{
 "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",
    "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",
    "    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]) / 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": "1c8dd79f",
   "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": 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,xAll):\n",
    "\n",
    "    fVHM = 1./(8.*h*h)\n",
    "    fFDM = 1./(2.*hFD*hFD)\n",
    "    \n",
    "    dim = 2*nFD + n + 3\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",
    "    # Interpolate the last FD node\n",
    "    weights = interpolate_lagrange(xAll[nFD-1], [xAll[nFD],xAll[nFD+1],xAll[nFD+2],xAll[nFD+3]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[nFD-1][nFD-1] = -1 # FM node at 1 \n",
    "    M[nFD-1][nFD] = weights[0]\n",
    "    M[nFD-1][nFD+1] = weights[1]\n",
    "    M[nFD-1][nFD+2] = weights[2]\n",
    "    M[nFD-1][nFD+3] = weights[3]\n",
    "                      \n",
    "    # Interpolate the first PD node\n",
    "    weights = interpolate_lagrange(xAll[nFD], [xAll[nFD-4],xAll[nFD-3],xAll[nFD-2],xAll[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(xAll[nFD+1], [xAll[nFD-4],xAll[nFD-3],xAll[nFD-2],xAll[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):\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(xAll[mid], [xAll[mid+2],xAll[mid+3],xAll[mid+4],xAll[mid+5]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[mid][mid] = -1 \n",
    "    M[mid][mid+2] = weights[0]\n",
    "    M[mid][mid+3] = weights[1]\n",
    "    M[mid][mid+4] = weights[2]\n",
    "    M[mid][mid+5] = weights[3]\n",
    "\n",
    "    # Interpolate the second PD node\n",
    "    weights = interpolate_lagrange(xAll[mid+1], [xAll[mid+2],xAll[mid+3],xAll[mid+4],xAll[mid+5]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[mid+1][mid+1] = -1\n",
    "    M[mid+1][mid+2] = weights[0]\n",
    "    M[mid+1][mid+3] = weights[1]\n",
    "    M[mid+1][mid+4] = weights[2]\n",
    "    M[mid+1][mid+5] = weights[3]\n",
    "    \n",
    "    # Same end node and start node\n",
    "    weights = interpolate_lagrange(xAll[mid+2], [xAll[mid-2],xAll[mid-1],xAll[mid],xAll[mid+1]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[mid+2][mid+2] = -1\n",
    "    M[mid+2][mid-2] = weights[0]\n",
    "    M[mid+2][mid-1] = weights[1]\n",
    "    M[mid+2][mid] = weights[2]\n",
    "    M[mid+2][mid+1] = weights[3]\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",
    "    \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(1-1.5*h,2+1.5*h,n+3)\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",
    "    \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",
    "\n",
    "    forceCoupled[nFD-1] = 0\n",
    "    forceCoupled[nFD] = 0\n",
    "    forceCoupled[nFD+1] = 0\n",
    "\n",
    "    forceCoupled[nFD+n+1] = 0\n",
    "    forceCoupled[nFD+n+2] = 0\n",
    "    forceCoupled[nFD+n+3] = 0    \n",
    "\n",
    "    MCoupling = CouplingMDCM(n,h,nFD,hFD,xAll)\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": 10,
   "id": "e2e388b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "xAll = []\n",
    "xFull = []\n",
    "uCoupled = []\n",
    "uFDM = []\n",
    "nFD = []\n",
    "n = []\n",
    "for i in range(5, 9):\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": 11,
   "id": "52675529",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x10e9888e0>"
      ]
     },
     "execution_count": 11,
     "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": [
    "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]+2],[xAll[i][nFD[i]-1]],xAll[i][nFD[i]+2:nFD[i]+n[i]+1],[xAll[i][nFD[i]+n[i]+3]],xAll[i][nFD[i]+n[i]+1:nFD[i]+n[i]+3],xAll[i][nFD[i]+n[i]+4:]]))\n",
    "    uSlice.append(np.concatenate([uCoupled[i][0:nFD[i]-1],uCoupled[i][nFD[i]:nFD[i]+2],[uCoupled[i][nFD[i]-1]],uCoupled[i][nFD[i]+2:nFD[i]+n[i]+1],[uCoupled[i][nFD[i]+n[i]+3]],uCoupled[i][nFD[i]+n[i]+1:nFD[i]+n[i]+3],uCoupled[i][nFD[i]+n[i]+4:]]))\n",
    "    plt.plot(xSlice[i],uSlice[i],label=\"m=\"+str(i+4))\n",
    "    \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": 12,
   "id": "7e9fe4f5",
   "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 = [2,3,4,5]\n",
    "\n",
    "for i in range(0, len(xAll)):\n",
    "    plt.plot(xSlice[i],uSlice[i]-exactSolution(xSlice[i]),color=\"black\",marker=markers[i],markevery=level[i],label=\"n=\"+str(i+4))\n",
    "    \n",
    "plt.gca().yaxis.set_major_formatter(FormatStrFormatter('%0.3f')) \n",
    "plt.xlabel(r\"$x$\")\n",
    "plt.ylabel(r\"Error in displacement w.r.t exact solution\")\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-non-matching-cubic-\"+str(example).lower()+\".pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d071c871",
   "metadata": {},
   "outputs": [],
   "source": [
    "if has_condition :\n",
    "    np.savetxt(\"con_mdcm_n-cubic-non-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
}