A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes

Daniele Antonio Di Pietro 1, * Jean-Marc Gratien 2 Christophe Prud'Homme 3
* Auteur correspondant
1 ACSIOM
I3M - Institut de Mathématiques et de Modélisation de Montpellier
3 EDP - Equations aux Dérivées Partielles
LJK - Laboratoire Jean Kuntzmann
Abstract : In this work we propose an original implementation of a large family of lowest-order methods for diffusive problems including standard and hybrid finite volume methods, mimetic finite difference-type schemes, and cell centered Galerkin methods. The key idea is to regard the method at hand as a (Petrov-)Galerkin scheme based on possibly incomplete, broken affine spaces defined from a gradient reconstruction and a point value. The resulting unified framework serves as a basis for the development of a FreeFEM-like domain specific embedded language targeted at defining discrete linear and bilinear forms. Both the back-end and the front-end of the language are extensively discussed, and several examples of applications are provided. The overhead of the language is evaluated by comparing with a more traditional implementation. A benchmark including the comparison with more classical finite element methods on standard meshes is also proposed.
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BIT Numerical Mathematics, Springer Verlag, 2013, 53 (1), pp.111-152. 〈10.1007/s10543-012-0403-3〉
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Daniele Antonio Di Pietro, Jean-Marc Gratien, Christophe Prud'Homme. A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes. BIT Numerical Mathematics, Springer Verlag, 2013, 53 (1), pp.111-152. 〈10.1007/s10543-012-0403-3〉. 〈hal-00654406〉

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