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BIT Numerical Mathematics
Erschienen in: BIT Numerical Mathematics 1/2013

01.03.2013

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

verfasst von: Daniele A. Di Pietro, Jean-Marc Gratien, Christophe Prud’homme

Erschienen in: BIT Numerical Mathematics | Ausgabe 1/2013

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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 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 with respect to a more traditional implementation. A benchmark including the comparison with more classical finite element methods on standard meshes is also proposed.
Vorheriger Artikel Error bounds on the approximation of functions and partial derivatives by quadratic spline quasi-interpolants on non-uniform criss-cross triangulations of a rectangular domain
Nächster Artikel Minimization of functionals on the solution of a large-scale discrete ill-posed problem

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Metadaten
Titel
A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes
verfasst von
Daniele A. Di Pietro
Jean-Marc Gratien
Christophe Prud’homme
Publikationsdatum
01.03.2013
Verlag
Springer Netherlands
Erschienen in
BIT Numerical Mathematics / Ausgabe 1/2013
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI
https://doi.org/10.1007/s10543-012-0403-3

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