notebook/1D heat equation, finite difference, direct method.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fadaa6d5",
   "metadata": {},
   "source": [
    "# 1D heat equation, finite difference, direct method\n",
    "_Gilbert Francois Duivesteijn_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25b314db",
   "metadata": {},
   "source": [
    "Let's consider the following equation:\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial u}{\\partial t} = \\kappa \\frac{\\partial^2 u}{\\partial x^2} + f(x)\n",
    "\\end{equation}\n",
    "\n",
    "When the heat equation is static over time, the $\\frac{\\partial u}{\\partial t} = 0$. This is now an elliptic equation. In matrix notation, the equation can be written as:\n",
    "\\begin{equation}\n",
    "\\begin{bmatrix}\n",
    "0 \\\\\n",
    "\\vdots \\\\\n",
    "0\n",
    "\\end{bmatrix} = \\kappa \\frac{1}{\\Delta x^2}\\begin{bmatrix}\n",
    "\\ddots &        &  0 \\\\\n",
    "       & \\ddots &   \\\\\n",
    "  0    &        & \\ddots\n",
    "\\end{bmatrix} \\begin{bmatrix}\n",
    "u_1 \\\\\n",
    "\\vdots \\\\\n",
    "u_{n-1}\n",
    "\\end{bmatrix}\n",
    "+\n",
    "\\begin{bmatrix}\n",
    "b_1 \\\\\n",
    "\\vdots \\\\\n",
    "b_{n-1}\n",
    "\\end{bmatrix}\n",
    "+\n",
    "\\begin{bmatrix}\n",
    "f_1 \\\\\n",
    "\\vdots \\\\\n",
    "f_{n-1}\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "and\n",
    "\\begin{equation}\n",
    "f_i := f(i\\Delta x)\n",
    "\\end{equation}\n",
    "\n",
    "This is a system of equations that can be solved with a direct method:\n",
    "\n",
    "\\begin{align}\n",
    "Au + b + f = 0\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "98c861ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.linalg import toeplitz\n",
    "from scipy.linalg import solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d32233f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constant kappa\n",
    "k = 0.001\n",
    "\n",
    "# Spacial domain\n",
    "n = 100\n",
    "L = 1\n",
    "dx = L / n\n",
    "x = np.linspace(0, L, n)\n",
    "\n",
    "# Boundary conditions\n",
    "U0 = 1\n",
    "Un = -1\n",
    "\n",
    "# Initial condition, u(x,0)=0\n",
    "Uinit = np.zeros(shape=(n,))\n",
    "\n",
    "# Discretization matrix A\n",
    "A = k/dx**2 * toeplitz([-2.0, 1.0] + [0.0]*(n-2))\n",
    "\n",
    "# Vector with boundary conditions b\n",
    "b = np.zeros(shape=(n))\n",
    "b[0] = k/dx**2 * U0\n",
    "b[n-1] = k/dx**2 * Un\n",
    "\n",
    "# Discretize spacial function f(x)=cos(x)\n",
    "f = 3e-2 * np.cos(3*np.pi*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5d141417",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "A =\n",
      "[[-20.  10.   0. ...   0.   0.   0.]\n",
      " [ 10. -20.  10. ...   0.   0.   0.]\n",
      " [  0.  10. -20. ...   0.   0.   0.]\n",
      " ...\n",
      " [  0.   0.   0. ... -20.  10.   0.]\n",
      " [  0.   0.   0. ...  10. -20.  10.]\n",
      " [  0.   0.   0. ...   0.  10. -20.]]\n",
      "\n",
      "b =\n",
      "[ 10.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0. -10.]\n",
      "\n",
      "x =\n",
      "[0.         0.01010101 0.02020202 0.03030303 0.04040404 0.05050505\n",
      " 0.06060606 0.07070707 0.08080808 0.09090909 0.1010101  0.11111111\n",
      " 0.12121212 0.13131313 0.14141414 0.15151515 0.16161616 0.17171717\n",
      " 0.18181818 0.19191919 0.2020202  0.21212121 0.22222222 0.23232323\n",
      " 0.24242424 0.25252525 0.26262626 0.27272727 0.28282828 0.29292929\n",
      " 0.3030303  0.31313131 0.32323232 0.33333333 0.34343434 0.35353535\n",
      " 0.36363636 0.37373737 0.38383838 0.39393939 0.4040404  0.41414141\n",
      " 0.42424242 0.43434343 0.44444444 0.45454545 0.46464646 0.47474747\n",
      " 0.48484848 0.49494949 0.50505051 0.51515152 0.52525253 0.53535354\n",
      " 0.54545455 0.55555556 0.56565657 0.57575758 0.58585859 0.5959596\n",
      " 0.60606061 0.61616162 0.62626263 0.63636364 0.64646465 0.65656566\n",
      " 0.66666667 0.67676768 0.68686869 0.6969697  0.70707071 0.71717172\n",
      " 0.72727273 0.73737374 0.74747475 0.75757576 0.76767677 0.77777778\n",
      " 0.78787879 0.7979798  0.80808081 0.81818182 0.82828283 0.83838384\n",
      " 0.84848485 0.85858586 0.86868687 0.87878788 0.88888889 0.8989899\n",
      " 0.90909091 0.91919192 0.92929293 0.93939394 0.94949495 0.95959596\n",
      " 0.96969697 0.97979798 0.98989899 1.        ]\n",
      "\n",
      "f =\n",
      "[ 0.03        0.02986416  0.02945786  0.02878479  0.02785104  0.02666506\n",
      "  0.02523761  0.02358159  0.02171202  0.01964582  0.01740171  0.015\n",
      "  0.01246245  0.00981204  0.00707277  0.00426945  0.00142746 -0.00142746\n",
      " -0.00426945 -0.00707277 -0.00981204 -0.01246245 -0.015      -0.01740171\n",
      " -0.01964582 -0.02171202 -0.02358159 -0.02523761 -0.02666506 -0.02785104\n",
      " -0.02878479 -0.02945786 -0.02986416 -0.03       -0.02986416 -0.02945786\n",
      " -0.02878479 -0.02785104 -0.02666506 -0.02523761 -0.02358159 -0.02171202\n",
      " -0.01964582 -0.01740171 -0.015      -0.01246245 -0.00981204 -0.00707277\n",
      " -0.00426945 -0.00142746  0.00142746  0.00426945  0.00707277  0.00981204\n",
      "  0.01246245  0.015       0.01740171  0.01964582  0.02171202  0.02358159\n",
      "  0.02523761  0.02666506  0.02785104  0.02878479  0.02945786  0.02986416\n",
      "  0.03        0.02986416  0.02945786  0.02878479  0.02785104  0.02666506\n",
      "  0.02523761  0.02358159  0.02171202  0.01964582  0.01740171  0.015\n",
      "  0.01246245  0.00981204  0.00707277  0.00426945  0.00142746 -0.00142746\n",
      " -0.00426945 -0.00707277 -0.00981204 -0.01246245 -0.015      -0.01740171\n",
      " -0.01964582 -0.02171202 -0.02358159 -0.02523761 -0.02666506 -0.02785104\n",
      " -0.02878479 -0.02945786 -0.02986416 -0.03      ]\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nA =\")\n",
    "print(A)\n",
    "print(\"\\nb =\")\n",
    "print(b)\n",
    "print(\"\\nx =\")\n",
    "print(x)\n",
    "print(\"\\nf =\")\n",
    "print(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d608f902",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Au + b = 0\n",
    "u_Ab = solve(A, -b)\n",
    "\n",
    "# Au + b + f(x) = 0\n",
    "u_Abf = solve(A, -b-f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "64690eaf",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 2, figsize=(12, 6))\n",
    "axs[0].plot(x, f, label=\"$f(x)$\")\n",
    "axs[0].set_title(\"$f(x)$\")\n",
    "axs[1].plot(x, u_Ab, label=\"$Au + b = 0$\")\n",
    "axs[1].plot(x, u_Abf, label=\"$Au + b + f = 0$\")\n",
    "axs[1].set_title(\"Solution $u$\")\n",
    "axs[1].legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8c8e2f16",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}