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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 las matrices de rigidez locales están dadas por\n",
"\n",
"$$K_\\text{local} = \\frac{1}{|J|}\\begin{bmatrix} 2 & -2\\\\ -2 &2\\end{bmatrix}$$\n",
"\n",
"y\n",
"\n",
"$$b_\\text{local} = -|J|\\begin{bmatrix} f(x_m)\\\\ f(x_{m})\\end{bmatrix}\\, ,$$\n",
"\n",
"donde $|J|$ es el determinante jacobian de la transformación y $x_m$ es\n",
"el punto medio del elemento. Acá estamos asumiendo que el término fuente\n",
"es constante sobre el elemento. Bien podríamos usar una mejor aproximación\n",
"para esta integral.\n",
"\n",
"\n",
"<div class=\"alert alert-warning\">\n",
"\n",
"Acá estamos dejando por fuera muchos detalles del ensamblaje de la\n",
"matriz y del mapeo del ordenamiento local al global.\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"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"plt.rcParams[\"mathtext.fontset\"] = \"cm\""
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def FEM1D(coords, source):\n",
" N = len(coords)\n",
" stiff_loc = np.array([[2.0, -2.0],\n",
" [-2.0, 2.0]])\n",
" eles = [np.array([cont, cont + 1]) for cont in range(0, N - 1)]\n",
" stiff = np.zeros((N, N))\n",
" rhs = np.zeros(N)\n",
" for ele in eles: ## Ensamblaje\n",
" jaco = coords[ele[1]] - coords[ele[0]]\n",
" x_mid = np.mean(coords[ele])\n",
" rhs[ele] = rhs[ele] - jaco*source(np.array([x_mid, x_mid]))\n",
" for cont1, row in enumerate(ele):\n",
" for cont2, col in enumerate(ele):\n",
" stiff[row, col] = stiff[row, col] + stiff_loc[cont1, cont2]/jaco\n",
" return stiff, 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 = 100\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)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Podemo usar ``FEM1D`` para obtener la matriz de rigidez y el vector de cargas."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"stiff, rhs = FEM1D(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": "c3dfafe6ed134a9e9447b9485205c471",
"version_major": 2,
"version_minor": 0
},
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",
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"\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))\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": [
"Pruebe a cambiar el número de nodos usados."
]
},
{
"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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