Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods

¹ Laboratoire Jean Kuntzmann, Université Joseph Fourier Grenoble 1, BP53 38041 Grenoble, Cedex 9, France,
Tel. : +33476635497, Fax : +33476631263, e-mail: christophe.prudhomme@ujf-grenoble.fr, vincent.chabannes@imag.fr, abdoulaye.samake@imag.fr
² Université de Strasbourg / CNRS, IRMA / UMR 7501. Strasbourg, F-67000, France
³ Université Grenoble 1 / CNRS, Laboratoire Interdisciplinaire de Physique / UMR 5588. Grenoble, F-38041, France
e-mail: vincent.doyeux@ujf-grenoble.fr, mourad.ismail@ujf-grenoble.fr
⁴ CMUC, University of Coimbra, Largo D. Dinis, Apartado 3008, 3001-454 Coimbra, Portugal,
e-mail: gpena@mat.uc.pt

Abstract

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.