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@nicoguaro
Last active September 29, 2023 01:57
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Notebooks con implementaciones sencillas del método de elementos finitos para la ecuación de Poisson y de Helmholtz.
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Elementos finitos en 1D"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Queremos resolver al ecuación de Poisson en 1D usando\n",
"el método de elementos finitos.\n",
"\n",
"$$-\\frac{d^2 u}{dx^2} = f(x)\\, ,$$\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",
"$$\\int_{0}^{1} \\frac{d u}{d x} \\frac{d \\phi_n}{d x} dx\n",
"= \\int_{0}^{1} \\phi_n f(x) dx\\, \\quad \\forall \\phi_n\\, .$$\n",
"\n",
"Si remplazamos $u(x)$ en este sistema obtenemos\n",
"\n",
"$$\\sum_{j=0}^N \\left[\\int_{0}^{1} \\frac{d \\phi_i}{d x} \\frac{d \\phi_j}{d x} dx\\right] u_j\n",
"= \\int_{0}^{1} \\phi_j f(x) dx\\, \\quad \\forall \\phi_j\\, .$$\n",
"\n",
"Esto lleva al siguiente sistema de ecuaciones\n",
"\n",
"$$[K]\\{\\mathbf{u}\\} = \\{\\mathbf{b}\\}$$\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 el vector de cargas es\n",
"\n",
"$$b_\\text{local} = \\frac{h}{4}\\begin{bmatrix}\n",
"f(x_0) + f(x_1)\\\\\n",
"f(x_0) + 2f(x_1) + f(x_2)\\\\\n",
"f(x_1) + 2f(x_2) + f(x_3)\\\\\n",
"\\vdots\\\\\n",
"f(x_{N - 2}) + 2f(x_{N - 1}) + f(x_{N})\\\\\n",
"f(x_{N - 1}) + f(x_N)\n",
"\\end{bmatrix}\\, ,$$\n",
"\n",
"donde $h$ es el tamaño del elemento. Acá estamos asumiendo que el término fuente\n",
"es constante sobre cada elemento, es decir, que para el elemento\n",
"entre los nodos $i$ e $i + 1$ toma el valor\n",
"\n",
"$$\\frac{f_{i} + f_{i + 1}}{2}\\, $$\n",
"\n",
"\n",
"<div class=\"alert alert-info\">\n",
"\n",
"Demuestre que la integral para el término fuente 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 sympy import *"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Warning: Cannot change to a different GUI toolkit: notebook. Using widget instead.\n"
]
}
],
"source": [
"%matplotlib notebook\n",
"init_printing()\n",
"\n",
"# Configuracion graficos\n",
"gris = '#757575'\n",
"plt.rcParams[\"mathtext.fontset\"] = \"cm\"\n",
"plt.rcParams[\"text.color\"] = gris\n",
"plt.rcParams[\"font.size\"] = 12\n",
"plt.rcParams[\"xtick.color\"] = gris\n",
"plt.rcParams[\"ytick.color\"] = gris\n",
"plt.rcParams[\"axes.labelcolor\"] = gris\n",
"plt.rcParams[\"axes.edgecolor\"] = gris\n",
"plt.rcParams[\"axes.spines.right\"] = False\n",
"plt.rcParams[\"axes.spines.top\"] = False"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def global_mats(coords, source):\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",
" rhs = np.zeros((N))\n",
" f = source(coords)\n",
" for cont in range(N):\n",
" if cont == 0:\n",
" rhs[0] = f[0] + f[1]\n",
" if cont == N - 1:\n",
" rhs[-1] = f[-2] + f[-1]\n",
" else:\n",
" rhs[cont] = f[cont - 1] + 2*f[cont] + f[cont + 1]\n",
" return stiff/h, 0.25 * h * rhs"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Probemos la implementación con la función $f(x) = 20 x^3$, que lleva a\n",
"la solución\n",
"\n",
"$$u(x) = - x (x^4 - 1)$$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"N = 21\n",
"N_eval = 200\n",
"fun = lambda x: 20*x**3\n",
"x = np.linspace(0, 1, N)\n",
"x_eval = np.linspace(0, 1, N_eval)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Podemo usar ``global_mats`` para obtener la matriz de rigidez y el vector de cargas."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"stiff, rhs = global_mats(x, fun)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Y esta matriz y vector podemos usarla para resolver el sistema de ecuaciones\n",
"resultante con ``np.linalg.solve``.\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": [
"sol = np.zeros(N)\n",
"sol[1:-1] = np.linalg.solve(stiff[1:-1, 1:-1], rhs[1:-1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Podemos comparar la solución numérica con la solución analítica."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "054a4f620b4c46c081980993ac499de3",
"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_eval, -x_eval*(x_eval**4 - 1), color=\"red\")\n",
"plt.plot(x, sol, 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.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-info\">\n",
"\n",
"Pruebe a cambiar el número de nodos usados o el término fuente.\n",
"\n",
"</div>"
]
},
{
"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
}
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