Notebooks con implementaciones sencillas del método de elementos finitos para la ecuación de Poisson y de Helmholtz.

01a_fem1d_global_sym.ipynb

01b_fem1d_global.ipynb

02a_fem1d_eigs_global_sym.ipynb

02b_fem1d_eigs_global.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problema de valores propios en 1D con elementos finitos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Queremos resolver el siguiente problema de valores propios\n",
    "\n",
    "$$\\frac{d^2 u}{dx^2} = -k^2 u(x)\\, ,$$\n",
    "\n",
    "con $u(0) = u(1)  = 0$.\n",
    "\n",
    "Vamos a usar una solución aproximada de la forma\n",
    "\n",
    "$$u(x) = \\sum_{n=0}^{N} u_n \\phi_n(x)\\, ,$$\n",
    "\n",
    "Si usamos el método de Galerkin, la ecuación diferencial es equivalente\n",
    "al siguiente problema\n",
    "\n",
    "$$\\int_{0}^{1} \\frac{d u}{d x} \\frac{d \\phi_n}{d x} dx\n",
    "= \\lambda^2 \\int_{0}^{1}  u(x)\\phi_n dx\\, \\quad \\forall \\phi_n\\, .$$\n",
    "\n",
    "Si remplazamos $u(x)$ en este sistema obtenemos\n",
    "\n",
    "$$\\sum_{j=0}^N \\left[\\int_{0}^{1} \\frac{d \\phi_i}{d x} \\frac{d \\phi_j}{d x} dx\\right] u_j\n",
    "= \\lambda^2 \\sum_{j=0}^N \\left[\\int_{0}^{1} \\phi_i \\phi_j dx\\right] u_j\\, \\quad \\forall \\phi_j\\, .$$\n",
    "\n",
    "Esto lleva al siguiente problema de valores propios generalizado\n",
    "\n",
    "$$[K]\\{\\mathbf{u}\\} = \\lambda^2[M]\\{\\mathbf{u}\\}$$\n",
    "\n",
    "donde la matriz de rigidez global está dada por\n",
    "\n",
    "$$[K] =  \\frac{1}{h}\\begin{bmatrix}\n",
    "1 &-1 &0 &\\cdots &\\cdots &0\\\\\n",
    "-1 &2 &-1 & & &0\\\\\n",
    "0 &-1 &2 & & &0\\\\\n",
    "\\vdots & & &\\ddots & &\\vdots\\\\\n",
    "\\vdots & & & &2 &-1\\\\\n",
    "0 &\\cdots &\\cdots &\\cdots &-1 &1\\\\\\end{bmatrix}$$\n",
    "\n",
    "y la matriz de masa es\n",
    "\n",
    "$$[M] =  \\frac{h}{6}\\begin{bmatrix}\n",
    "2 &1 &0 &\\cdots &\\cdots &0\\\\\n",
    "1 &4 &1 & & &0\\\\\n",
    "0 &1 &4 & & &0\\\\\n",
    "\\vdots & & &\\ddots & &\\vdots\\\\\n",
    "\\vdots & & & &4 &1\\\\\n",
    "0 &\\cdots &\\cdots &\\cdots &1 &2\\\\\\end{bmatrix}\\, ,$$\n",
    "\n",
    "$h$ es el tamaño del elemento.\n",
    "\n",
    "\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Demuestre que la integral para la matriz de masa da la expresión\n",
    "mostrada anteriormente.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.linalg import eigh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[\"mathtext.fontset\"] = \"cm\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def global_mats(coords):\n",
    "    h = coords[1] - coords[0]\n",
    "    N = len(coords)\n",
    "    stiff = np.diag(np.full(N, 2), 0)\\\n",
    "        + np.diag(np.full(N-1, -1), -1)\\\n",
    "        + np.diag(np.full(N-1, -1), 1)\n",
    "    stiff[0, 0] = stiff[-1, -1] = 1\n",
    "    mass = np.diag(np.full(N, 4), 0)\\\n",
    "        + np.diag(np.full(N-1, 1), -1)\\\n",
    "        + np.diag(np.full(N-1, 1), 1)\n",
    "    mass[0, 0] = mass[-1, -1] = 2\n",
    "    return stiff/h, h/6 * mass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para este caso, la solución analítica del problema es\n",
    "\n",
    "$$u_n = \\sin(n \\pi x)\\, ,\\quad \\lambda_n = n \\pi\\, .$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 201\n",
    "nvals = 10\n",
    "x = np.linspace(0, 1, N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemo usar ``global_mats`` para obtener las matrices de rigidez y masa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "stiff, mass = global_mats(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y estas matrices podemos usarlas para resolver el problema de valores\n",
    "propios generalizado con ``eigh``.\n",
    "\n",
    "En este caso no tomamos la matriz completa sino que dejamos por\n",
    "fuera las filas/columnas correspondientes al primer y último\n",
    "grado de libertad ya que tenemos condiciones de Dirichlet homogéneas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "vals, vecs = eigh(stiff[1:-1, 1:-1],\n",
    "                  mass[1:-1, 1:-1],\n",
    "                  subset_by_index=(0, nvals - 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  9.8698,  39.4817,  88.8429, 157.9656, 246.867 , 355.5688,\n",
       "       484.0981, 632.4863, 800.7703, 988.9915])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(vals, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y podemos comparar esto con la solución analítica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  9.8696,  39.4784,  88.8264, 157.9137, 246.7401, 355.3058,\n",
       "       483.6106, 631.6547, 799.438 , 986.9604])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vals_ex = np.round([k**2 * np.pi**2 for k in range(1, nvals + 1)], 4)\n",
    "vals_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$\\\\lambda_n^2$')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d92f2b095540405785004bd90eaf72b9",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(range(1, nvals + 1), vals, \"o\", color=\"green\")\n",
    "plt.plot(range(1, nvals + 1), vals_ex, \"s\", mec=\"black\",\n",
    "         mfc=\"#FFFFFF00\")\n",
    "plt.xlabel(r\"$n$\", fontsize=16)\n",
    "plt.ylabel(r\"$\\lambda_n^2$\", fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos comparar la solución numérica con la solución analítica.\n",
    "\n",
    "Para ello completamos los vectores propios con los ceros en los extremos\n",
    "primero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "vecs_comp = np.zeros((N, nvals))\n",
    "vecs_comp[1:-1, :] = vecs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b7db4be0ce38460eb8891c2078ddf2b4",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(x, vecs_comp[:, 1])\n",
    "plt.plot(x, np.sqrt(2) * np.sin(2*np.pi*x), linestyle=\"dashed\")\n",
    "plt.xlabel(r\"$x$\", fontsize=16)\n",
    "plt.ylabel(r\"$y$\", fontsize=16)\n",
    "plt.legend([\"Solución numérica\", \"Solución exacta\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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": "3.11.5"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}

03_fem1d.ipynb

04_fem1d_eigs.ipynb

05_fem2d.ipynb

06_fem2d_eigs.ipynb

07_fem2d_transitorio.ipynb

08_fem2d_difusion_reaccion.ipynb

README.md

cuadrado.geo

cuadrado101.msh

cuadrado11.msh

cuadrado21.msh

cuadrado51.msh

fem_202309.yml