Coupling-MDCM-Neumann-Cubic-Interpolation.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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "67219f28",
   "metadata": {},
   "outputs": [],
   "source": [
    "example = \"Quartic\"\n",
    "save_results = True\n",
    "has_condition = True\n",
    "g = -1\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 x * x * x\n",
    "    elif example == \"Quartic\":\n",
    "        return x * x * x * x\n",
    "    elif example == \"Quadratic\":\n",
    "        return x * x\n",
    "    elif example == \"Linear\":\n",
    "        return x\n",
    "    elif example == \"Linear-cubic\":\n",
    "        return np.where(x < 1.5, x, x + (x-1.5) * (x-1.5) * (x-1.5) )\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",
    "    global g \n",
    "\n",
    "    if example == \"Cubic\":\n",
    "        g = 27\n",
    "        return -6*x\n",
    "    elif example == \"Quartic\":\n",
    "        g = 108\n",
    "        return -12 * x*x\n",
    "    elif example == \"Quadratic\":\n",
    "        g = 6\n",
    "        return -2\n",
    "    elif example == \"Linear\":\n",
    "        g = 1\n",
    "        return 0\n",
    "    elif example == \"Linear-cubic\":\n",
    "        g = 31./4.\n",
    "        if x < 1.5:\n",
    "            return 0 \n",
    "        else:\n",
    "            return 9-6*x\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]) / exactSolution(x[n-1])\n",
    "    \n",
    "    force[n-1] = g / exactSolution(x[n-1])\n",
    "    \n",
    "    return force\n",
    "\n",
    "def forceCoupling(n,x):\n",
    "    \n",
    "    dim = 2*n + 2*n-1 + 4\n",
    "    \n",
    "    force = np.zeros(dim)\n",
    "   \n",
    "    for i in range(1,dim-1):\n",
    "        force[i] = f(x[i]) / exactSolution(x[dim-1])\n",
    "    \n",
    "    force[dim-1] = g / exactSolution(x[dim-1])\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",
    "    \n",
    "    M[n-1][n-1] = 11*h / 3\n",
    "    M[n-1][n-2] = -18*h / 3\n",
    "    M[n-1][n-3] = 9 * h / 3\n",
    "    M[n-1][n-4] = -2 * h / 3\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 - VHM - FDM\n",
    "#############################################################################\n",
    "\n",
    "def CouplingMDCM(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 + 4\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+2] = 1  \n",
    "    \n",
    "    M[n][n] = -1\n",
    "    M[n][n-2] = 1\n",
    "    \n",
    "    M[n+1][n+1] = -1\n",
    "    M[n+1][n-4] = 1/16\n",
    "    M[n+1][n-3] = -5/16\n",
    "    M[n+1][n-2] = 15/16\n",
    "    M[n+1][n-1] = 5/16\n",
    "         \n",
    "    mid = n+2*n+1\n",
    "    \n",
    "    for i in range(n+2,mid):\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][mid] = -1 \n",
    "    M[mid][mid+2] = 5/16\n",
    "    M[mid][mid+3] = 15/16\n",
    "    M[mid][mid+4] = -5/16\n",
    "    M[mid][mid+5] = 1/16\n",
    "    \n",
    "\n",
    "    M[mid+1][mid+1] = -1\n",
    "    M[mid+1][mid+3] = 1\n",
    "    \n",
    "    M[mid+2][mid+2] = -1\n",
    "    M[mid+2][mid-1] = 1\n",
    "    \n",
    "    for i in range(mid+3,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] = 11 *  h * fFDM / 3\n",
    "    M[dim-1][dim-2] =  -18 * h * fFDM  / 3\n",
    "    M[dim-1][dim-3] = 9 * h * fFDM / 3\n",
    "    M[dim-1][dim-4] = -2 * h * fFDM / 3\n",
    "    \n",
    "    if has_condition:\n",
    "        con.append(np.linalg.cond(M))\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(1-2*h/2,2.+2*h/2,2*nodes-1+4)\n",
    "    x3 = np.linspace(2,3.,nodes)\n",
    "    x = np.array(np.concatenate((x1,x2,x3)))\n",
    "  \n",
    "    M = CouplingMDCM(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",
    "    \n",
    "    mid = n+2*n+3\n",
    "     \n",
    "    f[mid+1] = 0\n",
    "    f[mid+2] = 0\n",
    "    f[mid+3] = 0\n",
    "    \n",
    "    u = solve(M,f)\n",
    "      \n",
    "    x1 = x[0:nodes-1]\n",
    "    x2 = x[nodes+2:mid+1:2]\n",
    "    x3 = x[mid+4:len(x)]\n",
    "    \n",
    "    u1 = u[0:nodes-1]\n",
    "    u2 = u[nodes+2:mid+1:2]\n",
    "    u3 = u[mid+4: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(\"u_mdcm_n_cubic_\"+str(n)+\".csv\", u, delimiter=\",\")\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",
    "uExact = []\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",
    "    uExact.append(exactSolution(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)/exactSolution(x[len(x)-1]),label=\"Exact solution\")#\n",
    "plt.legend()\n",
    "plt.xlabel(r\"Position $x$\")\n",
    "plt.ylabel(r\"Displacement $u$\")\n",
    "plt.title(r\"Quadratic solution \")\n",
    "#plt.savefig(\"coupling-vhm-\"+str(example)+\"-dirchelt.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3ae8f2b3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0000446\n",
      "0.0000123\n",
      "0.0000032\n",
      "0.0000008\n"
     ]
    },
    {
     "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",
    "    plt.plot(xLocal[i],uExact[i]/81-uCoupled[i],color=\"black\",marker=markers[i],markevery=level[i],label=r\"$\\delta$=1/\"+str(int(n/2)))\n",
    "\n",
    "    print(\"%.7f\" % max(abs(uLocal[i]-uCoupled[i])))\n",
    "    \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 MDCM 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(\"coupling-MDCM-\"+str(example)+\"-neumann-error.pdf\",bbox_inches='tight')\n",
    "\n",
    "if has_condition :\n",
    "    np.savetxt(\"con_mdcm_n-cubic.csv\", con, delimiter=\",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "013ae10c",
   "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
}