Feel++: A Computational Framework for Galerkin Methods and Advanced Numerical Methods

Christophe Prud'Homme (1, 2) , Vincent Chabannes (3) , Vincent Doyeux (4) , Mourad Ismail (5) , Abdoulaye Samake (1) , Gonçalo Pena (6)

1 LJK - Laboratoire Jean Kuntzmann
2 IRMA - Institut de Recherche Mathématique Avancée
3 EDP - Equations aux Dérivées Partielles
4 LIPhy - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères]
5 LSP - Laboratoire de Spectrométrie Physique
6 CMUC - Center for Mathematics [Coimbra]

This paper presents an overview of a unified framework for finite element and spectral element methods in 1D, 2D and 3D in \cpp 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 ficticious domain-like methods (the Fat Boundary Method and the Penalty Method) are presented and numerically solved in the scope of the library.

Mots clés: Galerkin methods; finite element; domain decomposition; ficticious domain; domain specific embedded language; programming paradigms

Domaines: Logiciel mathématique [cs.MS]; Modélisation et simulation; Equations aux dérivées partielles [math.AP]

Christophe Prud'Homme, Vincent Chabannes, Vincent Doyeux, Mourad Ismail, Abdoulaye Samake, et al.. Feel++: A Computational Framework for Galerkin Methods and Advanced Numerical Methods. 2012. ⟨hal-00662868v1⟩