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Mathematica implementation of the high order finite element method applied to eigenproblems

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Abstract

In this paper an \(hp\)-FEM implementation on Mathematica is discussed. FEM-implementations on higher-level programming platforms are useful for prototyping new algorithms and ideas, but also serve as testing ground for interesting programming techniques. Here, an \(hp\)-adaptive algorithm for eigenproblems, and the use of precomputed data and generation of highly graded \(hp\)-meshes, are examples of the former and latter, respectively. The performance of the code is evaluated in relation to a suite of benchmark problems for the Laplacian and thin solids in elasticity.

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Notes

  1. MATLAB follows the model of C++ and similar languages, whereas Mathematica follows the Common Lisp.

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Authors and Affiliations

  1. Department of Mathematics and Systems Analysis, Aalto University, 11100, 00076 , Aalto, Finland

    Harri Hakula & Tomi Tuominen

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  1. Harri Hakula
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  2. Tomi Tuominen
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Correspondence to Harri Hakula.

Appendices

Implementation of the integrated legendre polynomials

figure a5

Typical main programme

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Hakula, H., Tuominen, T. Mathematica implementation of the high order finite element method applied to eigenproblems. Computing 95 (Suppl 1), 277–301 (2013). https://doi.org/10.1007/s00607-012-0262-4

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