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Sparsity Optimized High Order Finite Element Functions on Simplices

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Book cover Numerical and Symbolic Scientific Computing

Part of the book series: Texts & Monographs in Symbolic Computation ((TEXTSMONOGR))

Abstract

This article reports several results on sparsity optimized basis functions for hp-FEM on triangular and tetrahedral finite element meshes obtained within the Special Research Program “Numerical and Symbolic Scientific Computing” and within the Doctoral Program “Computational Mathematics” both supported by the Austrian Science Fund FWF under the grants SFB F013 and DK W1214, respectively. We give an overview on the sparsity pattern for mass and stiffness matrix in the spaces L 2, H 1, H({ div}) and H(curl). The construction relies on a tensor-product based construction with properly weighted Jacobi polynomials.

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Acknowledgements

This work has been supported by the FWF-projects P20121-N12 and P20162-N18, the Austrian Academy of Sciences, the Spezialforschungsbereich “Numerical and Symbolic Scientific Computing” (SFB F013) , the doctoral program “Computational Mathematics” (W1214) and the FWF Start Project Y-192 on “3D hp-Finite Elements: Fast Solvers and Adaptivity”.

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Authors and Affiliations

  1. Institute for Numerical Simulation, University of Bonn, Wegelerstr. 6, 53115, Bonn, Germany

    Sven Beuchler

  2. Research Institute for Symbolic Computation, Johannes Kepler University Linz, 4040, Linz, Austria

    Veronika Pillwein

  3. Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstr. 8–10, 1040, Wien, Austria

    Joachim Schöberl

  4. Computer Simulation Technology, 64289, Darmstadt, Germany

    Sabine Zaglmayr

Authors
  1. Sven Beuchler
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  2. Veronika Pillwein
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  3. Joachim Schöberl
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  4. Sabine Zaglmayr
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Correspondence to Sven Beuchler .

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Editors and Affiliations

  1. Inst. Numerische Mathematik, Universität Linz, Altenbergerstr. 69, Linz, 4040, Austria

    Ulrich Langer

  2. , Research Institute for Symbolic Computat, Johannes Kepler University, Altenbergerstr. 69, Linz, 4040, Austria

    Peter Paule

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Beuchler, S., Pillwein, V., Schöberl, J., Zaglmayr, S. (2012). Sparsity Optimized High Order Finite Element Functions on Simplices. In: Langer, U., Paule, P. (eds) Numerical and Symbolic Scientific Computing. Texts & Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0794-2_2

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