HAL: hal-00662868, version 3

DOI: 10.1051/proc/201238024

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ESAIM: Proc. 38 (2012) 429 - 455

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v1 (2012-01-26)

v2 (2012-01-27)

v3 (2012-01-27)

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

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

For the Feel++ collaboration(s)

(2012-12)

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.

1:	Laboratoire Jean Kuntzmann (LJK)
	CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
2:	Institut de Recherche Mathématique Avancée (IRMA)
	CNRS : UMR7501 – Université de Strasbourg
3:	Laboratoire Interdisciplinaire de Physique (LIPhy)
	CNRS : UMR5588 – Université Joseph Fourier - Grenoble I
4:	Center for Mathematics [Coimbra] (CMUC)
	University of Coimbra

Research team: EDP

Subject

:

Computer Science/Mathematical Software Computer Science/Modeling and Simulation Mathematics/Analysis of PDEs

Keyword(s): Galerkin methods – finite element – domain decomposition – ficticious domain – domain specific embedded language – programming paradigms

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From: Christophe Prud'Homme <>

Submitted on: Friday, 27 January 2012 14:57:21

Updated on: Monday, 11 February 2013 14:17:08