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Convergence analysis of geometrical multigrid methods for solving data-sparse boundary element equations

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Computing and Visualization in Science

Abstract

The convergence analysis of multigrid methods for boundary element equations arising from negative-order pseudo-differential operators is quite different from the usual finite element multigrid analysis for elliptic partial differential equations. In this paper, we study the convergence of geometrical multigrid methods for solving large-scale, data-sparse boundary element equations. In particular, we investigate multigrid methods for \(\mathcal{H}\)-matrices arising from the adaptive cross approximation to the single layer potential operator.

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Authors and Affiliations

  1. Institute of Computational Mathematics, Johannes Kepler University Linz, Altenbergerstr. 69, A-4040, Linz, Austria

    Ulrich Langer

  2. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Science, Altenbergerstr. 69, A-4040, Linz, Austria

    Ulrich Langer & David Pusch

Authors
  1. Ulrich Langer
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  2. David Pusch
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Correspondence to Ulrich Langer.

Additional information

Communicated by P. Hemker.

This work has been supported by the Austrian Science Fund ‘Fonds zur Förderung der wissenschaftlichen Forschung (FWF)’ under the grant P14953 “Robust Algebraic Multigrid Methods and their Parallelization”.

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Langer, U., Pusch, D. Convergence analysis of geometrical multigrid methods for solving data-sparse boundary element equations. Comput. Visual Sci. 11, 181–189 (2008). https://doi.org/10.1007/s00791-007-0067-8

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