FDM_Adv_BC.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false
      },
      "source": [
        "<div style=\"display: flex; align-items: center;\">\n",
        "    <img src=\"https://github.com/nagelt/Teaching_Scripts/raw/9d9e29ecca4b04eaf7397938eacbf116d37ddc93/Images/TUBAF_Logo_blau.png\" width=\"500\" height=\"auto\" height=\"auto\" style=\"margin-right: 100px;\" />\n",
        "    <div>\n",
        "        <p><strong>Prof. Dr. Thomas Nagel</strong></p>\n",
        "        <p>Chair of Soil Mechanics and Foundation Engineering<br>Geotechnical Institute<br>Technische Universität Bergakademie Freiberg.</p>\n",
        "        <p><a href=\"https://tu-freiberg.de/en/soilmechanics\">https://tu-freiberg.de/en/soilmechanics</a></p>\n",
        "    </div>\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 727,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "#Some plot settings\n",
        "import plot_functions.plot_settings"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Constraints, periodic boundary conditions, static condensation -- FDM"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "PDE\n",
        "\n",
        "$$\n",
        "    0 = \\frac{\\partial c}{\\partial t} + v \\frac{\\partial c}{\\partial x}\n",
        "$$\n",
        "\n",
        "FDM\n",
        "\n",
        "$$\n",
        "    0 = \\frac{c_i - c_i^n}{\\Delta t} + v \\frac{c_i - c_{i-1}}{\\Delta x}\n",
        "$$\n",
        "\n",
        "Matrix\n",
        "\n",
        "$$\n",
        "    c_i^n = \\left[\\delta_{ij} + \\frac{v \\Delta t}{\\Delta x}(\\delta_{ij} - \\delta_{i(j-1)}) \\right] c_j\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 730,
      "metadata": {},
      "outputs": [],
      "source": [
        "L = 1.\n",
        "number_of_points = 1000\n",
        "dx = L/(number_of_points - 1)\n",
        "x = np.linspace(0,L,number_of_points)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The right-hand side is identical in every point, unless the stiffness or the specific weight changes with depth."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 732,
      "metadata": {},
      "outputs": [],
      "source": [
        "v = 1\n",
        "dt = dx/np.abs(v)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 733,
      "metadata": {},
      "outputs": [],
      "source": [
        "c0 = np.copy(x)*0.\n",
        "c0[np.where(np.abs(x-L/2)<L/6)] = 1."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 734,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x2ac27221ee0>]"
            ]
          },
          "execution_count": 734,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(x,c0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 735,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "execution_count": 735,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "I = np.identity(len(x))\n",
        "int(np.sign(v))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 736,
      "metadata": {},
      "outputs": [],
      "source": [
        "A = I + v*dt/dx*(I-np.diag([1]*(len(x)-1),-1))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 737,
      "metadata": {},
      "outputs": [],
      "source": [
        "Ainv = np.linalg.inv(A)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 738,
      "metadata": {},
      "outputs": [],
      "source": [
        "def operate(n,alpha=0.5):\n",
        "    cn = np.copy(c0)\n",
        "    for i in range(n):\n",
        "        cimp = Ainv@cn\n",
        "        cexp = cn - (A-I).dot(cn) \n",
        "        cn = alpha*cimp + (1-alpha)*cexp\n",
        "    return cn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 739,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "for i in range(0,50,10):\n",
        "    plt.plot(x,operate(i,0),color='b',alpha=(i/50)+.1,label=r'explicit')\n",
        "    plt.plot(x,operate(i,1),color='r',alpha=(i/50)+.1,label=r'implicit')\n",
        "\n",
        "#plt.plot(x,operate(40))\n",
        "#plt.plot(x,operate(40,0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Periodic bc is added by introducing neighbourhood directly for backward difference."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 741,
      "metadata": {},
      "outputs": [],
      "source": [
        "def operate_pbc(n,alpha=0.5):\n",
        "    K_pbc=np.copy(A)\n",
        "    K_pbc[0,-1] = K_pbc[1,0]\n",
        "    K_pbc_inv = np.linalg.inv(K_pbc)\n",
        "    cn = np.copy(c0)\n",
        "    cn[-1] = 0.\n",
        "    for i in range(n):\n",
        "        cn = K_pbc_inv@cn\n",
        "        #cexp = cn - (A-I).dot(cn) \n",
        "        #cn = alpha*cimp + (1-alpha)*cexp\n",
        "    return cn"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now with Lagrange multiplier ..."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 743,
      "metadata": {},
      "outputs": [],
      "source": [
        "def operate_pbc_lagr(n,lagr=1):\n",
        "    A_ = np.copy(A)\n",
        "    A_[0,1] = -1 #switch to forward diff\n",
        "    C = np.array(np.zeros((1,len(x))))\n",
        "    C[0,0] = lagr\n",
        "    C[0,-1] = -lagr\n",
        "    d = np.array([0])\n",
        "    zero_block = np.zeros((C.shape[0], C.shape[0]))\n",
        "    K_pbc = np.block([[A_ , C.T],[C, zero_block]])\n",
        "    K_pbc_inv = np.linalg.inv(K_pbc)\n",
        "    cn = np.append(np.copy(c0),0)\n",
        "    for i in range(n):\n",
        "        cn = K_pbc_inv@cn\n",
        "    return cn[:-1]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now with Least Squares"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 745,
      "metadata": {},
      "outputs": [],
      "source": [
        "def operate_pbc_ls(n,mult=1):\n",
        "    A_ = np.copy(A)\n",
        "    A_[0,1] = -1 #switch to forward diff\n",
        "    C = np.array(np.zeros((1,len(x))))\n",
        "    C[0,0] = mult\n",
        "    C[0,-1] = -mult\n",
        "    d = np.array([0])\n",
        "    K_pbc = np.block([[A_],[C]])\n",
        "    K_pbc_inv = np.linalg.inv(np.dot(K_pbc.T,K_pbc))\n",
        "    cn = np.copy(c0)\n",
        "    for i in range(n):\n",
        "        cn = K_pbc_inv@(K_pbc.T@(np.append(cn,0)))\n",
        "    return cn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 746,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(0.0, 1.0)"
            ]
          },
          "execution_count": 746,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "for i in [0,500,1000]:\n",
        "    lagr = operate_pbc_lagr(i)\n",
        "    #lam = lagr[-1]\n",
        "    plt.plot(x,operate_pbc(i),color='b',alpha=(i/1500)+0.1)\n",
        "    plt.plot(x,lagr,color='r',alpha=(i/1500)+0.1)\n",
        "    plt.plot(x,operate_pbc_ls(i),color='g',alpha=(i/1500)+0.1)\n",
        "plt.ylim(0,1)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 747,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(0.0, 1.0)"
            ]
          },
          "execution_count": 747,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "for i in [0,500,1000]:\n",
        "    lagr = operate_pbc_lagr(i,-1e1)\n",
        "    lam = lagr[-1]\n",
        "    #print(lam)\n",
        "    plt.plot(x,operate_pbc(i),color='b',alpha=(i/1500)+0.1)\n",
        "    plt.plot(x,lagr,color='r',alpha=(i/1500)+0.1)\n",
        "    plt.plot(x,operate_pbc_ls(i,1e1),color='g',alpha=(i/1500)+0.1)\n",
        "plt.ylim(0,1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 748,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "a = np.zeros(10)\n",
        "for i in range(0,10):\n",
        "    a[i] = operate(i*100)[-1]\n",
        "    plt.plot(i*100,a[i],marker='d',ls='',color='b')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 749,
      "metadata": {},
      "outputs": [],
      "source": [
        "K_aa = A[0:-1,0:-1]\n",
        "K_ab = A[:-1, -1].reshape(-1, 1)\n",
        "K_ba = A[-1, :-1].reshape(1, -1)\n",
        "K_bb = A[-1,-1].reshape(1,1)\n",
        "c_a = c0[0:-1]\n",
        "c_b = c0[-1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 750,
      "metadata": {},
      "outputs": [],
      "source": [
        "def operate_reduced(n):\n",
        "    c_rest = np.copy(c_a)\n",
        "    K_aa_inv = np.linalg.inv(K_aa)\n",
        "    K_eff = K_bb + K_ba@K_aa_inv@K_ab\n",
        "    K_eff_inv = np.linalg.inv(K_eff)\n",
        "    cn = np.copy(c_b)\n",
        "    for i in range(n):\n",
        "        ceff = cn - K_ba@K_aa_inv@c_rest\n",
        "        cn = K_eff_inv@ceff\n",
        "        c_rest = K_aa_inv@(c_rest - K_ab@cn)\n",
        "    return cn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 781,
      "metadata": {},
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "C:\\Users\\nagelt\\AppData\\Local\\Temp\\ipykernel_12380\\135155360.py:3: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
            "  b[i] = operate_reduced(i*100)\n"
          ]
        },
        {
          "data": {
            "image/png": 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P55Pf75fX6z0vYwIAAKDnOdpR3b59u+rr6zVy5MgOIVWScnJyJElbt27tdKw9e/bok08+0cSJE89bSAUAAEDkcBRUd+3aJUkaMmRI2Pa24+Xl5Z2OtWPHDknS97//fb311lvKzc2V1+tVXFycRo0apccff1zffvutk+kBAAAggjgKqkeOHJEkJScnh21PSkoK6Xc2+/btkyS9+eabys/P1/z583XgwAHt379fOTk5WrRokW644Qa1tLScdZxgMKhAIBDyAAAAQN/nKKg2NjZK0hlP1cfExIT0Oxu/3y9Jqqys1MqVKzVnzhwlJSUpPT1dTz31lK666iq9/vrr+v3vf3/WcQoLC+Xz+dofGRkZTkoCAACApRwF1bi4OEnSiRMnwrYHg8GQfl01Z86cDsfmzp0rSXrppZfO+tylS5fK7/e3P6qqqhy9NgAAAOx0kZPOqampkqSampqw7bW1tZKktLS0Tsdqu3wgJSUlbLC97LLLJElffvnlWceJiYlp38kFAABA5HC0ozpq1ChJrafrw2k7npWV1elYV1xxhaQz7862fWtWv37c5RUAAMCNHKXA3NxcDRgwQOXl5WpoaOjQXlpaKkmaOXNmp2P96Ec/Ur9+/RQIBMLu0H711VeSpB/+8IdOpggAAIAI4fga1QULFigYDGrdunUhbRUVFSorK9OECRM0adKk9uPFxcUaP368Vq1aFdI/LS1Nt9xyiyRp7dq1HV6rbfyf//znTqYIAACACOHozlRS6yf68/LyVFFRoRdeeEEzZszQnj17dPvtt6u6ulolJSUaOnRoe//rr79er732muLj41VXVxcy1jfffKNJkybp66+/1vPPP6+ZM2fK7/frX/7lX/TUU09p/vz5eu655xwVxJ2pAAAAIoPjC0Dj4uJUXFyshQsXasmSJUpMTNR1112n8ePHa+fOnSEhVZJuvvlmJSQkqKCgoMNYAwcO1Icffqi7775bv/rVr5SYmKhhw4apoqJCGzZscBxSAQAAEDkc76jajh1VAACAyMBH6gEAAGAlgioAAACsRFAFAACAlQiqAAAAsBJBFQAAAFYiqAIAAMBKBFUAAABYiaAKAAAAKxFUAQAAYCWCKgAAAKxEUAUAAICVCKoAAACwEkEVAAAAViKoAgAAwEoEVQAAAFiJoAoAAAArEVQBAABgJYIqAAAArERQBQAAgJUIqgAAALASQRUAAABWIqgCAADASgRVAAAAWImgCgAAACsRVAEAAGAlgioAAACsRFAFAACAlQiqAAAAsBJBFQAAAFYiqAIAAMBKBFUAAABYiaAKAAAAKxFUAQAAYCWCKgAAAKxEUAUAAICVCKoAAACwEkEVAAAAViKoAgAAwEoEVQAAAFiJoAoAAAArEVQBAABgJYIqAAAArERQBQAAgJUIqgAAALASQRUAAABWIqgCAADASgRVAAAAWImgCgAAACsRVAEAAGAlgioAAACsRFAFAACAlQiqAAAAsBJBFQAAAFYiqAIAAMBKBFUAAABYiaAKAAAAKxFUAQAAYCWCKgAAAKxEUAUAAICVCKoAAACwEkEVAAAAViKoAgAAwEoEVQAAAFiJoAoAAAArEVQBAABgJYIqAAAArERQBQAAgJUIqgAAALBSt4Jqc3Ozli1bpszMTMXGxio9PV0FBQU6fPjwOU3m4MGD8nq98ng8euedd85pLAAAAPRtjoNqc3Oz8vLyVFRUpMLCQtXW1mrbtm0qKyvT6NGjtX///m5P5uc//7nq6uq6/XwAAABEDsdBdfny5SotLVVhYaFmz56t/v37a8yYMdq0aZOOHTumefPmdWsizz33nD7++GMNGzasW88HAABAZHEUVJuamrRq1SpFR0dr7ty5IW1XXnmlsrOzVVJSoh07djiaxMGDB/XAAw/ot7/9rQYPHuzouQAAAIhMjoLq9u3bVV9fr5EjRyo+Pr5De05OjiRp69atjiYxf/58TZw4sUP4BQAAgHtd5KTzrl27JElDhgwJ2952vLy8vMtjPv/88/rggw+0e/duJ1MBAABAhHMUVI8cOSJJSk5ODtuelJQU0q8zVVVVWrx4sVauXKmMjAwnU2kXDAYVDAbbfw4EAt0aBwAAAHZxdOq/sbFRkhQdHR22PSYmJqRfZ+bPn69x48Zp/vz5TqYRorCwUD6fr/3R3cALAAAAuzgKqnFxcZKkEydOhG1v29ls63c2a9as0Y4dO7RmzRonU+hg6dKl8vv97Y+qqqpzGg8AAAB2cHTqPzU1VZJUU1MTtr22tlaSlJaWdtZxDh06pEWLFunRRx/VZZdd5mQKHcTExLTv5AIAACByONpRHTVqlCSpsrIybHvb8aysrLOO8+c//1mBQEC/+MUv5PF4Qh7vvvuuJCk3N7f9GHepAgAAcB9HQTU3N1cDBgxQeXm5GhoaOrSXlpZKkmbOnHnWcebNmydjTNjHlClTJEnFxcXtx6ZOnepkmgAAAIgAjq9RXbBggYLBoNatWxfSVlFRobKyMk2YMEGTJk1qP15cXKzx48dr1apV52fGAAAAcAXHt1B9+OGHlZ2drQcffFBbtmxRU1OT/vKXvyg/P1/f+973tHbt2pD+RUVF+vjjj/XQQw+drzkDAADABRwH1bi4OBUXF2vhwoVasmSJEhMTdd1112n8+PHauXOnhg4dGtL/5ptvVkJCggoKCs445ldffXXGa1Q57Q8AAOBOHmOM6e1JnE+BQEA+n09+v19er7e3pwMAAIBucryjCgAAAPQEgioAAACsRFAFAACAlQiqAAAAsBJBFQAAAFYiqAIAAMBKBFUAAABYiaAKAAAAKxFUAQAAYCWCKgAAAKxEUAUAAICVCKoAAACwEkEVAAAAViKoAgAAwEoEVQAAAFiJoAoAAAArEVQBAABgJYIqAAAArERQBQAAgJUIqgAAALASQRUAAABWIqgCAADASgRVAAAAWImgCgAAACsRVAEAAGAlgioAAACsRFAFAACAlQiqAAAAsBJBFQAAAFYiqAIAAMBKBFUAAABYiaAKAAAAKxFUAQAAYCWCKgAAAKxEUAUAAICVCKoAAACwEkEVAAAAViKoAgAAwEoEVQAAAFiJoAoAAAArEVQBAABgJYIqAAAArERQBQAAgJUIqgAAALASQRUAAABWIqgCAADASgRVAAAAWImgCgAAACsRVAEAAGAlgioAAACsRFAFAACAlQiqAAAAsBJBFQAAAFYiqAIAAMBKBFUAAABYiaAKAAAAKxFUAQAAYCWCKgAAAKxEUAUAAICVCKoAAACwEkEVAAAAViKoAgAAwEoEVQAAAFiJoAoAAAArEVQBAABgJYIqAAAArERQBQAAgJUIqgAAALBSt4Jqc3Ozli1bpszMTMXGxio9PV0FBQU6fPiwo3G2b9+un/3sZxo6dKhiY2MVFxen4cOHa8mSJTp27Fh3pgYAAIAI4TioNjc3Ky8vT0VFRSosLFRtba22bdumsrIyjR49Wvv37+/SOE899ZTy8vL0ySefaPXq1frmm2+0b98+zZ07V7/97W+VlZXV5bEAAAAQeRwH1eXLl6u0tFSFhYWaPXu2+vfvrzFjxmjTpk06duyY5s2b16VxmpqaFB0drVdffVXTpk1TQkKC/uZv/kZLlizRL3/5Sx05ckT33nuv0+kBAAAgQjgKqk1NTVq1apWio6M1d+7ckLYrr7xS2dnZKikp0Y4dOzodKzU1VbfeeqsyMjI6tM2cOVOS9Pbbb6ulpcXJFAEAABAhHAXV7du3q76+XiNHjlR8fHyH9pycHEnS1q1bOx3rtttu09q1a8O2+Xw+SZLH45ExxskUAQAAECEcBdVdu3ZJkoYMGRK2ve14eXn5OU3qiy++kNQafC+66KJzGgsAAAB9k6MUeOTIEUlScnJy2PakpKSQft21bt06eTwe/frXv+60bzAYVDAYbP85EAic02sDAADADo52VBsbGyVJ0dHRYdtjYmJC+nXHG2+8oT/96U+6//77NW3atE77FxYWyufztT/CXfMKAACAvsdRUI2Li5MknThxImx7285mWz+n9u7dqzvuuEOzZ8/WY4891qXnLF26VH6/v/1RVVXVrdcGAACAXRyd+k9NTZUk1dTUhG2vra2VJKWlpTmeSGVlpa699lpNnDhRGzZsUFRUVJeeFxMT076TCwAAgMjhaEd11KhRklpDZThtx7OyshxNYt++fZo8ebKuueYa/fGPfzzjpQUAAABwD0dBNTc3VwMGDFB5ebkaGho6tJeWlkr6v+9B7YrPP/9ckydP1vTp0/Xiiy+GfMp/5cqVnMoHAABwKcfXqC5YsEDBYFDr1q0LaauoqFBZWZkmTJigSZMmtR8vLi7W+PHjtWrVqg7jffbZZ5oyZYpuuukmrVmzRv36hU7ngQce0F//+lcnUwQAAECE8BiH36jf2NiovLw8VVRU6IUXXtCMGTO0Z88e3X777aqurlZJSYmGDh3a3v/666/Xa6+9pvj4eNXV1bUf/+STTzR9+nQFg0H95Cc/CftaL7/8soqLizV16tQuzy8QCMjn88nv98vr9TopDQAAABZx/G36cXFxKi4uVmFhoZYsWaJbbrlFycnJmjFjhlasWKFLLrkkpP/NN9+s9957T3feeWfI8RdffLH9w1cvv/zyOZQAAACASOR4R9V27KgCAABEBkfXqAIAAAA9haAKAAAAKxFUAQAAYCWCKgAAAKxEUAUAAICVCKoAAACwEkEVAAAAViKoAgAAwEoEVQAAAFiJoAoAAAArEVQBAABgJYIqAAAArERQBQAAgJUIqgAAALASQRUAAABWIqgCAADASgRVAAAAWImgCgAAACsRVAEAAGAlgioAAACsRFAFAACAlQiqAAAAsBJBFQAAAFYiqAIAAMBKBFUAAABYiaAKAAAAKxFUAQAAYCWCKgAAAKxEUAUAAICVCKoAAACwEkEVAACE2LRJSkuTXnmlt2cCt/MYY0xvT+J8CgQC8vl88vv98nq9vT0dAAD6lOpqKTNTOn5cSkyU9u6VBg3q7VnBrdhRBQAAkiRjpLvukurqWn+uq5Puvrt35wR3I6gCAABJraf8t2yRWlpaf25pkTZvbj0O9AZO/QMAgPZT/n5/685qG49H8vm4BAC9gx1VAABc7vRT/t/dvjKGSwDQewiqAAC4XEVF6Cn/72q7BKCiomfnBRBUAQBwueHDpVmzpKio8O1RUdLs2a39gJ5EUAUAwOU8Hmn1aikhofW/v9vm9UrPPNM7c4O7EVQBAIAGDWoNq+GuUV29mg9SoXcQVAEAgCQpPz/0EoC2U/75+b07L7gXQRUAAEgKvQRA4pQ/eh9BFQAAtBs0SHr2WSk1tfVPTvmjN/GF/wAAALASO6oAAACwEkEVAAAAViKoAgAAwEoEVQAAAFiJoAoAAAArEVQBAABgJYIqAAAArERQBQAAgJUIqgAAALASQRUAAABWIqgCAADASgRVAF22aZOUlia98kpvzwQA4AYeY4zp7UmcT4FAQD6fT36/X16vt7enA0SM6mopM1M6flxKTJT27pUGDertWQEAIhk7qgA6ZYx0111SXV3rz3V10t139+6cAACRj6AKoFObNklbtkgtLa0/t7RImze3HgcA4ELh1D+As2o75e/3t+6stvF4JJ+PSwAAABcOO6oAzuj0U/7f/SetMVwCAAC4sAiqAM6ooiL0lP93tV0CUFHRs/MCALgDQRXAGQ0fLs2aJUVFhW+PipJmz27tBwDA+UZQBXBGHo+0erWUkND6399t83qlZ57pnbkBACIfQRXAWQ0a1BpWw12juno1H6QCAFw4BFUAncrPD70EoO2Uf35+784LABDZCKoAOnX6JQASp/wBAD2DoAqgSwYNkp59VkpNbf2TU/4AgAutW0G1ublZy5YtU2ZmpmJjY5Wenq6CggIdPny4V8cCcGHl50tHjkg//WlvzwQA4AaOg2pzc7Py8vJUVFSkwsJC1dbWatu2bSorK9Po0aO1f//+Xhmrt5Qu3KTqqDSV/fKV3p5Kj3Nr7W6tW1LrPVPT0qRXqN013Fq3RO0urN3N7+/W1m4cWrp0qZFknnzyyZDj5eXlxuPxmJycnF4Zq43f7zeSjN/vd/xcp6p3HzW1SjSnJFOrRFO9++gFf01buLV2t9ZtjDHm6FFjEhONkVr/PErtEc+tdRtD7S6s3c3v7zbX7iioNjY2mvj4eBMdHW3q6uo6tE+YMMFIMu+//36PjnW6ngqqp1pOmbK0WeakooyRzElFmdL02Rf0NW3h1trdWrcxxphTp4yZNcuYqNbaTVSUMbOpPaK5tW5jqN2Ftbv5/d322h0F1VdffdVIMuPGjQvbvnjxYiPJLF68uEfHOl1PBdWSeze2/iX+zqPk/pcv6OvawK21u7VuY4wxG8PXbl6m9ojl1rqNoXYX1u7m93fba3cUVB955BEjyeTn54dtf+qpp4wkM3369B4d63Q9EVTbtshb5AlZ1BZ5rNsyP9/cWrtb6zbG/N9pQE9o7cbjifzTgm6t3a11G0PtLqzdze/vfaF2Rx+mOnLkiCQpOTk5bHtSUlJIv54YKxgMKhAIhDwuJHPK6K/X3qV41amfQm/V009G8arT/ul3X9A59Ba31u7WuiW1vmXddZdUVxf+1lR1ddLd1B5R3Fq3RO0urN3N7+99pXZHQbWxsVGSFB0dHbY9JiYmpF9PjFVYWCifz9f+yMjI6PS1z8X+rRXKPrJFF6klbPtFatGErzdr/9aKCzqP3uDW2t1atySpokLaskVqCV+7WlqkzZtb+0Uat9bu1rolandh7W5+f+8rtTsKqnFxcZKkEydOhG0PBoMh/XpirKVLl8rv97c/qqqqOn3tc/GDG4brg7RZ+lZRYdu/VZTK0mfrBzcMv6Dz6A1urd2tdUuShg8PvXfqd7XdS3U4tUcMt9YtUbsLa3fz+3tfqd1RUE1NTZUk1dTUhG2vra2VJKWlpfXYWDExMfJ6vSGPC8nTz6PL316teiXolDwhbafkUb3Hqx+8FZn3lnRr7W6tW1LovVM9no5tkXwvVbfW7ta6JWp3Ye1ufn/vK7U7CqqjRo2SJFVWVoZtbzuelZXVo2P1tIHDB+nze1eHvabj8/tWa+DwyL23pFtrd2vdklrvlbp6dfjr1lavjux7qbq1drfWLVG7C2t38/t7n6jdySevGhoazIABA0xMTIypr6/v0D5x4kQjybz33ns9Otbpeut7VE9Y9r1jF5Jba3dr3cYY1363ojHGvbW7tW5jqN2Ftbv5/d322h0FVWOMefDBB40k8/TTT4cc3717t/F4PGbChAkhx7dv327GjRtnnnjiiXMeqyt67c5UniQrvsahp7i1drfWbYwJvVtNUlLEflVNWG6t3a11G0PtLqzdze/vNtfuOKg2NDSY7Oxsk5CQYDZv3mwaGxvNp59+aq644gqTkpJi9u7dG9L/uuuuM5JMfHz8OY/VFT0ZVI0xpuT+l83RfqmmdOGmHnk9m7i1drfWbYxp/dLv1FRjNlG7a7i1bmOo3YW1u/n93dbaPcZ892KUzjU3N6uwsFAvvfSSDh48qOTkZM2YMUMrVqzQJZdcEtJ3/fr1uueee3TnnXfqd7/73TmN1RWBQEA+n09+v/+Cf7AKAAAAF063gqrNCKoAAACRwdGn/gEAAICeQlAFAACAlQiqAAAAsBJBFQAAAFYiqAIAAMBKBFUAAABYiaAKAAAAKxFUAQAAYCWCKgAAAKxEUAUAAICVCKoAAACw0kW9PYHzzRgjSQoEAr08EwAAAJxNQkKCPB7PGdsjLqjW1dVJkjIyMnp5JgAAADgbv98vr9d7xnaPaduCjBCnTp3S119/3WlCP18CgYAyMjJUVVV11v/RiBysuTux7u7DmrsPa97zXLej2q9fP11yySU9/rper5dfapdhzd2JdXcf1tx9WHN78GEqAAAAWImgCgAAACsRVM9RTEyM/vmf/1kxMTG9PRX0ENbcnVh392HN3Yc1t0/EfZgKAAAAkYEdVQAAAFiJoAoAAAArEVQBAABgJYIqAAAArERQ7abm5mYtW7ZMmZmZio2NVXp6ugoKCnT48OHenho6sX37dv3sZz/T0KFDFRsbq7i4OA0fPlxLlizRsWPHzvi89evX6+qrr9aAAQOUnJysv/3bv1VZWdlZX+uDDz7Qddddp+TkZA0YMEDjx4/XunXrzndJcOjgwYPyer3yeDx65513ztiPNe/7PvvsM91xxx269NJLFRMTo4EDB+rqq6/WAw88oPr6+g79WfO+r7S0VDfddJMuv/xyxcbGKikpSVOnTtWGDRvO+BzW3WIGjjU1NZmJEyeahIQE8x//8R+msbHRfPLJJ2bYsGFm4MCBZt++fb09RZzBk08+aSSZrKws81//9V8mEAiYQ4cOmX/7t38zF198sUlLSwu7fgsXLjSSzPLly83x48fNgQMHzKxZs0xUVJTZvHlz2NfavHmziYqKMrNmzTIHDhwwx48fN8uWLTOSzMKFCy90qTiLa6+91kgykkxxcXHYPqx537d69WoTExNjVqxYYQ4ePGiam5vNzp07zYQJE4wkU1lZGdKfNe/7nn76aSPJjBgxwpSUlJiGhgbz5ZdfmhtvvNFIMvfff3+H57DudiOodsPSpUuNJPPkk0+GHC8vLzcej8fk5OT00szQmccee8xER0ebgwcPdmh78MEHjSTz4x//OOT4W2+9ZSSZm266KeR4Y2OjycjIMD6fz3zzzTchbdXV1cbr9ZqMjAzT1NQU0tb2hvn222+fp6rgxLPPPmsSExPNsGHDzhhUWfO+79133zUej8cUFRV1aNu7d6/JzMw0hw4daj/Gmvd9J06cMF6v10gyH330UUhbY2OjSU5ONpLM3r1724+z7vYjqDrU2Nho4uPjTXR0tKmrq+vQ3vYv9ffff78XZofOrF+/3sydOzdsW0lJiZFkLrroIvPtt9+2H582bZqRZN56660Oz2n7R8uKFStCji9fvtxIMg899FCH57z55ptGksnLyzu3YuDYgQMHjNfrNWvXrjVTpkw5Y1Blzfu+sWPHGp/PZ4LBYJf6s+Z939GjR9vPlDQ0NHRoHzdunJFkNm7c2H6MdbcfQdWhV1991Ugy48aNC9u+ePFiI8ksXry4h2eGc7V7924jyVx88cXm5MmTxhhj/H6/iYqKMh6PJ+w/TNp+H8aOHRtyfOzYsUaSee211zo8p66uzng8HhMVFWX8fv+FKQZhTZ8+3cyYMcMYY84YVFnzvu/zzz8Pe3bkTFjzyJGRkRF2R7Wpqal9R/Xdd981xrDufQUfpnJo165dkqQhQ4aEbW87Xl5e3mNzwvnxxRdfSJJycnJ00UUXSZJ2796tlpYWDRw4UPHx8R2e07beu3fv1qlTpyRJLS0t2r17d0j76eLj45WSkqKWlhZVVFRckFrQ0fPPP68PPvhAzz333Fn7seZ9344dOyRJ3//+9/XWW28pNzdXXq9XcXFxGjVqlB5//HF9++237f1Z88jx4osvavDgwSooKFBZWZmampq0b98+3XbbbaqpqdG4ceOUk5MjiXXvKwiqDh05ckSSlJycHLY9KSkppB/6jnXr1snj8ejXv/51+7Gurndzc7OOHz8uSTp+/Liam5u79Dx+T3pGVVWVFi9erJUrVyojI+OsfVnzvm/fvn2SpDfffFP5+fmaP3++Dhw4oP379ysnJ0eLFi3SDTfcoJaWFkmseSSZPHmyPvzwQ2VmZmrixImKi4vT0KFDVVxcrLvuuktvv/22oqKiJLHufQVB1aHGxkZJUnR0dNj2mJiYkH7oG9544w396U9/0v33369p06a1H+/qep/e9/S15/fEDvPnz9e4ceM0f/78Tvuy5n2f3++XJFVWVmrlypWaM2eOkpKSlJ6erqeeekpXXXWVXn/9df3+97+XxJpHkm3btmn06NGqrKzUjh07VFdXpz179mjevHkKBoOqq6tr78u69w0EVYfi4uIkSSdOnAjbHgwGQ/rBfnv37tUdd9yh2bNn67HHHgtp6+p6n9739LXn96T3rVmzRjt27NCaNWu61J81jyxz5szpcGzu3LmSpJdeekkSax4pDhw4oFtuuUUnT57U66+/rpycHMXHx2vYsGFauXKlysvLlZWVpQMHDkhi3fsKgqpDqampkqSampqw7bW1tZKktLS0HpsTuq+yslLXXnutJk6cqA0bNrSfEmrT1fWOjY1VYmKiJCkxMVGxsbFdeh6/JxfWoUOHtGjRIj366KO67LLLuvQc1rzvazslm5KSEjYstP0ufPnll5JY80ixceNGNTY2atq0aRo8eHBIm8fj0a233qra2lr95je/kcS69xUEVYdGjRolqTXghNN2PCsrq6emhG7at2+fJk+erGuuuUZ//OMfw57GufLKK9WvXz998803amho6NDett4jRoxQv36tf52ioqI0YsSIkPbT1dfX69ixY4qKitLw4cPPZ0n4jj//+c8KBAL6xS9+IY/HE/J49913JUm5ubntx9555x3WPAJcccUVks6842WMkaT29WPNI0PbOpwpIKanp0uSPv30U0mse19BUHUoNzdXAwYMUHl5edhf7NLSUknSzJkze3pqcODzzz/X5MmTNX36dL344ovtn/KXpJUrV6qqqkqS5PV6NWXKFBljwt5O70zr/ZOf/CSk/XRlZWUyxmjKlCnyer3nrSZ0NG/ePJnWr+Hr8JgyZYokqbi4uP3Y1KlTWfMI8KMf/Uj9+vVTIBAIu+v11VdfSZJ++MMfSuLveaRISUmRJH399ddh29uOt21KsO59RI9/IVYEaLuD0dNPPx1yfPfu3cbj8ZgJEyb00szQFTt37jQpKSlmwYIF5tSpUx3a9Z3v1vzP//xPI8nk5+eH9GtqajKXXnqp8Xq9prq6OqTt6NGjJiEhwVx66aUd7lzy05/+1Egyb7zxxvkrCo6d7Qv/WfO+b86cOUZS2DtTXXXVVR2++J017/s+/PBDI8nEx8ebo0ePhrSdOnWq/ftP//Ef/7H9OOtuP4JqNzQ0NJjs7GyTkJBgNm/ebBobG82nn35qrrjiCpOSkhJyezbY5eOPPzZJSUkmLi7O3HzzzWEf4cLLvffe236HEr/fbw4ePGhuvPFG069fP/PKK6+Efa1XXnnF9OvXz9x4443m4MGDxu/3mxUrVhhJ5t577+2BanE2ZwuqxrDmfV11dbXJzMw0CQkJZuPGjaaxsdEcOXLE3HPPPUaSmT9/fofnsOZ93y9/+cv2L+kvLS019fX15osvvjB/93d/ZySZESNGmNra2pDnsO52I6h2U1NTk3n44YfND37wAxMdHW1SU1PNvHnzTFVVVW9PDWdx3333td9i72yPcOHlhRdeMGPHjjVxcXHG5/OZGTNmmJKSkrO+XklJifnxj39sfD6fiYuLM2PHjjV/+MMfLkxx6FRlZeUZ13zKlCkd+rPmfdvx48fNkiVL2t+nfT6fmTp1qtmwYcMZn8Oa931btmwxM2bMMCkpKSYqKsrEx8ebMWPGmEceecTU19eHfQ7rbi+PMf//qnIAAADAInyYCgAAAFYiqAIAAMBKBFUAAABYiaAKAAAAKxFUAQAAYCWCKgAAAKxEUAUAAICVCKoAAACwEkEVAAAAViKoAgAAwEoEVQAAAFiJoAoAAAAr/T8pZSSQO6jmpwAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "b = np.zeros(10)\n",
        "for i in range(0,10):\n",
        "    b[i] = operate_reduced(i*100)\n",
        "    plt.plot(i*100,a[i],marker='d',ls='',color='b')\n",
        "    plt.plot(i*100,b[i],marker='d',ls='',color='r')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Abweichungen implizit durch time stepping (LHS zu RHS)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 753,
      "metadata": {},
      "outputs": [],
      "source": [
        "A2 = I + v*dt*0.1/dx*(I-np.diag([1]*(len(x)-1),-1))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 754,
      "metadata": {},
      "outputs": [],
      "source": [
        "K_aa = A2[0:-1,0:-1]\n",
        "K_ab = A2[:-1, -1].reshape(-1, 1)\n",
        "K_ba = A2[-1, :-1].reshape(1, -1)\n",
        "K_bb = A2[-1,-1].reshape(1,1)\n",
        "c_a = c0[0:-1]\n",
        "c_b = c0[-1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 755,
      "metadata": {},
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "C:\\Users\\nagelt\\AppData\\Local\\Temp\\ipykernel_12380\\3680911035.py:3: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
            "  c[i] = operate_reduced(i*1000)\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "c = np.zeros(10)\n",
        "for i in range(0,10):\n",
        "    c[i] = operate_reduced(i*1000)\n",
        "    plt.plot(i*100,a[i],marker='d',ls='',color='b')\n",
        "    plt.plot(i*100,b[i],marker='d',ls='',color='r')\n",
        "    plt.plot(i*100,c[i],marker='d',ls='',color='g')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "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": "3.9.7"
    },
    "widgets": {
      "application/vnd.jupyter.widget-state+json": {
        "state": {},
        "version_major": 2,
        "version_minor": 0
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 4
}