{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Offline Phase: PBDW offline - computing the inf-sup constant\n", "\n", "**Aim of the tutorial:** this notebook shows how to calculate the $inf-sup$ constant, bounding the approximation error of the PBDW.\n", "\n", "----\n", "\n", "*To execute this notebook* it is necessary to have the POD modes stored in `Offline_results/BasisFunctions` folder, placed in this directory (otherwise modify `path_off` variable) and the basis sensors in `Offline_results/BasisSensors`." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from IPython.display import clear_output\n", "\n", "from dolfinx.fem import FunctionSpace\n", "\n", "from pyforce.tools.write_read import ImportH5, StoreFunctionsList as store\n", "\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "\n", "path_off ='./Offline_results/'" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "The geometry is imported from \"ANL11A2_octave.geo\", generated with GMSH. Then, the mesh is created with the gmsh module." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from neutronics import create_anl11a2_mesh\n", "\n", "domain, _, _ = create_anl11a2_mesh(use_msh=True, save_mesh=False)\n", "\n", "fuel1_marker = 1\n", "fuel2_marker = 2\n", "fuel_rod_marker = 3\n", "refl_marker = 4\n", "\n", "void_marker = 10\n", "sym_marker = 20\n", "\n", "clear_output()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Importing basis function and sensors\n", "\n", "The functional space and the names of the fields are defined." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Defining the functional space\n", "V = FunctionSpace(domain, (\"Lagrange\", 1))\n", "\n", "# Define the variables to load\n", "var_names = [\n", " 'phi_1',\n", " 'phi_2'\n", " ]\n", "\n", "tex_var_names = [\n", " r'\\phi_1',\n", " r'\\phi_2'\n", " ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us import the POD modes using `ImportH5`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "bf = dict()\n", "\n", "for field_i in range(len(var_names)):\n", " \n", " bf[var_names[field_i]] = ImportH5(V, path_off+'/BasisFunctions/basisPOD_'+var_names[field_i], 'POD_'+var_names[field_i])[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us import the basis sensors generated with SGREEDY." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "s = 2\n", "\n", "is_H1 = [False, True]\n", "fun_space_label = ['L2', 'H1']\n", "\n", "bs = dict()\n", "\n", "for field in var_names:\n", " bs[field] = dict()\n", " for space in fun_space_label:\n", " bs[field][space] = ImportH5(V, \n", " path_off+'/BasisSensors/sensorsSGREEDYPOD_' + field+'_s_{:.2e}_'.format(s)+space,\n", " 'SGREEDYPOD_' +field+'_s_{:.2e}'.format(s))[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PBDW-Offline: Compute the *inf-sup* constant\n", "The *inf-sup* constant is a measure of the approximation capabilities of the PBDW, in particular highlights how the sensors are able to include more information into the background model, encoded in the basis functions. The *inf-sup* constant is computed by solving an eigenvalue problem, as reported in [Maday and Taddei (2019)](https://epubs.siam.org/doi/10.1137/18M116544X).\n", "\n", "Given the background space $Z_N = \\text{span}\\{\\zeta_1, \\zeta_2, \\dots, \\zeta_N\\}$, spanned by the POD modes, and the update space $\\mathcal{U}_M=\\text{span}\\{g_1, g_2, \\dots, g_M\\}$, spanned by the sensors selected by SGREEDY, the following matrices can be defined\n", "\\begin{equation*}\n", "A_{mm'} = \\left(g_m, g_{m'}\\right)_{\\mathcal{U}}\\qquad\n", "K_{mn} = \\left(g_m, \\zeta_{n}\\right)_{\\mathcal{U}} = v_m(\\zeta_n)\\qquad\n", "B_{nn'} = \\left(\\zeta_n, \\zeta_{n'}\\right)_{\\mathcal{U}}\n", "\\end{equation*}\n", "The *inf-sup* constant $\\beta_{N,M}$ is the square-root of the minimum eigenvalue of the following problem\n", "\\begin{equation*}\n", "K^TA^{-1}K \\mathbf{w}_j = \\lambda_j B\\mathbf{w}_j\n", "\\end{equation*}\n", "that is $\\beta_{N,M} = \\sqrt{\\min\\limits_{j=1,\\dots, N} \\lambda_j}$.\n", "\n", "This eigenvalue problem can be solved using the `PBDW` offline class, using the method `compute_infsup`. This class must be initialised with the basis functions, the basis sensors and the flag for the Riesz representation, either $L^2$ or $H^1$.\n", "\n", "To compute the *inf-sup* constant the dimension of the reduced space must be fixed, a good approximation of the manifold can be reached with $N=10$, obtained by observabing the POD eigenvalues." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Compute Inf-Sup for phi_1 with s=2.00 and Riesz representation in L2\n", "Compute Inf-Sup for phi_1 with s=2.00 and Riesz representation in H1\n", "Compute Inf-Sup for phi_2 with s=2.00 and Riesz representation in L2\n", "Compute Inf-Sup for phi_2 with s=2.00 and Riesz representation in H1\n" ] } ], "source": [ "from pyforce.offline.pbdw import PBDW\n", "\n", "Nmax = 10\n", "Mmax = 20\n", "\n", "inf_sup_constants = dict()\n", "\n", "for field in var_names:\n", " inf_sup_constants[field] = dict()\n", " \n", " inf_sup_constants[field]['s = {:.2f}'.format(s)] = dict()\n", " for kk, space in enumerate(fun_space_label):\n", " \n", " print('Compute Inf-Sup for '+field+' with s={:.2f}'.format(s)+' and Riesz representation in '+space)\n", " \n", " pbdw = PBDW(bf[field], bs[field][space], is_H1[kk])\n", " inf_sup_constants[field]['s = {:.2f}'.format(s)][space] = pbdw.compute_infsup(Nmax, Mmax)\n", " \n", " del pbdw" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us plot the constant for the different configurations." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(nrows = len(var_names), ncols = 1, sharey=True, sharex=True, figsize = (7, 5 * len(var_names)))\n", "\n", "Mplot = np.arange(1, Mmax + 1, 1)\n", "\n", "for field_i, field in enumerate(var_names):\n", " \n", " axs[field_i].plot(Mplot, inf_sup_constants[field]['s = {:.2f}'.format(s)]['L2'], \n", " '--o', c='r', label=r'$L^2$')\n", " axs[field_i].plot(Mplot, inf_sup_constants[field]['s = {:.2f}'.format(s)]['H1'], \n", " '--^', c='b', label=r'$H^1$')\n", " \n", " axs[field_i].set_ylim(0, 0.4)\n", " axs[field_i].set_xlim(1, Mmax)\n", " axs[field_i].grid()\n", " axs[field_i].legend(framealpha=1, fontsize=20)\n", " \n", " axs[0,].set_title(r'Point Spread $s={:.2f}$'.format(s), fontsize=20)\n", " axs[-1].set_xlabel(r'Number of sensors $M$', fontsize=20)\n", " \n", " axs[field_i].set_ylabel(r'Inf-Sup Constant $\\beta_{10,M}$', fontsize=20)\n", "\n", "fig.subplots_adjust(hspace=0.05, wspace=0.025)" ] } ], "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": "3.10.14" }, "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "e5b3af111de828d84cfea01c8e4cc990d7262e947155f31e208c22ad6b78199b" } } }, "nbformat": 4, "nbformat_minor": 2 }