Coupling-MDCM-Neumann.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 = \"Cubic\"\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 1/27 * x * x * x\n",
    "    elif example == \"Quartic\":\n",
    "        return x * x * x * x / 81\n",
    "    elif example == \"Quadratic\":\n",
    "        return 1/9 *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 = 3/27*3*3\n",
    "        return -6/27*x\n",
    "    elif example == \"Quartic\":\n",
    "        g = 4/81 * 3 * 3 * 3\n",
    "        return -12/81 * x*x\n",
    "    elif example == \"Quadratic\":\n",
    "        g = 6/9\n",
    "        return -2/9\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]) \n",
    "    \n",
    "    force[n-1] = g \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]) \n",
    "    \n",
    "    force[dim-1] = g \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-3] = -1/8\n",
    "    M[n+1][n-2] = 3/4\n",
    "    M[n+1][n-1] = 3/8\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] = 3/8 \n",
    "    M[mid][mid+3] = 3/4\n",
    "    M[mid][mid+4] = -1/8\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",
    "    hPD = h / 2\n",
    "    nPD = int(1 / hPD)+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",
    "    xAll = np.array(np.concatenate((x1,x2,x3)))\n",
    "    xFine = np.linspace(0,3*1,3*nPD-2)\n",
    "\n",
    "  \n",
    "    M = CouplingMDCM(nodes,h,xAll)\n",
    "    \n",
    "    f = forceCoupling(nodes,xAll)\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",
    "    uCoupled = solve(M,f)\n",
    "      \n",
    "    x1 = xAll[0:nodes-1]\n",
    "    x2 = xAll[nodes+1:mid+1:2]\n",
    "    x3 = xAll[mid+4:len(xAll)]\n",
    "    \n",
    "    u1 = uCoupled[0:nodes-1]\n",
    "    u2 = uCoupled[nodes+1:mid+1:2]\n",
    "    u3 = uCoupled[mid+4:len(xAll)]\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",
    "    forceFD = forceFull(len(xFine),xFine)\n",
    "    MFD = FDM(len(xFine),h/2)\n",
    "    \n",
    "    uFDMFine = solve(MFD,forceFD)\n",
    "        \n",
    "    if save_results:\n",
    "        np.savetxt(\"u_mdcm_n_\"+str(n)+\"_\"+example+\".csv\", u, delimiter=\",\")\n",
    "        \n",
    "    \n",
    "    return uCoupled , uFD , xAll, xFine , uFDMFine"
   ]
  },
  {
   "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",
    "xAll = []\n",
    "xFine = []\n",
    "uFDFine = []\n",
    "max_iteration = 8\n",
    "\n",
    "for i in range(4,max_iteration):\n",
    "    u , uFD , x, xF, uFDMFine = compute(i)\n",
    "    uCoupled.append(u)\n",
    "    uLocal.append(uFD)\n",
    "    xAll.append(x)\n",
    "    xFine.append(xF)\n",
    "    uFDFine.append(uFDMFine)\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(r\"Quadratic solution \")\n",
    "#plt.savefig(\"coupling-vhm-\"+str(example)+\"-dirchelt.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "539d150d-70d1-4ff2-b5b7-b45ca11633c6",
   "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(xAll)):\n",
    "    n = np.power(2,i+4)\n",
    "    leftindex = np.where(np.isclose(xAll[i],1))[0][0]\n",
    "    rightindex = np.where(np.isclose(xAll[i],2))[0][0]\n",
    "    xClean = np.concatenate([xAll[i][0:leftindex],xAll[i][leftindex+3:rightindex+1],xAll[i][rightindex+4:]])\n",
    "    uClean = np.concatenate([uCoupled[i][0:leftindex],uCoupled[i][leftindex+3:rightindex+1],uCoupled[i][rightindex+4:]])\n",
    "    #\n",
    "    oneindex = np.where(np.isclose(xFine[i],1))[0][0]\n",
    "    twoindex = np.where(np.isclose(xFine[i],2))[0][0]\n",
    "    uCleanFD = []\n",
    "    for j in range(0,oneindex):\n",
    "        if j % 2 == 0:\n",
    "            uCleanFD.append(uFDFine[i][j])\n",
    "    for j in range(oneindex,twoindex):\n",
    "        uCleanFD.append(uFDFine[i][j])\n",
    "    for j in range(twoindex,len(xFine[i])):\n",
    "        if j % 2 == 0:\n",
    "            uCleanFD.append(uFDFine[i][j])\n",
    "    \n",
    "    \n",
    "    plt.plot(xClean,uClean-uCleanFD,color=\"black\",marker=markers[i],markevery=level[i],label=r\"$\\delta$=1/\"+str(int(n/2)))\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 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(\"MDCM-\"+str(example)+\"-n-error.pdf\",bbox_inches='tight')\n",
    "\n",
    "if has_condition :\n",
    "    np.savetxt(\"con_mscm_n.csv\", con, delimiter=\",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0f4171eb-ac4c-4754-92e2-8b465a8b4460",
   "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
}