Geodesic
Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods
Christophe Prud’homme1 ; Vincent Chabannes2 ; Vincent Doyeux3 ; Mourad Ismail3 ; Abdoulaye Samake2 ; Goncalo Pena4
1 Université de Strasbourg / CNRS, IRMA / UMR 7501. Strasbourg, F-67000, France
2 Laboratoire Jean Kuntzmann, Université Joseph Fourier Grenoble 1, BP53 38041 Grenoble, Cedex 9, France
3 Université Grenoble 1 / CNRS, Laboratoire Interdisciplinaire de Physique / UMR 5588. Grenoble, F-38041, France
4 CMUC, University of Coimbra, Largo D. Dinis, Apartado 3008, 3001-454 Coimbra, Portugal
ESAIM. Proceedings, Tome 38 (2012), pp. 429-455.

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This paper presents an overview of a unified framework for finite element and spectral element methods in 1D, 2D and 3D in C++ called Feel++. The article is divided in two parts. The first part provides a digression through the design of the library as well as the main abstractions handled by it, namely, meshes, function spaces, operators, linear and bilinear forms and an embedded variational language. In every case, the closeness between the language developed in Feel++ and the equivalent mathematical objects is highlighted. In the second part, examples using the mortar, Schwartz (non)overlapping, three fields and two fictitious domain-like methods (the Fat Boundary Method and the Penalty Method) are presented and numerically solved in the scope of the library.
DOI : 10.1051/proc/201238024

Christophe Prud’homme 1 ; Vincent Chabannes 2 ; Vincent Doyeux 3 ; Mourad Ismail 3 ; Abdoulaye Samake 2 ; Goncalo Pena 4

1 Université de Strasbourg / CNRS, IRMA / UMR 7501. Strasbourg, F-67000, France
2 Laboratoire Jean Kuntzmann, Université Joseph Fourier Grenoble 1, BP53 38041 Grenoble, Cedex 9, France
3 Université Grenoble 1 / CNRS, Laboratoire Interdisciplinaire de Physique / UMR 5588. Grenoble, F-38041, France
4 CMUC, University of Coimbra, Largo D. Dinis, Apartado 3008, 3001-454 Coimbra, Portugal 
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     title = {Feel++ : {A} computational framework for {Galerkin} {Methods} and {Advanced} {Numerical} {Methods}},
     journal = {ESAIM. Proceedings},
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Christophe Prud’homme; Vincent Chabannes; Vincent Doyeux; Mourad Ismail; Abdoulaye Samake; Goncalo Pena. Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods. ESAIM. Proceedings, Tome 38 (2012), pp. 429-455. doi : 10.1051/proc/201238024. http://geodesic.mathdoc.fr/articles/10.1051/proc/201238024/

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