Coupling-MDCM-Adaptive-endpoint-matching-Cubic.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "be27c3a6",
   "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": "b5441b8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import Symbol, simplify, lambdify\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from functools import reduce\n",
    "import operator\n",
    "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": "c18283b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def interpolate_lagrange(x, x_values, y_values):\n",
    "    \"\"\"\n",
    "    x : value at which to evaluate y, should be between min and max x_values\n",
    "    x_values: list or numpy array containing values of x\n",
    "    y_values: list or numpy array contaning values of y\n",
    "    \"\"\"\n",
    "    def _basis(j):\n",
    "        p = [(x - x_values[m])/(x_values[j] - x_values[m]) for m in range(k) if m != j]\n",
    "        return reduce(operator.mul, p)\n",
    "    assert len(x_values) != 0 and (len(x_values) == len(y_values)), 'x and y cannot be empty and must have the same length'\n",
    "    k = len(x_values)\n",
    "    basis = []\n",
    "    for j in range(k):\n",
    "        basis.append(_basis(j))\n",
    "    #return sum(_basis(j)*y_values[j] for j in range(k)) \n",
    "    return basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3c932c81",
   "metadata": {},
   "outputs": [],
   "source": [
    "example = \"Quartic\"\n",
    "save_results = False\n",
    "g = -1\n",
    "has_condition = True\n",
    "con = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0102259b",
   "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": "c4d97d3c",
   "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/3\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": 6,
   "id": "b7c775d1",
   "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 = 1/3\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 = n\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": 7,
   "id": "ebed63f7",
   "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] = 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": 8,
   "id": "97eb7677",
   "metadata": {},
   "outputs": [],
   "source": [
    "#############################################################################\n",
    "# Assemble the stiffness matrix for the coupling of FDM - VHM - FDM\n",
    "#############################################################################\n",
    "\n",
    "def CouplingMDCM(n,h,nFD,hFD,x1,x2,x3):\n",
    "\n",
    "    fVHM = 1./(8.*h*h)\n",
    "    fFDM = 1./(2.*hFD*hFD)\n",
    "    \n",
    "    dim = 2*nFD + n + 4\n",
    "    \n",
    "    M = np.zeros([dim,dim])\n",
    "        \n",
    "    M[0][0] = 1 \n",
    "\n",
    "    for i in range(1,nFD-1):\n",
    "        M[i][i-1] = -2 * fFDM\n",
    "        M[i][i] = 4 * fFDM\n",
    "        M[i][i+1] = -2 * fFDM \n",
    "    \n",
    "    # Same end node and start node\n",
    "    M[nFD-1][nFD-1] = -1 \n",
    "    M[nFD-1][nFD+2] = 1  \n",
    "    \n",
    "    # Interpolate the first PD node\n",
    "    weights = interpolate_lagrange(x2[0], [x1[nFD-4],x1[nFD-3],x1[nFD-2],x1[nFD-1]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[nFD][nFD] = -1\n",
    "    M[nFD][nFD-1] = weights[3] \n",
    "    M[nFD][nFD-2] = weights[2]\n",
    "    M[nFD][nFD-3] = weights[1]\n",
    "    M[nFD][nFD-4] = weights[0]\n",
    "    \n",
    "    # Interpolate the second PD node\n",
    "    weights = interpolate_lagrange(x2[1], [x1[nFD-4],x1[nFD-3],x1[nFD-2],x1[nFD-1]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[nFD+1][nFD+1] = -1\n",
    "    M[nFD+1][nFD-1] = weights[3] \n",
    "    M[nFD+1][nFD-2] = weights[2]\n",
    "    M[nFD+1][nFD-3] = weights[1]\n",
    "    M[nFD+1][nFD-4] = weights[0]\n",
    "         \n",
    "    mid = nFD+n+1\n",
    "    \n",
    "    for i in range(nFD+2,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",
    "    # Interpolate the first PD node\n",
    "    weights = interpolate_lagrange(x2[len(x2)-2], [x3[0],x3[1],x3[2],x3[3]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[mid+1][mid+1] = -1 \n",
    "    M[mid+1][mid+3] = weights[0]\n",
    "    M[mid+1][mid+4] = weights[1]\n",
    "    M[mid+1][mid+5] = weights[2]\n",
    "    M[mid+1][mid+6] = weights[3]\n",
    "\n",
    "    # Interpolate the second PD node\n",
    "    weights = interpolate_lagrange(x2[len(x2)-1], [x3[0],x3[1],x3[2],x3[3]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[mid+2][mid+2] = -1\n",
    "    M[mid+2][mid+3] = weights[0]\n",
    "    M[mid+2][mid+4] = weights[1]\n",
    "    M[mid+2][mid+5] = weights[2]\n",
    "    M[mid+2][mid+6] = weights[3]\n",
    "    \n",
    "    # Same end node and start node\n",
    "    M[mid+3][mid+3] = -1\n",
    "    M[mid+3][mid] = 1\n",
    "    \n",
    "    for i in range(mid+4,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 *  hFD * fFDM / 3\n",
    "    M[dim-1][dim-2] =  -18 * hFD * fFDM  / 3\n",
    "    M[dim-1][dim-3] = 9 * hFD * fFDM / 3\n",
    "    M[dim-1][dim-4] = -2 * hFD * fFDM / 3\n",
    "    \n",
    "    if has_condition:\n",
    "        con.append(np.linalg.cond(M))\n",
    "        \n",
    "    return M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "323c7f42",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute(amount):\n",
    "\n",
    "\n",
    "    hFD = 1./ amount\n",
    "    h = hFD / 5\n",
    "    nFD = int(1 / hFD)+1\n",
    "    n = int(1 / h)+1\n",
    "    \n",
    "    x1 = np.linspace(0,1,nFD)  \n",
    "    x2 = np.linspace(1-2*h,2*1+2*h,n+4)\n",
    "    x3 = np.linspace(2*1,3*1,nFD)\n",
    "    xFull = np.linspace(0,3*1,3*nFD-2)\n",
    "    xFine = np.linspace(0,3*1,3*n-2)\n",
    "    xAll = np.concatenate([x1,x2,x3])\n",
    "    \n",
    "    forceFD = forceFull(len(xFull),xFull)\n",
    "    MFD = FDM(len(xFull),hFD)\n",
    "    \n",
    "    uFDM = solve(MFD,forceFD) \n",
    "\n",
    "    forceFD = forceFull(len(xFine),xFine)\n",
    "    MFD = FDM(len(xFine),h)\n",
    "    \n",
    "    uFDMFine = solve(MFD,forceFD) \n",
    "\n",
    "    forceCoupled = forceCoupling(len(xAll),xAll)\n",
    "\n",
    "    forceCoupled[nFD-1] = 0\n",
    "    forceCoupled[nFD] = 0\n",
    "    forceCoupled[nFD+1] = 0\n",
    "\n",
    "    forceCoupled[nFD+n+2] = 0\n",
    "    forceCoupled[nFD+n+3] = 0\n",
    "    forceCoupled[nFD+n+4] = 0\n",
    "\n",
    "    MCoupling = CouplingMDCM(n,h,nFD,hFD,x1,x2,x3)\n",
    "    #np.savetxt(\"m.csv\", MCoupling, delimiter=\",\")\n",
    "    uCoupled = solve(MCoupling,forceCoupled) \n",
    "    uExact = exactSolution(xFull)\n",
    "    \n",
    "    return xAll, xFull, uCoupled, uFDM , nFD, n, uExact, xFine, uFDMFine\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "90929201",
   "metadata": {},
   "outputs": [],
   "source": [
    "xAll = []\n",
    "xFull = []\n",
    "uCoupled = []\n",
    "uFDM = []\n",
    "nFD = []\n",
    "n = []\n",
    "uExact = []\n",
    "xFine = []\n",
    "uFDFine = []\n",
    "for i in range(4, 8):\n",
    "    \n",
    "    res = compute(i)\n",
    "    xAll.append(res[0])\n",
    "    xFull.append(res[1])\n",
    "    uCoupled.append(res[2])\n",
    "    uFDM.append(res[3])\n",
    "    nFD.append(res[4])\n",
    "    n.append(res[5])\n",
    "    uExact.append(res[6])\n",
    "    xFine.append(res[7])\n",
    "    uFDFine.append(res[8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d623925b",
   "metadata": {},
   "outputs": [
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xSlice = []\n",
    "uSlice = []\n",
    "\n",
    "for i in range(0, len(xAll)):\n",
    "    xSlice.append(np.concatenate([xAll[i][0:nFD[i]-1],xAll[i][nFD[i]:nFD[i]+n[i]+4],xAll[i][nFD[i]+n[i]+5:]]))\n",
    "    uSlice.append(np.concatenate([uCoupled[i][0:nFD[i]-1],uCoupled[i][nFD[i]:nFD[i]+n[i]+4],uCoupled[i][nFD[i]+n[i]+5:]]))\n",
    "    plt.plot(xSlice[i],uSlice[i],label=\"m=\"+str(i+5))\n",
    "\n",
    "plt.plot(xFull[0],uFDM[0],label=\"FDM\")\n",
    "plt.plot(xFull[0],uExact[0],label=\"Exact\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.axvline(x=1,c=\"#536872\")\n",
    "plt.axvline(x=2,c=\"#536872\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a0309a9e",
   "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 = [2,5,6,7]\n",
    "\n",
    "for i in range(0, len(xAll)):\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",
    "    #xClean = np.concatenate([xSlice[i][0:nFD[i]-1],xSlice[i][nFD[i]+1:nFD[i]+n[i]+1:5],xSlice[i][nFD[i]+n[i]+3:]])\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,int(oneindex/5)):\n",
    "        uCleanFD.append(uFDFine[i][j*5])\n",
    "    for j in range(oneindex,twoindex):\n",
    "        uCleanFD.append(uFDFine[i][j])\n",
    "    for j in range(0,int(oneindex/5)+1):\n",
    "        uCleanFD.append(uFDFine[i][twoindex+j*5])\n",
    "\n",
    "    uClean = np.concatenate([uCoupled[i][0:leftindex],uCoupled[i][leftindex+3:rightindex+1],uCoupled[i][rightindex+4:]])\n",
    "    #uClean = np.concatenate([uSlice[i][0:nFD[i]-1],uSlice[i][nFD[i]+1:nFD[i]+n[i]+1:5],uSlice[i][nFD[i]+n[i]+3:]])\n",
    "    #UFDMFine = np.concatenate([xAll[0][0:np.where(xAll[0] == 1)[0][0]+1],xFine[0][np.where(xFine[0] == 1)[0][0]+1:np.where(xFine[0] == 2)[0][0]],xAll[0][np.where(xAll[0] == 2)[0][0]:]])\n",
    "    plt.plot(xClean,uClean-uCleanFD,color=\"black\",marker=markers[i],markevery=level[i],label=\"n=\"+str(i+4))\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-adaptive-endpoint-matching-cubic-\"+str(example).lower()+\".pdf\",bbox_inches='tight')\n",
    "\n",
    "if has_condition :\n",
    "    np.savetxt(\"con_mdcm_n-cubic-matching.csv\", con, delimiter=\",\")"
   ]
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