Avec cedram.org english version Accueil Présentation Recherche avancée Tous les articles en ligne Derniers articles Rechercher un article Table des matières de ce volume | Article précédent | Article suivant François Alouges; Matthieu AussalFEM and BEM simulations with the Gypsilab frameworkSMAI-Journal of computational mathematics, 4 (2018), p. 297-318, doi: 10.5802/smai-jcm.36 Article PDF Class. Math.: 65N30, 65N38, 65Y99Mots clés: Finite Element Method, Boundary Element Method, $\protect \mathcal{H}$-matrices, Matlab AbstractGypsilab is a Matlab framework which aims at simplifying the development of numerical methods that apply to the solution of problems in multiphysics, in particular, those involving FEM or BEM simulations. The peculiarities of the framework, with a focus on its ease of use, are shown together with the methodology that have been followed for its development. Example codes that are short though representative enough are given both for FEM and BEM applications. A performance comparison with FreeFem++ is provided, and a particular emphasis is made on problems in acoustics and electromagnetics solved using the BEM and for which compressed $\mathcal{H}$-matrices are used. Bibliographie[1] J. Alberty, C. Carstensen & S. A. Funken, “Remarks around 50 lines of Matlab: short finite element implementation”, Numerical Algorithms 20 (1999) no. 2-3, p. 117-137 [2] F. Alouges & M. Aussal, “The sparse cardinal sine decomposition and its application for fast numerical convolution”, Numerical Algorithms 70 (2015) no. 2, p. 427-448 [3] F. Alouges, M. Aussal, A. Lefebvre-Lepot, F. Pigeonneau & A. Sellier, “Application of the sparse cardinal sine decomposition to 3D Stokes flows”, International Journal of Computational Methods and Experimental Measurements 5 (2017) no. 3, p. 387-394 [4] F. Alouges, M. Aussal & E. Parolin, “Fast Boundary Element Method for acoustics with the Sparse Cardinal Sine Decomposition”, European Journal of Computational Mechanics 26 (2017) no. 4, p. 377-393 [5] I. Anjam & J. Valdman, “Fast Matlab assembly of FEM matrices in 2D and 3D: Edge elements”, Applied Mathematics and Computation 267 (2015), p. 252-263 [6] , https://imacs.polytechnique.fr/ASERIS.htm, [Accessed - Sept. 2018] [7] H. Bang & Y. W Kwon, The finite element method using Matlab, CRC press, 2000 [8] D. Colton & R. Kress, Inverse acoustic and electromagnetic scattering theory 93, Springer Science & Business Media, 2012 [9] , https://www.comsol.fr, [Accessed - Sept. 2018] [10] F. Cuvelier, C. Japhet & G. Scarella, “An efficient way to assemble finite element matrices in vector languages”, BIT Numerical Mathematics 56 (2016) no. 3, p. 833-864 [11] , https://www.esi-group.com/software-solutions/virtual-environment/electromagnetics/cem-one/efield-time-domain-solvers, [Accessed - Sept. 2018] [12] , http://www.feelpp.org, [Accessed - Sept. 2018] [13] , https://fenicsproject.org, [Accessed - Sept. 2018] [14] , http://firedrakeproject.org, [Accessed - Sept. 2018] [15] , http://www.cims.nyu.edu/cmcl/fmm3dlib/fmm3dlib.html, [Accessed - Sept. 2018] [16] S. Funken, D. Praetorius & P. Wissgott, “Efficient implementation of adaptive P1-FEM in Matlab”, Computational Methods in Applied Mathematics Comput. Methods Appl. Math. 11 (2011) no. 4, p. 460-490 [17] C. Geuzaine, GetDP: a general finite-element solver for the de Rham complex, in PAMM: Proceedings in Applied Mathematics and Mechanics, Wiley Online Library, See also "http://getdp.info", 2007, p. 1010603-1010604 [18] L. Greengard, The rapid evaluation of potential fields in particle systems, MIT press, 1988 [19] , www.cmap.polytechnique.fr/~aussal/gypsilab, Gypsilab is freely available under GPL 3.0 license. (It is also available on GitHub at "https://github.com/matthieuaussal/gypsilab") [20] W. Hackbusch, Hierarchische Matrizen: Algorithmen und Analysis, Springer Science & Business Media, 2009 [21] F. Hecht, “New development in FreeFem++”, Journal of numerical mathematics 20 (2012) no. 3-4, p. 251-266, See also http://www.freefem.org [22] J.-C. Nédélec, Acoustic and electromagnetic equations: integral representations for harmonic problems 144, Springer Science & Business Media, 2001 [23] T. Rahman & J. Valdman, “Fast Matlab assembly of FEM matrices in 2D and 3D: Nodal elements”, Applied mathematics and computation 219 (2013) no. 13, p. 7151-7158 [24] W. Śmigaj, T. Betcke, S. Arridge, J. Phillips & M. Schweiger, “Solving boundary integral problems with BEM++”, ACM Transactions on Mathematical Software (TOMS) 41 (2015) no. 2 [25] O. J. Sutton, “The virtual element method in 50 lines of Matlab”, Numerical Algorithms 75 (2017) no. 4, p. 1141-1159 [26] , https://www.esi-group.com/fr/solutions-logicielles/performance-virtuelle/vibro-acoustique, [Accessed - Sept. 2018] [27] , https://uma.ensta-paristech.fr/soft/XLiFE++/, [Accessed - Sept. 2018] © 2015SMAI Journal of Computational Mathematics ISSN 2426-8399 Les articles sont publiés sous licence Creative Commons CC BY-NC-ND 3.0