Copupling-MDCM-Dirchelet-Adaptive-endpoint-matching.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"
   ]
  },
  {
   "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 = \"Cubic\"\n",
    "save_results = False\n",
    "con = []\n",
    "has_condition = True"
   ]
  },
  {
   "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": "b7c775d1",
   "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 = 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] = 0\n",
    "    \n",
    "    return force"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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] = 1\n",
    "\n",
    "    M *= 1./(2.*h*h)\n",
    "\n",
    "    return M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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-3],x1[nFD-2],x1[nFD-1]], [\"u1\",\"u2\",\"u3\"])\n",
    "    M[nFD][nFD] = -1\n",
    "    M[nFD][nFD-1] = weights[2] \n",
    "    M[nFD][nFD-2] = weights[1]\n",
    "    M[nFD][nFD-3] = weights[0]\n",
    "    \n",
    "    # Interpolate the second PD node\n",
    "    weights = interpolate_lagrange(x2[1], [x1[nFD-3],x1[nFD-2],x1[nFD-1]], [\"u1\",\"u2\",\"u3\"])\n",
    "    M[nFD+1][nFD+1] = -1\n",
    "    M[nFD+1][nFD-1] = weights[2] \n",
    "    M[nFD+1][nFD-2] = weights[1]\n",
    "    M[nFD+1][nFD-3] = 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]], [\"u1\",\"u2\",\"u3\"])\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",
    "\n",
    "    # Interpolate the second PD node\n",
    "    weights = interpolate_lagrange(x2[len(x2)-1], [x3[0],x3[1],x3[2]], [\"u1\",\"u2\",\"u3\"])\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",
    "    \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] = 1\n",
    "    \n",
    "    if has_condition:\n",
    "        con.append(np.linalg.cond(M))\n",
    "        \n",
    "    return M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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",
    "    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",
    "    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",
    "    \n",
    "    return xAll, xFull, uCoupled, uFDM , nFD, n\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "352f943d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#mid = nFD+n+1\n",
    "#print(xAll[nFD+2])\n",
    "#print(xAll[nFD-1])\n",
    "#print(xAll[nFD-2])\n",
    "#print(xAll[nFD-3])\n",
    "\n",
    "xAll = []\n",
    "xFull = []\n",
    "uCoupled = []\n",
    "uFDM = []\n",
    "nFD = []\n",
    "n = []\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])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0de9a3fd",
   "metadata": {},
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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+4))\n",
    "    \n",
    "plt.plot(xFull[0],uFDM[0],label=\"FDM\")\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": 11,
   "id": "a859189f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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",
    "    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",
    "    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",
    "    plt.plot(xClean,uClean-uFDM[i],color=\"black\",marker=markers[i],markevery=level[i],label=\"m=\"+str(i+4))\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(\"MDCM-Dirchelet-adaptive-endpoint-matching-\"+str(example).lower()+\".pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b74c1a5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "if has_condition :\n",
    "    np.savetxt(\"con_mdcm_d-quadratic-matching.csv\", con, delimiter=\",\")"
   ]
  }
 ],
 "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
}