FEM and BEM simulations with the Gypsilab framework
The SMAI journal of computational mathematics, Volume 4 (2018) , pp. 297-318.

Gypsilab 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 $ℋ$-matrices are used.

Published online: 2018-10-31
DOI: https://doi.org/10.5802/smai-jcm.36
Classification: 65N30,  65N38,  65Y99
Keywords: Finite Element Method, Boundary Element Method, $ℋ$-matrices, Matlab
@article{SMAI-JCM_2018__4__297_0,
author = {Fran\c cois Alouges and Matthieu Aussal},
title = {FEM and BEM simulations with the <span class="smallcaps">Gypsilab</span> framework},
journal = {The SMAI journal of computational mathematics},
pages = {297--318},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {4},
year = {2018},
doi = {10.5802/smai-jcm.36},
mrnumber = {3883671},
zbl = {1416.65429},
language = {en},
url = {smai-jcm.centre-mersenne.org/item/SMAI-JCM_2018__4__297_0/}
}
François Alouges; Matthieu Aussal. FEM and BEM simulations with the Gypsilab framework. The SMAI journal of computational mathematics, Volume 4 (2018) , pp. 297-318. doi : 10.5802/smai-jcm.36. https://smai-jcm.centre-mersenne.org/item/SMAI-JCM_2018__4__297_0/

[1] J. Alberty; C. Carstensen; S. A. Funken Remarks around 50 lines of Matlab: short finite element implementation, Numerical Algorithms, Volume 20 (1999) no. 2-3, pp. 117-137 | Article | MR 1709562 | Zbl 0938.65129

[2] F. Alouges; M. Aussal The sparse cardinal sine decomposition and its application for fast numerical convolution, Numerical Algorithms, Volume 70 (2015) no. 2, pp. 427-448 | Article | MR 3401042 | Zbl 1326.65183

[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, Volume 5 (2017) no. 3, pp. 387-394 | Article

[4] F. Alouges; M. Aussal; E. Parolin Fast Boundary Element Method for acoustics with the Sparse Cardinal Sine Decomposition, European Journal of Computational Mechanics, Volume 26 (2017) no. 4, pp. 377-393 | Article | MR 3765208

[5] I. Anjam; J. Valdman Fast Matlab assembly of FEM matrices in 2D and 3D: Edge elements, Applied Mathematics and Computation, Volume 267 (2015), pp. 252-263 | Article | MR 3399045 | Zbl 1410.65441

[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 Volume 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, Volume 56 (2016) no. 3, pp. 833-864 | Article | MR 3540462 | Zbl 1351.65088

[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., Volume 11 (2011) no. 4, pp. 460-490 | Article | MR 2875100 | Zbl 1284.65197

[17] C. Geuzaine GetDP: a general finite-element solver for the de Rham complex, PAMM: Proceedings in Applied Mathematics and Mechanics, Volume 7(1) (2007), p. 1010603-1010604 (See also "http://getdp.info") | Article

[18] L. Greengard The rapid evaluation of potential fields in particle systems, MIT press, 1988 | Article

[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 | Zbl 1180.65004

[21] F. Hecht New development in FreeFem++, Journal of numerical mathematics, Volume 20 (2012) no. 3-4, pp. 251-266 (See also http://www.freefem.org) | Article | MR 3043640 | Zbl 1266.68090

[22] J.-C. Nédélec Acoustic and electromagnetic equations: integral representations for harmonic problems Volume 144, Springer Science & Business Media, 2001 | Zbl 0981.35002

[23] T. Rahman; J. Valdman Fast Matlab assembly of FEM matrices in 2D and 3D: Nodal elements, Applied mathematics and computation, Volume 219 (2013) no. 13, pp. 7151-7158 | Article | MR 3030557 | Zbl 1288.65169

[24] W. Śmigaj; T. Betcke; S. Arridge; J. Phillips; M. Schweiger Solving boundary integral problems with BEM++, ACM Transactions on Mathematical Software (TOMS), Volume 41 (2015) no. 2, 6 pages | Article | MR 3318078 | Zbl 1371.65127

[25] O. J. Sutton The virtual element method in 50 lines of Matlab, Numerical Algorithms, Volume 75 (2017) no. 4, pp. 1141-1159 | Article | MR 3674245 | Zbl 1375.65155

[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])