr82c040sBlAJA93gaZ9nYqTNF47gZy2NxEtWp0/4wGe1qUGr2EvGtZAeAbo7rXe15QVmwviEtE5EtAIYCWBLpIAFVnaeqJapakp2dHXdS7NSZonHcjOWxOOzUSV6WiGKzAkCBiPQQkXQAYwEsCd6oqvtVtaOq5qtqPoDlAEZHsxmtKdipM0XjeDEnduqkVKCqxicAVwHYCGAzrH0zADADVlEJHbsMQEk0cQcPHqxNsWhWmebd51OZBs27z6eLZpXFGWiRal6eqoh1uWgR43g5jhdzcimOa8u0DUC5JuAzglPzn3i6GiKKKNwBAkTx4JEkRERkHIsNEREZx2JDRETGsdgQEZFxLDZERGQciw0RERnHYkNERMax2BARkXEsNkREZByLDRERGZfSxYadOlM0jhdzOrM6dRLFLtknZ2vK1JQTcS6aVaaZU6CYfmrKnILYT1y4aJFqZqaq1WPRmjIzYz+RIuMkJo4Xc3IpjmvLtAN4Ik5OLk0peyJOdupM0ThezOkM69RJFI+ULTZp0wUapoO6KBCYHsNrkpZmfRc9LZAAgQDjeC2OF3NyKY5ry3S9FFhsyB0pu8+GnTpTNI6bsTwWh506yctSttiwU2eKxvFiTuzUSakg2TuNmjKxUyfjxM1rObFTJ6dmPqXsPhsiahz32ZBbUnYzGhERJQ6LDRERGcdiQ0RExrHYEBGRcSw2RERkHIsNEREZx2JDRETGsdgQEZFxLDZERGQciw0RERmXkGIjIqNEZIOIbBKRyWFuv1dE1onIpyLytojkJSIvdupM0ThezImdOqm5M33yNQA+AJsB9ASQDmA1gKKQMZcCyLT/LgPwUjSx2amTcdip0xGGnTo5eXgyfiJOERkGYLqqftu+/oBd5H4eYfxAAP+rqsMbi81OnYzDTp2OMOzUSR6WiM1ouQC2Oa5vt+dF8gMAf4x0o4iUiki5iJRXV1fHndTW1qf/UzY0P3KgrbHNZ5zkxnEzlsfiuLZMExngqQMERORmACUAHos0RlXnqWqJqpZkZ2fH/Vjs1JmicdyM5bE47NRJXpaIYrMDQDfH9a72vHpEZCSAKQBGq+ox00mxU2eKxvFiTuzUSanA9E4hAH4AXwLogVMHCBSHjBkI6yCCglhis1Mn48TNazmxUyenZj4lpFOniFwF4ClYR6YtUNWHRGSGvSAvEZG/AOgPoNK+y1ZVHd1YXHbqJDKLBwiQW/yJeBBV/QOAP4TMm+r4e2Qi8iAiouTw1AECRETUPLHYEBGRcSw2RERkHIsNEREZx2JDRETGsdgQEZFxLDZERGQciw0RERnHYkNERMax2BARkXEpXWxca6E7cSLg9wMi1uVEtpf2dBwv5sS20NTcJftMoE2ZPNEWuqxM67XzDU5lbC/tyThezIltoTmlwJSQsz6b4om20H4/UBemE6LPB9SyvbTn4ngxJ7aFphSQssUmbbpA5fT5okBgegyviYQJEhTLa5uWFn68CBAIMI5bcbyYk0txXFum66XAYkPuSNl9Nq610PVFGB9pfsSEvNViuNnGcTOWx+KwLTR5WcoWG9da6JZGGB9pfsSEvNViuNnG8WJObAtNqSDZO42aMnmmLXRZmarPpwpYl7EeHHAyIW+1GG62cbyYE9tCc2rmU8rusyGixnGfDbklZTejERFR4rDYEBGRcSw2RERkHIsNEREZx2JDRETGsdgQEZFxLDZERGQciw0RERnHYkNERMYlpNiIyCgR2SAim0RkcpjbW4rIS/btH4lIfiLyIiKixDBebETEB+BpAFcCKAJwo4gUhQz7AYC9qtoLwJMAHjGdFwBMfGIk/NMEMl3gnyaY+MTIuOK41R2RcRITx4s5uRXHrWWayG2JWLO5AMAmVf1SVY8DeBHANSFjrgHwG/vvVwFcJtJQo5imm/jESMw+8Dbq0gAIUJcGzD7wdsz/nItnT0TpjtmoaFMHFaCiTR1Kd8yO+cOCcRITx4s5uRXHrWWayATjJ+IUkesAjFLVCfb1cQCGqOpdjjFr7DHb7eub7TG7GordlBNx+qeJ9U8ZwhcAah+M/jVxqzsi4yQmjhdzciuOW8u0E0/ESW454w4QEJFSESkXkfLq6uq449RFWG+KND+Sra3DtIRuYD7jJDeOF3NyK45byzSRCYkoNjsAdHNc72rPCztGRPwA2gHYHS6Yqs5T1RJVLcnOzo47KV+EL3qR5kfiVndExklMHC/m5FYct5ZpIhMSUWxWACgQkR4ikg5gLIAlIWOWAPg3++/rAPxVDW/fK213GRD6CGrPj4Fb3REZJzFxvJiTW3HcWqaJjEhEhzYAVwHYCGAzgCn2vBkARtt/ZwB4BcAmAP8A0DOauE3t1Fn2+GXqmwrFNKhvKrTs8cviiuNWd0TGSUwcL+bkVhy3lukgsFMnJ5cmduokooh4gAC55Yw7QICIiM48LDZERGQciw0RERnHYkNERMax2BARkXEsNkREZByLDRERGcdiQ0RExrHYEBGRcSw2RERkHIsNEREZx2JDRETGsdgQEZFxZ/RZn0WkGkCFC6E6AmiwBXWCMZ+GeS0fwHs5uZVPnqrG36WQyHZGFxu3iEi5l06jznwa5rV8AO/l5LV8iLgZjYiIjGOxISIi41hsLPOSnUAI5tMwr+UDeC8nr+VDKY77bIiIyDiu2RARkXEpU2xEZJSIbBCRTSIyOcztLUXkJfv2j0Qk3wM53Ssi60TkUxF5W0TykpmPY9y1IqIiYvRop2jyEZEb7NdorYg8n8x8RKS7iPxNRFbZ79lVhvNZICLfiMiaCLeLiMy08/1URAaZzIeoQara7CcAPgCbAfQEkA5gNYCikDETAcyx/x4L4CUP5HQpgEz77zKTOUWTjz0uC8C7AJYDKEny61MAYBWA9vb1c5KczzwAZfbfRQC2GF6GLgYwCMCaCLdfBeCPAATAUAAfmcyHE6eGplRZs7kAwCZV/VJVjwN4EcA1IWOuAfAb++9XAVwmIpLMnFT1b6p62L66HEDXZOZj+ymARwAcNZhLtPncDuBpVd0LAKr6TZLzUQBt7b/bAdhpMB+o6rsA9jQw5BoAC9WyHMBZIpJjMieiSFKl2OQC2Oa4vt2eF3aMqtYC2A/g7CTn5PQDWN9Sk5aPvRmmm6r+n8E8os4HQCGAQhH5QESWi8ioJOczHcDNIrIdwB8A3G0wn2jEuowRGeNPdgLUOBG5GUAJgEuSmEMagCcA3JKsHMLww9qUNgLWWt+7ItJfVfclKZ8bATyrqo+LyDAAz4lIP1UNJCkfIs9IlTWbHQC6Oa53teeFHSMiflibQXYnOSeIyEgAUwCMVtVjScwnC0A/AMtEZAusfQBLDB4kEM3rsx3AElU9oapfAdgIq/gkK58fAHgZAFT17wAyYJ2jLFmiWsaIEiFVis0KAAUi0kNE0mEdALAkZMwSAP9m/30dgL+qqskfITWak4gMBDAXVqExuT+i0XxUdb+qdlTVfFXNh7UPabSqlicjH9vrsNZqICIdYW1W+zKJ+WwFcJmdT19YxabaUD7RWAJgvH1U2lAA+1W1Mon5UApLic1oqlorIncBWArrqKIFqrpWRGYAKFfVJQB+BWuzxyZYO13HeiCnxwC0AfCKfazCVlUdncR8EibKfJYCuEJE1gGoA3C/qhpZG40ynx8BmC8ik2AdLHCLyS8sIvICrGLb0d5PNA1ACzvfObD2G10FYBOAwwBuNZULUWN4BgEiIjIuVTajERFRErHYEBGRcSw2RERkHIsNEREZx2JDRETGsdgQEZFxLDZERGQciw0ZJyLn2/1UMkSktd17pl+y8yKixOGPOikhROS/YZ2+pRWA7ar68ySnREQJxGJDCWGfT2wFrD44F6pqXZJTIqIE4mY0SpSzYZ3nLQvWGg4RpRCu2VBCiMgSWN0tewDIUdW7kpwSESVQSpz1mZJLRMYDOKGqz4uID8CHIvItVf1rsnMjosTgmg0RERnHfTZERGQciw0RERnHYkNERMax2BARkXEsNkREZByLDRERGcdiQ0RExrHYEBGRcf8fB4/7ZAPjdI4AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "aSaJdgsPDmS8" }, "source": [ "## Boundary Conditions\n", "\n", "The discrete boundary conditions are \n", "\\begin{equation} w_{i0}=w[i,0]=\\sin(2\\pi x[i]), \\text{ for } i=0,...,10, \\text{ upper},\\end{equation} \n", "\n", "\\begin{equation} w_{iN}=w[i,N]=\\sin(2\\pi x[i]), \\text{ for } i=0,...,10, \\text{ lower},\\end{equation}\n", "\n", "\\begin{equation} w_{0j}=w[0,j]=2\\sin(2\\pi y[j]), \\text{ for } j=0,...,10, \\text{ left},\\end{equation}\n", "\\begin{equation} w_{Nj}=w[N,j]=2\\sin(2\\pi y[j]), \\text{ for } i=0,...,10,\\text{ right}. \\end{equation}\n", "\n", "The Figure below plots the boundary values of $w[i,j]$." ] }, { "cell_type": "code", "metadata": { "id": "crs8blshDmS9", "outputId": "cb7e3917-be23-42a0-eb53-84774a2b5127", "colab": { "base_uri": "https://localhost:8080/", "height": 272 } }, "source": [ "w=np.zeros((N+1,N+1))\n", "\n", "for i in range (0,N):\n", " w[i,0]=np.sin(2*np.pi*x[i]) #left Boundary\n", " w[i,N]=np.sin(2*np.pi*x[i]) #Right Boundary\n", "\n", "for j in range (0,N):\n", " w[0,j]=2*np.sin(2*np.pi*y[j]) #Lower Boundary\n", " w[N,j]=2*np.sin(2*np.pi*y[j]) #Upper Boundary\n", "\n", " \n", "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "# Plot a basic wireframe.\n", "ax.plot_wireframe(X, Y, w,color='r', rstride=10, cstride=10)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')\n", "ax.set_zlabel('w')\n", "plt.title(r'Boundary Values',fontsize=24,y=1.08)\n", "plt.show()" ], "execution_count": 3, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "vzAn6YuDDmS-" }, "source": [ "## Numerical Method\n", "The Poisson Equation is discretised using \n", "$\\delta_x^2$ is the central difference approximation of the second derivative in the $x$ direction\n", "\\begin{equation}\\delta_x^2=\\frac{1}{h^2}(w_{i+1j}-2w_{ij}+w_{i-1j}), \\end{equation}\n", "and $\\delta_y^2$ is the central difference approximation of the second derivative in the $y$ direction\n", "\\begin{equation}\\delta_y^2=\\frac{1}{h^2}(w_{ij+1}-2w_{ij}+w_{ij-1}). \\end{equation}\n", "The gives the Poisson Difference Equation,\n", "\\begin{equation}-(\\delta_x^2w_{ij}+\\delta_y^2w_{ij})=f_{ij} \\ \\ (x_i,y_j) \\in \\Omega_h, \\end{equation}\n", "\\begin{equation}w_{ij}=g_{ij} \\ \\ (x_i,y_j) \\in \\partial\\Omega_h, \\end{equation}\n", "where $w_ij$ is the numerical approximation of $U$ at $x_i$ and $y_j$.\n", "Expanding the the Poisson Difference Equation gives the five point method,\n", "\\begin{equation}-(w_{i-1j}+w_{ij-1}-4w_{ij}+w_{ij+1}+w_{i+1j})=h^2f_{ij} \\end{equation}\n", "for $i=1,...,N-1$ and $j=1,...,N-1.$\n", "\n", "### Matrix form\n", "This can be written as a system of $(N-1)\\times(N-1)$ equations can be arranged in matrix form\n", "\\begin{equation} A\\mathbf{w}=\\mathbf{r},\\end{equation}\n", "where $A$ is an $(N-1)^2\\times(N-1)^2$ matrix made up of the following block tridiagonal structure\n", "\\begin{equation}\\left(\\begin{array}{ccccccc}\n", "T&I&0&0&.&.&.\\\\\n", "I&T&I&0&0&.&.\\\\\n", ".&.&.&.&.&.&.\\\\\n", ".&.&.&0&I&T&I\\\\\n", ".&.&.&.&0&I&T\\\\\n", "\\end{array}\\right),\n", "\\end{equation}\n", "where $I$ denotes an $N-1 \\times N-1$ identity matrix and $T$ is the tridiagonal matrix of the form:\n", "\\begin{equation} T=\\left(\\begin{array}{ccccccc}\n", "-4&1&0&0&.&.&.\\\\\n", "1&-4&1&0&0&.&.\\\\\n", ".&.&.&.&.&.&.\\\\\n", ".&.&.&0&1&-4&1\\\\\n", ".&.&.&.&0&1&-4\\\\\n", "\\end{array}\\right).\n", "\\end{equation}\n", "The plot below shows the matrix $A$ and its inverse $A^{-1}$ as a colourplot." ] }, { "cell_type": "code", "metadata": { "id": "_oOi7MR0DmS_", "outputId": "9c1c18c7-d2d1-4e8b-dfee-47509e86bb2a", "colab": { "base_uri": "https://localhost:8080/", "height": 297 } }, "source": [ "N2=(N-1)*(N-1)\n", "A=np.zeros((N2,N2))\n", "## Diagonal \n", "for i in range (0,N-1):\n", " for j in range (0,N-1): \n", " A[i+(N-1)*j,i+(N-1)*j]=-4\n", "\n", "# LOWER DIAGONAL \n", "for i in range (1,N-1):\n", " for j in range (0,N-1): \n", " A[i+(N-1)*j,i+(N-1)*j-1]=1 \n", "# UPPPER DIAGONAL \n", "for i in range (0,N-2):\n", " for j in range (0,N-1): \n", " A[i+(N-1)*j,i+(N-1)*j+1]=1 \n", "\n", "# LOWER IDENTITY MATRIX\n", "for i in range (0,N-1):\n", " for j in range (1,N-1): \n", " A[i+(N-1)*j,i+(N-1)*(j-1)]=1 \n", " \n", " \n", "# UPPER IDENTITY MATRIX\n", "for i in range (0,N-1):\n", " for j in range (0,N-2): \n", " A[i+(N-1)*j,i+(N-1)*(j+1)]=1\n", "Ainv=np.linalg.inv(A) \n", "fig = plt.figure(figsize=(12,4));\n", "plt.subplot(121)\n", "plt.imshow(A,interpolation='none');\n", "clb=plt.colorbar();\n", "clb.set_label('Matrix elements values');\n", "plt.title('Matrix A ',fontsize=24)\n", "plt.subplot(122)\n", "plt.imshow(Ainv,interpolation='none');\n", "clb=plt.colorbar();\n", "clb.set_label('Matrix elements values');\n", "plt.title(r'Matrix $A^{-1}$ ',fontsize=24)\n", "\n", "fig.tight_layout()\n", "plt.show();" ], "execution_count": 4, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "lSbJPnWuDmTB" }, "source": [ "\n", "\n", "The vector $\\mathbf{w}$ is of length $(N-1)\\times(N-1)$ which made up of $N-1$ subvectors $\\mathbf{w}_j$ of length $N-1$ of the form\n", "\\begin{equation}\\mathbf{w}_j=\\left(\\begin{array}{c}\n", "w_{1j}\\\\\n", "w_{2j}\\\\\n", ".\\\\\n", ".\\\\\n", "w_{N-2j}\\\\\n", "w_{N-1j}\\\\\n", "\\end{array}\\right).\n", "\\end{equation}\n", "The vector $\\mathbf{r}$ is of length $(N-1)\\times(N-1)$ which made up of $N-1$ subvectors of the form $\\mathbf{r}_j=-h^2\\mathbf{f}_j-\\mathbf{bx}_{j}-\\mathbf{by}_j$, \n", "where $\\mathbf{bx}_j $ is the vector of left and right boundary conditions \n", "\\begin{equation}\\mathbf{bx}_j =\\left(\\begin{array}{c}\n", "w_{0j}\\\\\n", "0\\\\\n", ".\\\\\n", ".\\\\\n", "0\\\\\n", "w_{Nj}\n", "\\end{array}\\right),\n", "\\end{equation}\n", "\n", "for $j=1,..,N-1$, where $\\mathbf{by}_j$ is the vector of the lower boundary condition for $j=1$,\n", "\n", "\\begin{equation}\n", "\\mathbf{by}_{1} =\\left(\\begin{array}{c}\n", "w_{10}\\\\\n", "w_{20}\\\\\n", ".\\\\\n", ".\\\\\n", "w_{N-20}\\\\\n", "w_{N-10}\\\\\n", "\\end{array}\\right),\n", "\\end{equation}\n", "upper boundary condition for $j=N-1$\n", "\n", "\\begin{equation}\n", "\\mathbf{by}_{N-1} =\\left(\\begin{array}{c}\n", "w_{1N}\\\\\n", "w_{2N}\\\\\n", ".\\\\\n", ".\\\\\n", "w_{N-2N}\\\\\n", "w_{N-1N}\\\\\n", "\\end{array}\\right),\n", "\\end{equation}\n", "for $j=2,...,N-2$ \\begin{equation}\\mathbf{by}_j=0,\\end{equation}\n", "and \n", "\\begin{equation}\\mathbf{f}_j =100\\left(\\begin{array}{c}\n", "x_1^2+y_j^2\\\\\n", "x_2^2+y_j^2\\\\\n", ".\\\\\n", ".\\\\\n", "x_{N-2}^2+y_j^2\\\\\n", "x_{N-1}^2+y_j^2\n", "\\end{array}\\right)\n", "\\end{equation}\n", "for $j=1,...,N-1$.\n" ] }, { "cell_type": "code", "metadata": { "id": "79-gPbyKDmTB" }, "source": [ "r=np.zeros(N2)\n", "\n", "# vector r \n", "for i in range (0,N-1):\n", " for j in range (0,N-1): \n", " r[i+(N-1)*j]=100*h*h*(x[i+1]*x[i+1]+y[j+1]*y[j+1]) \n", "# Boundary \n", "b_bottom_top=np.zeros(N2)\n", "for i in range (0,N-1):\n", " b_bottom_top[i]=np.sin(2*np.pi*x[i+1]) #Bottom Boundary\n", " b_bottom_top[i+(N-1)*(N-2)]=np.sin(2*np.pi*x[i+1])# Top Boundary\n", " \n", "b_left_right=np.zeros(N2)\n", "for j in range (0,N-1):\n", " b_left_right[(N-1)*j]=2*np.sin(2*np.pi*y[j+1]) # Left Boundary\n", " b_left_right[N-2+(N-1)*j]=2*np.sin(2*np.pi*y[j+1])# Right Boundary\n", " \n", "b=b_left_right+b_bottom_top" ], "execution_count": 5, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "1vFANQAMDmTC" }, "source": [ "## Results\n", "\n", "To solve the system for $\\mathbf{w}$ invert the matrix $A$\n", "\\begin{equation} A\\mathbf{w}=\\mathbf{r},\\end{equation}\n", "such that\n", "\\begin{equation} \\mathbf{w}=A^{-1}\\mathbf{r}.\\end{equation}\n", "Lastly, as $\\mathbf{w}$ is in vector it has to be reshaped into grid form to plot.\n", "\n", "The figure below shows the numerical approximation of the homogeneous Equation." ] }, { "cell_type": "code", "metadata": { "scrolled": true, "id": "7kGzPyzcDmTC", "outputId": "2e2c292e-fdfb-415a-beb4-f89dc95b2fc5", "colab": { "base_uri": "https://localhost:8080/", "height": 380 } }, "source": [ "C=np.dot(Ainv,r-b)\n", "w[1:N,1:N]=C.reshape((N-1,N-1))\n", "\n", "fig = plt.figure(figsize=(8,6))\n", "ax = fig.add_subplot(111, projection='3d');\n", "# Plot a basic wireframe.\n", "ax.plot_wireframe(X, Y, w,color='r');\n", "ax.set_xlabel('x');\n", "ax.set_ylabel('y');\n", "ax.set_zlabel('w');\n", "plt.title(r'Numerical Approximation of the Poisson Equation',fontsize=24,y=1.08);\n", "plt.show();" ], "execution_count": 6, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "id": "UUeDDDa4DmTD" }, "source": [ "# Consistency and Convergence\n", "We now ask how well the grid function determined by the five point scheme approximates the exact solution of the Poisson problem.\n", "## Consistency\n", "\n", "### Consitency (Definition)\n", "Let \n", "\\begin{equation}\\nabla^2_h(\\varphi)=-(\\varphi_{i-1j}+\\varphi_{ij-1}-4\\varphi_{ij}+\\varphi_{ij+1}+\\varphi_{i+1j})\\end{equation} \n", "denote the finite difference approximation associated with the grid $\\Omega_h$ having the mesh size $h$, to a partial differential operator \n", "\\begin{equation}\\nabla^2(\\varphi)=\\frac{\\partial^2 \\varphi}{\\partial x^2}+\\frac{\\partial^2 \\varphi}{\\partial y^2}\\end{equation} defined on\n", "a simply connected, open set $\\Omega \\subset R^2$. For a given function $\\varphi\\in C^{\\infty}(\\Omega)$,\n", "the truncation error of $\\nabla^2_h$ is\n", "\\begin{equation}\\tau_{h}(\\mathbf{x})=(\\nabla^2-\\nabla^2_h)\\varphi(\\mathbf{x}) \\end{equation}\n", "The approximation $\\nabla^2_h$ is consistent with $\\nabla^2$ if\n", "\\begin{equation} \\lim_{h\\rightarrow 0}\\tau_h(\\mathbf{x})=0,\\end{equation}\n", "for all $\\mathbf{x} \\in D$ and all $\\varphi \\in C^{\\infty}(\\Omega)$. The approximation is consistent to order $p$ if $\\tau_h(\\mathbf{x})=O(h^p)$.\n", "\n", "_In other words a method is consistent with the differential equation it is approximating._\n", "\n", "## Proof of Consistency\n", "The five-point difference analog $\\nabla^2_h$ is consistent to order 2 with $\\nabla^2$.\n", "\n", "__Proof__\n", "\n", "Pick $\\varphi \\in C^{\\infty}(D)$, and let $(x,y) \\in \\Omega$ be a point such that $(x\\pm h, y),(x,y \\pm h) \\in \\Omega\\bigcup \\partial\\Omega$. By the Taylor Theorem\n", "\\begin{eqnarray*}\n", "\\varphi(x\\pm h,y)&=&\\varphi(x,y) \\pm h \\frac{\\partial \\varphi}{\\partial x}(x,y)+\\frac{h^2}{2!}\\frac{\\partial^2 \\varphi}{\\partial x^2}(x,y) \\pm\\frac{h^3}{3!}\\frac{\\partial^3 \\varphi}{\\partial x^3}(x,y)+\\frac{h^4}{4!}\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{\\pm},y)\n", "\\end{eqnarray*}\n", "where $\\zeta^{\\pm} \\in (x-h,x+h)$. Adding this pair of equation together and rearranging , we get\n", "\\begin{equation}\\frac{1}{h^2}[\\varphi(x+h,y)-2\\varphi(x,y)+\\varphi(x-h,y) ] -\\frac{\\partial^2 \\varphi}{\\partial x^2}(x,y)=\\frac{h^2}{4!}\\left[\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{+},y)+\n", "\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{-},y)\n", " \\right]\n", "\\end{equation}\n", "By the intermediate value theorem\n", "\\begin{equation}\\left[\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{+},y)+\n", "\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{-},y)\n", " \\right]\n", "=2\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta,y),\\end{equation}\n", "for some $\\zeta \\in (x-h,x+h)$. Therefore,\n", "\\begin{equation}\\delta_x^2(x,y)\n", "=\\frac{\\partial^2 \\varphi}{\\partial x^2}(x,y)+\\frac{h^2}{2!}\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta,y)\\end{equation}\n", "Similar reasoning shows that\n", "\\begin{equation}\\delta_y^2(x,y)\n", "=\\frac{\\partial^2 \\varphi}{\\partial y^2}(x,y)+\\frac{h^2}{2!}\\frac{\\partial^4 \\varphi}{\\partial y^4}(x,\\eta)\n", "\\end{equation}\n", "for some $\\eta \\in (y-h,y+h)$. We conclude that $\\tau_h(x,y)=(\\nabla-\\nabla_h)\\varphi(x,y)=O(h^2).$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "ROYoKiI9DmTD" }, "source": [ "## Convergence\n", "### Definition\n", "Let $\\nabla^2_hw(\\mathbf{x}_j)=f(\\mathbf{x}_j)$ be a finite difference approximation, defined on a grid mesh size $h$, to a PDE $\\nabla^2U(\\mathbf{x})=f(\\mathbf{x})$ on a simply connected set $D \\subset R^n$. Assume that $w(x,y)=U(x,y)$ at all points $(x,y)$ on the boundary $\\partial\\Omega$. The finite difference scheme converges (or is convergent) if\n", "\\begin{equation} \\max_j|U(\\mathbf{x}_j)-w(\\mathbf{x}_j)| \\rightarrow 0 \\mbox{ as } h \\rightarrow 0.\\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": { "id": "fsqa6O-XDmTE" }, "source": [ "### Theorem (DISCRETE MAXIMUM PRINCIPLE).\n", "If $\\nabla^2_hV_{ij}\\geq 0$ for all points $(x_i,y_j) \\in \\Omega_h$, then\n", "\\begin{equation} \\max_{(x_i,y_j)\\in\\Omega_h}V_{ij}\\leq \\max_{(x_i,y_j)\\in\\partial\\Omega_h}V_{ij},\\end{equation}\n", "If $\\nabla^2_hV_{ij}\\leq 0$ for all points $(x_i,y_j) \\in \\Omega_h$, then\n", "\\begin{equation} \\min_{(x_i,y_j)\\in\\Omega_h}V_{ij}\\geq \\min_{(x_i,y_j)\\in\\partial\\Omega_h}V_{ij}.\\end{equation}" ] }, { "cell_type": "markdown", "metadata": { "id": "MDBZlDpzDmTE" }, "source": [ "### Propositions\n", "1. The zero grid function for which $U_{ij}=0$ for all $(x_i,y_j) \\in \\Omega_h \\bigcup \\partial\\Omega_h$\n", "is the only solution to the finite difference problem\n", "\\begin{equation}\\nabla_h^2U_{ij}=0 \\mbox{ for }(x_i,y_j)\\in\\Omega_h,\\end{equation}\n", "\\begin{equation}U_{ij}=0 \\mbox{ for }(x_i,y_j)\\in\\partial\\Omega_h.\\end{equation}\n", "\n", "2. For prescribed grid functions $f_{ij}$ and $g_{ij}$, there exists a unique solution to the problem\n", "\\begin{equation}\\nabla_h^2U_{ij}=f_{ij} \\mbox{ for }(x_i,y_j)\\in\\Omega_h,\\end{equation}\n", "\\begin{equation}U_{ij}=g_{ij} \\mbox{ for }(x_i,y_j)\\in\\partial\\Omega_h.\\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": { "id": "8QLlWLtbDmTE" }, "source": [ "### Definition\n", "For any grid function $V:\\Omega_h\\bigcup\\partial\\Omega_h \\rightarrow R$,\n", "\\begin{equation}||V||_{\\Omega} =\\max_{(x_i,y_j)\\in\\Omega_h}|V_{ij}|, \\end{equation}\n", "\\begin{equation}||V||_{\\partial\\Omega} =\\max_{(x_i,y_j)\\in\\partial\\Omega_h}|V_{ij}|. \\end{equation}\n", "\n", "### Lemma\n", "If the grid function $V:\\Omega_h\\bigcup\\partial\\Omega_h\\rightarrow R$ satisfies the boundary condition $V_{ij}=0$ for $(x_i,y_j)\\in \\partial\\Omega_h$, then\n", "\\begin{equation}||V_||_{\\Omega}\\leq \\frac{1}{8}||\\nabla_h^2V||_{\\Omega}. \\end{equation}" ] }, { "cell_type": "markdown", "metadata": { "id": "29gr4JaUDmTF" }, "source": [ "Given these Lemmas and Propositions, we can now prove that the solution to the five point scheme $\\nabla^2_h$ is convergent to the exact solution of the Poisson Equation $\\nabla^2$.\n", "### Convergence Theorem\n", "Let $U$ be a solution to the Poisson equation and let $w$ be the grid function\n", "that satisfies the discrete analog\n", "\\begin{equation}-\\nabla_h^2w_{ij}=f_{ij} \\ \\ \\mbox{ for } (x_i,y_j)\\in\\Omega_h, \\end{equation}\n", "\\begin{equation}w_{ij}=g_{ij} \\ \\ \\mbox{ for } (x_i,y_j)\\in\\partial\\Omega_h. \\end{equation}\n", "Then there exists a positive constant $K$ such that\n", "\\begin{equation}||U-w||_{\\Omega}\\leq KMh^2, \\end{equation}\n", "where\n", "\\begin{equation} M=\\left\\{\n", "\\left|\\left|\\frac{\\partial^4 U}{\\partial x^4} \\right|\\right|_{\\infty},\n", "\\left|\\left|\\frac{\\partial^4 U}{\\partial y^4} \\right|\\right|_{\\infty}\n", " \\right\\}\\end{equation}\n", " \n", " __Proof__\n", " \n", " The statement of the theorem assumes that $U\\in C^4(\\bar{\\Omega})$. This assumption\n", "holds if $f$ and $g$ are smooth enough.\n", "\\begin{proof}\n", "Following from the proof of the Proposition we have\n", "\\begin{equation} (\\nabla_h^2-\\nabla^2)U_{ij}=\\frac{h^2}{12}\\left[ \\frac{\\partial^4 U}{\\partial x^4}(\\zeta_i,y_j)+\\frac{\\partial^4 U}{\\partial y^4}(x_i,\\eta_j) \\right],\\end{equation}\n", "for some $\\zeta \\in (x_{i-1},x_{i+1})$ and $\\eta_j\\in(y_{j-1},y_{j+1})$. Therefore,\n", "\\begin{equation} -\\nabla_h^2U_{ij}=f_{ij}-\\frac{h^2}{12}\\left[ \\frac{\\partial^4 U}{\\partial x^4}(\\zeta_i,y_j)+\\frac{\\partial^4 U}{\\partial y^4}(x_i,\\eta_j) \\right].\\end{equation}\n", "If we subtract from this the identity equation $-\\nabla_h^2w_{ij}=f_{ij}$ and note\n", "that $U-w$ vanishes on $\\partial\\Omega_h$, we find that\n", "\\begin{equation} \\nabla_h^2(U_{ij}-w_{ij})=\\frac{h^2}{12}\\left[ \\frac{\\partial^4 U}{\\partial x^4}(\\zeta_i,y_j)+\\frac{\\partial^4 U}{\\partial y^4}(x_i,\\eta_j) \\right].\\end{equation}\n", "It follows that\n", "\n", "\\begin{equation} ||U-w||_{\\Omega}\\leq\\frac{1}{8}||\\nabla_h^2(U-w)||_{\\Omega}\\leq KMh^2.\\end{equation}" ] }, { "cell_type": "code", "metadata": { "id": "JcVcmDIVDmTF" }, "source": [ "" ], "execution_count": 6, "outputs": [] } ] }