Coupling-MSCM-Dirchelet.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dea91a05",
   "metadata": {},
   "source": [
    "This file is part of https://github.com/diehlpk/reusommer21.\n",
    "\n",
    "Copyright (c) 2021 Patrick Diehl\n",
    "\n",
    "This program is free software: you can redistribute it and/or modify  \n",
    "it under the terms of the GNU General Public License as published by  \n",
    "the Free Software Foundation, version 3.\n",
    "\n",
    "This program is distributed in the hope that it will be useful, but \n",
    "WITHOUT ANY WARRANTY; without even the implied warranty of \n",
    "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU \n",
    "General Public License for more details.\n",
    "\n",
    "You should have received a copy of the GNU General Public License along with this program. \n",
    "If not, see <http://www.gnu.org/licenses/>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1fb24ff3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "from matplotlib.ticker import FormatStrFormatter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "67219f28",
   "metadata": {},
   "outputs": [],
   "source": [
    "example = \"Quadratic\"\n",
    "save_results = True\n",
    "has_condition = True\n",
    "con = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "99942545",
   "metadata": {},
   "outputs": [],
   "source": [
    "#############################################################################\n",
    "# Exact solution \n",
    "#############################################################################\n",
    "\n",
    "def exactSolution(x):\n",
    "    \n",
    "    if example == \"Cubic\":\n",
    "        return (2/3/np.sqrt(3)) * ( 9*x - 9*x*x + 2 * x * x * x )\n",
    "    elif example == \"Quartic\":\n",
    "        return 16/9 * x * x - 32/27 * x * x * x + 16/81 * x * x * x * x\n",
    "    elif example == \"Quadratic\":\n",
    "        return  4/3 * x - 4/9 * x * x\n",
    "    elif example == \"Linear\":\n",
    "        return x\n",
    "    else:\n",
    "        print(\"Error: Either provide Linear, Quadratic, Quartic, or Cubic\")\n",
    "        sys.exit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5e4233e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#############################################################################\n",
    "# Solve the system\n",
    "#############################################################################\n",
    "\n",
    "def solve(M,f):\n",
    "    return np.linalg.solve(M,f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ac200231",
   "metadata": {},
   "outputs": [],
   "source": [
    "#############################################################################\n",
    "# Loading\n",
    "#############################################################################\n",
    "\n",
    "def f(x):\n",
    "    \n",
    "    if example == \"Cubic\":\n",
    "        return -( 2/np.sqrt(3)) * ( -6 + 4*x )\n",
    "    elif example == \"Quartic\":\n",
    "        return  -32/9 + 64/9 * x - 64/27 * x * x\n",
    "    elif example == \"Quadratic\":\n",
    "        return 8/9\n",
    "    else:\n",
    "        print(\"Error: Either provide Quadratic, Quartic, or Cubic\")\n",
    "        sys.exit()\n",
    "\n",
    "def forceFull(n,x):\n",
    "    \n",
    "    force = np.zeros(n)\n",
    "   \n",
    "    for i in range(1,n-1):\n",
    "        force[i] = f(x[i])\n",
    "    \n",
    "    force[n-1] = 0\n",
    "    \n",
    "    return force\n",
    "\n",
    "def forceCoupling(n,x):\n",
    "    \n",
    "    dim = 2*n + 2*n-1 + 10\n",
    "    \n",
    "    force = np.zeros(dim)\n",
    "   \n",
    "    for i in range(1,dim-1):\n",
    "        force[i] = f(x[i])\n",
    "    \n",
    "    force[dim-1] = 0\n",
    "    \n",
    "    return force"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "aa6f956d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#############################################################################\n",
    "# Assemble the stiffness matrix for the finite difference model (FD)\n",
    "#############################################################################\n",
    "\n",
    "def FDM(n,h):\n",
    "\n",
    "    M = np.zeros([n,n])\n",
    "\n",
    "    M[0][0] = 1\n",
    "\n",
    "    for i in range(1,n-1):\n",
    "        M[i][i-1] = -2\n",
    "        M[i][i] = 4\n",
    "        M[i][i+1] = -2\n",
    "\n",
    "    M[n-1][n-1] = 1\n",
    "\n",
    "    M *= 1./(2.*h*h)\n",
    "\n",
    "    return M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "617de1e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "#############################################################################\n",
    "# Assemble the stiffness matrix for the coupling of FDM - MSCM - FDM\n",
    "#############################################################################\n",
    "\n",
    "def CouplingMSCM(n,h,x):\n",
    "\n",
    "    fVHM = 1./(8.*h/2*h/2)\n",
    "    fFDM = 1./(2.*h*h)\n",
    "    \n",
    "    dim = 2*n + 2*n-1 + 10\n",
    "    \n",
    "    M = np.zeros([dim,dim])\n",
    "    \n",
    "    M[0][0] = 1 \n",
    "\n",
    "    for i in range(1,n-1):\n",
    "        M[i][i-1] = -2 * fFDM\n",
    "        M[i][i] = 4 * fFDM\n",
    "        M[i][i+1] = -2 * fFDM \n",
    "    \n",
    "    M[n-1][n-1] = -1\n",
    "    M[n-1][n+5] = 1\n",
    "    \n",
    "    M[n][n] = -1\n",
    "    M[n][n-3] = 3/8\n",
    "    M[n][n-4] = 3/4\n",
    "    M[n][n-5] = -1/8\n",
    "    \n",
    "    M[n+1][n+1] = -1\n",
    "    M[n+1][n-3] = 1\n",
    "    \n",
    "    M[n+2][n+2] = -1\n",
    "    M[n+2][n-2] = 3/8\n",
    "    M[n+2][n-3] = 3/4\n",
    "    M[n+2][n-4] = -1/8\n",
    "    \n",
    "    M[n+3][n+6] = -2/6 / h * 2\n",
    "    M[n+3][n+5] = 9/6 / h * 2\n",
    "    M[n+3][n+4] = -18/6 / h * 2\n",
    "    M[n+3][n+3] = 11/6 / h * 2\n",
    "    \n",
    "    M[n+3][n-2] = 11/6 / h * 2\n",
    "    M[n+3][n+2] = -18/6 / h * 2\n",
    "    M[n+3][n+1] = 9/6 / h * 2\n",
    "    M[n+3][n] = -2/6 / h * 2\n",
    "    \n",
    "    M[n+4][n+4] = -1\n",
    "    M[n+4][n-1] = 3/8\n",
    "    M[n+4][n-2] = 3/4\n",
    "    M[n+4][n-3] = -1/8\n",
    "  \n",
    "    mid = n+2*n+3\n",
    "    \n",
    "    for i in range(n+5,mid+1):\n",
    "        M[i][i-2] = -1. * fVHM\n",
    "        M[i][i-1] = -4. * fVHM\n",
    "        M[i][i] = 10. * fVHM\n",
    "        M[i][i+1] =  -4. * fVHM\n",
    "        M[i][i+2] = -1. * fVHM\n",
    "     \n",
    "    M[mid+1][mid+1] = -1\n",
    "    M[mid+1][mid+8] = -1/8\n",
    "    M[mid+1][mid+7] = 3/4\n",
    "    M[mid+1][mid+6] = 3/8\n",
    "    \n",
    "    M[mid+2][mid-1] = -2/6 / h * 2\n",
    "    M[mid+2][mid] = 9/6 / h * 2\n",
    "    M[mid+2][mid+1] = -18/6 / h * 2\n",
    "    M[mid+2][mid+2] = 11/6 / h * 2 \n",
    "    \n",
    "    M[mid+2][mid+7] = 11/6 / h * 2 \n",
    "    M[mid+2][mid+3] = -18/6 / h * 2\n",
    "    M[mid+2][mid+4] = 9/6 / h * 2\n",
    "    M[mid+2][mid+5] = -2/6 / h * 2\n",
    "    \n",
    "    M[mid+3][mid+3] = -1\n",
    "    M[mid+3][mid+9] = -1/8\n",
    "    M[mid+3][mid+8] = 3/4\n",
    "    M[mid+3][mid+7] = 3/8\n",
    "    \n",
    "    M[mid+4][mid+4] = -1\n",
    "    M[mid+4][mid+8] = 1\n",
    "    \n",
    "    M[mid+5][mid+5] = -1\n",
    "    M[mid+5][mid+10] = -1/8\n",
    "    M[mid+5][mid+9] = 3/4\n",
    "    M[mid+5][mid+8] = 3/8\n",
    "    \n",
    "    M[mid+6][mid+6] = -1 \n",
    "    M[mid+6][mid] = 1\n",
    "    \n",
    "    for i in range(mid+7,dim-1):\n",
    "        M[i][i-1] = -2 * fFDM\n",
    "        M[i][i] = 4 * fFDM\n",
    "        M[i][i+1] = -2 * fFDM\n",
    "\n",
    "    M[dim-1][dim-1] = 1\n",
    "            \n",
    "    return M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "30793f57",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute(i):\n",
    "    \n",
    "    n = np.power(2,int(i))\n",
    "    h = 1./n\n",
    "    nodes = n + 1\n",
    "    \n",
    "    print(nodes,h)\n",
    "    x1 = np.linspace(0,1,nodes)\n",
    "    x2 = np.linspace(1-5*h/2,2.+5*h/2,2*nodes-1+10)\n",
    "    x3 = np.linspace(2,3.,nodes)\n",
    "    x = np.array(np.concatenate((x1,x2,x3)))\n",
    "    \n",
    "    \n",
    "    M = CouplingMSCM(nodes,h,x)\n",
    "    \n",
    "    f = forceCoupling(nodes,x)\n",
    "    \n",
    "    f[n] = 0\n",
    "    f[n+1] = 0\n",
    "    f[n+2] = 0\n",
    "    f[n+3] = 0\n",
    "    f[n+4] = 0\n",
    "    f[n+5] = 0\n",
    "    \n",
    "    mid = n+2*n+6\n",
    "     \n",
    "    f[mid+1] = 0\n",
    "    f[mid+2] = 0\n",
    "    f[mid+3] = 0\n",
    "    f[mid+4] = 0\n",
    "    f[mid+5] = 0\n",
    "    f[mid+6] = 0\n",
    "    \n",
    "    u = solve(M,f)\n",
    "      \n",
    "    x1 = x[0:nodes-1]\n",
    "    x2 = x[nodes+5:mid+1:2]\n",
    "    x3 = x[mid+7:len(x)]\n",
    "   \n",
    "    u1 = u[0:nodes-1]\n",
    "    u2 = u[nodes+5:mid+1:2]\n",
    "    u3 = u[mid+7:len(x)]\n",
    "    \n",
    "    x = np.concatenate([x1,x2,x3])\n",
    "    u = np.concatenate([u1,u2,u3])\n",
    "\n",
    "    plt.plot(x,u,label=\"$hFD=$\"+str(h))\n",
    "    plt.grid(True)\n",
    "    \n",
    "    x = np.arange(0,3+h,h)\n",
    "    interval = int(len(x)/3)\n",
    "    \n",
    "    forceFD = forceFull(len(x),x)\n",
    "    MFD = FDM(len(x),h)\n",
    "    \n",
    "    uFM = solve(MFD,forceFD)\n",
    "    \n",
    "    uFD = uFM\n",
    "\n",
    "    if save_results:\n",
    "        np.savetxt(\"x_\"+str(n)+\".csv\", x, delimiter=\",\")\n",
    "        np.savetxt(\"u_mscm_d_\"+str(n)+\".csv\", u, delimiter=\",\")\n",
    "        \n",
    "    if has_condition:\n",
    "        con.append(np.linalg.cond(M))\n",
    "\n",
    "    \n",
    "    return u  , uFD , x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "64a5e641",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17 0.0625\n",
      "33 0.03125\n",
      "65 0.015625\n",
      "129 0.0078125\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Quadratic solution ')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "uCoupled = []\n",
    "uLocal = []\n",
    "xLocal = []\n",
    "max_iteration = 8\n",
    "\n",
    "for i in range(4,max_iteration):\n",
    "    u , uFD , x = compute(i)\n",
    "    uCoupled.append(u)\n",
    "    uLocal.append(uFD)\n",
    "    xLocal.append(x)\n",
    "\n",
    "n = np.power(2,int(max_iteration))\n",
    "h = 1./n\n",
    "\n",
    "x = np.arange(0,3+h,h)\n",
    "plt.plot(x,exactSolution(x),label=\"Exact solution\")#\n",
    "plt.legend()\n",
    "plt.xlabel(r\"Position $x$\")\n",
    "plt.ylabel(r\"Displacement $u$\")\n",
    "plt.title(example+\" solution \")\n",
    "#plt.savefig(\"coupling-vhm-\"+str(example)+\"-dirchelt.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3ae8f2b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "markers = ['s','o','x','.']\n",
    "level = [8,16,32,64]\n",
    "\n",
    "for i in range(0,len(xLocal)):\n",
    "    n = np.power(2,i+4)\n",
    "    plt.plot(xLocal[i],uLocal[i]-uCoupled[i],color=\"black\",marker=markers[i],markevery=level[i],label=r\"$\\delta$=1/\"+str(int(n/2)))\n",
    "    np.savetxt(\"error-quadratic-\"+str(i)+\"-quartic.csv\",uLocal[i]-uCoupled[i], delimiter=\",\")\n",
    "    np.savetxt(\"x-\"+str(i)+\".csv\", xLocal[i], delimiter=\",\")\n",
    "\n",
    "plt.gca().yaxis.set_major_formatter(FormatStrFormatter('%0.6f')) \n",
    "plt.xlabel(r\"$x$\")\n",
    "plt.ylabel(r\"Error in displacement w.r.t FDM\")\n",
    "plt.title(r\"Example with \" + str(example).lower() + \" solution for MSCM with m = 2\")\n",
    "plt.grid()\n",
    "plt.axvline(x=1,c=\"#536872\")\n",
    "plt.axvline(x=2,c=\"#536872\")\n",
    "plt.legend()\n",
    "plt.savefig(\"MSCM-\"+str(example)+\"-d-error.pdf\",bbox_inches='tight')\n",
    "\n",
    "if has_condition :\n",
    "    np.savetxt(\"con_mscm_d.csv\", con, delimiter=\",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eb7e82f9",
   "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": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}