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

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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.

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Authors and Affiliations

  1. Institut de Mathématiques et de Modélisation de Montpellier, Université Montpellier 2, 34057, Montpellier Cedex 5, France

    Daniele A. Di Pietro

  2. Department of Information Technology, IFP Energies nouvelles, 1 & 4 avenue Bois Préau, 92852, Rueil-Malmaison Cedex, France

    Jean-Marc Gratien

  3. Université de Strasbourg, IRMA/CNRS UMR 7501, 7 rue René Descartes, 67084, Strasbourg Cedex, France

    Christophe Prud’homme

Authors
  1. Daniele A. Di Pietro
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  2. Jean-Marc Gratien
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  3. Christophe Prud’homme
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Correspondence to Daniele A. Di Pietro.

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Communicated by Hans Petter Langtangen.

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Di Pietro, D.A., Gratien, JM. & Prud’homme, C. A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes. Bit Numer Math 53, 111–152 (2013). https://doi.org/10.1007/s10543-012-0403-3

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  • DOI: https://doi.org/10.1007/s10543-012-0403-3

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