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 -matrices are used.
DOI : 10.5802/smai-jcm.36
Mots clés : Finite Element Method, Boundary Element Method, $\protect \mathcal{H}$-matrices, Matlab
@article{SMAI-JCM_2018__4__297_0,
author = {Alouges, Fran\c{c}ois and Aussal, Matthieu},
title = {FEM and {BEM} simulations with the {Gypsilab} 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 = {http://www.numdam.org/articles/10.5802/smai-jcm.36/}
}
TY - JOUR AU - Alouges, François AU - Aussal, Matthieu TI - FEM and BEM simulations with the Gypsilab framework JO - The SMAI Journal of computational mathematics PY - 2018 SP - 297 EP - 318 VL - 4 PB - Société de Mathématiques Appliquées et Industrielles UR - http://www.numdam.org/articles/10.5802/smai-jcm.36/ DO - 10.5802/smai-jcm.36 LA - en ID - SMAI-JCM_2018__4__297_0 ER -
%0 Journal Article %A Alouges, François %A Aussal, Matthieu %T FEM and BEM simulations with the Gypsilab framework %J The SMAI Journal of computational mathematics %D 2018 %P 297-318 %V 4 %I Société de Mathématiques Appliquées et Industrielles %U http://www.numdam.org/articles/10.5802/smai-jcm.36/ %R 10.5802/smai-jcm.36 %G en %F SMAI-JCM_2018__4__297_0
Alouges, François; Aussal, Matthieu. FEM and BEM simulations with the Gypsilab framework. The SMAI Journal of computational mathematics, Tome 4 (2018), pp. 297-318. doi : 10.5802/smai-jcm.36. http://www.numdam.org/articles/10.5802/smai-jcm.36/
[1] Remarks around 50 lines of Matlab: short finite element implementation, Numerical Algorithms, Volume 20 (1999) no. 2-3, pp. 117-137 | DOI | MR | Zbl
[2] The sparse cardinal sine decomposition and its application for fast numerical convolution, Numerical Algorithms, Volume 70 (2015) no. 2, pp. 427-448 | DOI | MR | Zbl
[3] 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 | DOI
[4] 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 | DOI | MR
[5] Fast Matlab assembly of FEM matrices in 2D and 3D: Edge elements, Applied Mathematics and Computation, Volume 267 (2015), pp. 252-263 | DOI | MR | Zbl
[6] https://imacs.polytechnique.fr/ASERIS.htm ([Accessed - Sept. 2018])
[7] The finite element method using Matlab, CRC press, 2000
[8] Inverse acoustic and electromagnetic scattering theory, 93, Springer Science & Business Media, 2012
[9] https://www.comsol.fr ([Accessed - Sept. 2018])
[10] An efficient way to assemble finite element matrices in vector languages, BIT Numerical Mathematics, Volume 56 (2016) no. 3, pp. 833-864 | DOI | MR | Zbl
[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] 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 | DOI | MR | Zbl
[17] GetDP: a general finite-element solver for the de Rham complex, PAMM: Proceedings in Applied Mathematics and Mechanics, Volume 7(1), Wiley Online Library (2007), pp. 1010603-1010604 (See also "http://getdp.info") | DOI
[18] The rapid evaluation of potential fields in particle systems, MIT press, 1988 | DOI | Zbl
[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] Hierarchische Matrizen: Algorithmen und Analysis, Springer Science & Business Media, 2009 | Zbl
[21] New development in FreeFem++, Journal of numerical mathematics, Volume 20 (2012) no. 3-4, pp. 251-266 (See also http://www.freefem.org) | DOI | MR | Zbl
[22] Acoustic and electromagnetic equations: integral representations for harmonic problems, 144, Springer Science & Business Media, 2001 | Zbl
[23] Fast Matlab assembly of FEM matrices in 2D and 3D: Nodal elements, Applied mathematics and computation, Volume 219 (2013) no. 13, pp. 7151-7158 | DOI | MR | Zbl
[24] Solving boundary integral problems with BEM++, ACM Transactions on Mathematical Software (TOMS), Volume 41 (2015) no. 2, 6 pages | DOI | MR | Zbl
[25] The virtual element method in 50 lines of Matlab, Numerical Algorithms, Volume 75 (2017) no. 4, pp. 1141-1159 | DOI | MR | Zbl
[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])
Cité par Sources :
