{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partial differential equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boundary condition problems\n",
    "\n",
    "#### Problem 1\n",
    "\n",
    "A square box of side $L = 1$ m has conducting walls. All walls are grounded at $V = 0$ volts, except the top one which is at $V = 1$ Volt. Considering these boundaries conditions, solve the Laplace's equation\n",
    "\n",
    "$\\nabla^2 \\phi = 0$,\n",
    "\n",
    "to find the value of the electrostatic potential $\\phi$ inside the box, considering an equally spaced grid of $100 \\times 100$ points. Set a precision requirement $\\delta = 10^{-6}$ volts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "#Solving the problem using Gauss-Seidel with overrelaxation\n",
    "def pde1_gauss_seidel(grid,omega,tol):\n",
    "    N = len(grid)\n",
    "    deltamax = 1.\n",
    "    # Iterate until the largest difference between phi[i,j] at the current iteration and phi[i,j] \n",
    "    # at the previous iteration becomes smaller than tol. The maximum is taken among all points in the grid.\n",
    "    demomode = False\n",
    "    if demomode:\n",
    "        count = 0\n",
    "    while (deltamax > tol):\n",
    "        if demomode:\n",
    "            count += 1\n",
    "        deltamax = 0.\n",
    "        for i in range(1,N-1):\n",
    "            for j in range(1,N-1):\n",
    "                gridold = grid[i,j]\n",
    "                # Updating grid points\n",
    "                grid[i,j] = ((1. + omega)/4.)*(grid[i+1,j] + grid[i-1,j] + grid[i,j-1] + grid[i,j+1]) - omega*grid[i,j]\n",
    "                # Computing the difference between the updated and old value of the potential for each point in the grid, \n",
    "                # and saving the largest difference among all points\n",
    "                delta = abs(grid[i,j] - gridold)\n",
    "                deltamax = max(delta,deltamax)\n",
    "        if demomode:\n",
    "            print(count)\n",
    "    return grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "grid = np.zeros((101,101),dtype='float')\n",
    "grid[0,:] = 1.0\n",
    "tol = 1e-6\n",
    "omega = 0.9\n",
    "\n",
    "grid = pde1_gauss_seidel(grid,omega,tol)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from pylab import imshow\n",
    "\n",
    "plt.imshow(grid,cmap='gray')\n",
    "plt.colorbar()\n",
    "plt.xlabel('x',size=16)\n",
    "plt.ylabel('y',size=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2\n",
    "\n",
    "A square box of side $L = 1$ m has conducting walls. All walls are grounded at $V = 0$ volts. Two square $20 \\, {\\rm cm} \\times 20 \\, {\\rm cm}$ charges are placed as in figure below ('Charge distribution'). Their charge density is $\\pm 1$ C$ {\\rm m}^{-2}$  Considering these boundaries conditions, solve the Laplace's equation\n",
    "\n",
    "$\\nabla^2 \\phi = 0$,\n",
    "\n",
    "to find the value of the electrostatic potential $\\phi$ inside the box, considering an equally spaced grid of $100 \\times 100$ points. Set a precision requirement $\\delta = 10^{-6}$ volts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rho = np.zeros((101,101),dtype='float')\n",
    "rho[20:40,60:80] = 1.0\n",
    "rho[60:80,20:40] = -1.0\n",
    "plt.imshow(rho,cmap='gray')\n",
    "plt.colorbar()\n",
    "plt.xlabel('x',size=16)\n",
    "plt.ylabel('y',size=16)\n",
    "plt.title('Charge distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Solving the problem using Gauss-Seidel with overrelaxation\n",
    "def pde2_gauss_seidel(phi,rho,omega,tol):\n",
    "    N = len(phi)\n",
    "    deltamax = 1.\n",
    "    eps0 = 8.9e-12\n",
    "    a = 0.01\n",
    "    # Iterate until the largest difference between phi[i,j] at the current iteration and phi[i,j] \n",
    "    # at the previous iteration becomes smaller than tol. The maximum is taken among all points in the grid.\n",
    "    demomode = False\n",
    "    if demomode:\n",
    "        count = 0\n",
    "    while (deltamax > tol):\n",
    "        if demomode:\n",
    "            count += 1\n",
    "        deltamax = 0.\n",
    "        for i in range(1,N-1):\n",
    "            for j in range(1,N-1):\n",
    "                phiold = phi[i,j]\n",
    "                # Updating grid points, now including source term\n",
    "                phi[i,j] =  ( ((1. + omega)/4.)*(phi[i+1,j] + phi[i-1,j] + phi[i,j-1] + phi[i,j+1]) \n",
    "                + a**2*rho[i,j]/(4.*eps0) - omega*phi[i,j] )\n",
    "                # Computing the difference between the updated and old value of the potential for each point in the grid, \n",
    "                # and saving the largest difference among all points\n",
    "                delta = abs(phi[i,j] - phiold)\n",
    "                deltamax = max(delta,deltamax)\n",
    "        if demomode:\n",
    "            print(count)\n",
    "    return phi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi = np.zeros((101,101),dtype='float')\n",
    "rho = np.zeros((101,101),dtype='float')\n",
    "rho[20:40,60:80] = 1.0\n",
    "rho[60:80,20:40] = -1.0\n",
    "tol = 1e-6\n",
    "omega = 0.9\n",
    "\n",
    "grid = pde2_gauss_seidel(phi,rho,omega,tol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from pylab import imshow\n",
    "\n",
    "plt.imshow(grid,cmap='gray')\n",
    "plt.colorbar()\n",
    "plt.xlabel('x',size=16)\n",
    "plt.ylabel('y',size=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initial value problems. The FTCS method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem: the heat equation\n",
    "\n",
    "The flat base of a container made of 1 cm thick stainless steel (thermal disffusivity $D = 4.25 \\times 10^{-6} \\, {\\rm m}^2 \\, {\\rm s}^{-1}$  is initially at a uniform temeprature of $293.16$ K everywhere. The container is placed in a bath of cold water at $273.16$ K and filled with hot water at $323.16$ K (see slides for picture). Calculate the temperature profile as a function of the distance x from the hot side to the cold side, as a function of time from $t_0 = 0$ s to $t_1 = 10$ s. Plot the profile at times $t = 0.01, 0.1, 0.4$ and $10$ s.\n",
    "\n",
    "One-dimensional diffusion equation:\n",
    "\n",
    "$\\large \\frac{\\partial{\\phi}}{\\partial{t}} = D \\frac{\\partial^2 \\phi}{\\partial x^2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Solving diffusion equation with FTCS\n",
    "def FTCS(T0,D,a,times,tol):\n",
    "    # Time step\n",
    "    h = times[1] - times[0]\n",
    "    N = len(T0)\n",
    "    temperature = np.zeros( (len(times),N) )\n",
    "    # Initial conditions\n",
    "    temperature[0,:] = np.copy(T0)\n",
    "    # Boundary conditions\n",
    "    temp = np.zeros(len(T0))\n",
    "    temp[0] = T0[0]\n",
    "    temp[N-1] = T0[N-1]\n",
    "    # Integrating equation using FTCS\n",
    "    for i in range(1,len(times)):\n",
    "        temp[1:N-1] = temperature[i-1,1:N-1] + h*(D/(a**2))*(temperature[i-1,2:N] + temperature[i-1,0:N-2] - \n",
    "                                                             2*temperature[i-1,1:N-1])\n",
    "        temperature[i,:] = np.copy(temp[:])\n",
    "    \n",
    "    return temperature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Diffusion coefficients\n",
    "D = 4.25*1e-6\n",
    "# Grid\n",
    "N = 101\n",
    "a = 1e-4\n",
    "# Initial and boundary conditions\n",
    "T0 = np.zeros(N)\n",
    "T0[0] = 323.16\n",
    "T0[N-1] = 273.16\n",
    "T0[1:N-1] = 293.16\n",
    "# Times at which the solution is computed (from 0 to 10 sec, with 1 millisecond step)\n",
    "times = np.arange(0.,10.001,1e-3)\n",
    "\n",
    "Tx = FTCS(T0,D,a,times,tol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.arange(0,1.01,0.01)\n",
    "plt.plot(x,Tx[10,:],label='t = 0.01 s')\n",
    "plt.plot(x,Tx[100,:],label='t = 0.1 s')\n",
    "plt.plot(x,Tx[400,:],label='t = 0.4 s')\n",
    "plt.plot(x,Tx[1000,:],label='t = 1 s')\n",
    "plt.plot(x,Tx[10000,:],label='t = 10 s')\n",
    "plt.legend()\n",
    "plt.xlabel('x (cm)',size = 16)\n",
    "plt.ylabel('T(x) (K)',size= 16)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.10.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
