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Direct Schur complement method by domain decomposition based on H-matrix approximation

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Computing and Visualization in Science

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The goal of this paper is the construction of a data-sparse approximation to the Schur complement on the interface corresponding to FEM and BEM approximations of an elliptic equation by domain decomposition. Using the hierarchical (H-matrix) formats we elaborate the approximate Schur complement inverse in an explicit form. The required cost O (N Γlog q N Γ) is almost linear in N Γ – the number of degrees of freedom on the interface. As input, we require the Schur complement matrices corresponding to subdomains and represented in the H-matrix format. In the case of piecewise constant coefficients these matrices can be computed via the BEM representation with the cost O(N Γlog q N Γ), while in the general case the FEM discretisation leads to the complexity O(N Ωlog q N Ω), where N Ω is the number of degrees of freedom in the domain.

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Authors and Affiliations

  1. Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22–26, D-04103, Leipzig, Germany

    Wolfgang Hackbusch, Boris N. Khoromskij & Ronald Kriemann

Authors
  1. Wolfgang Hackbusch
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  2. Boris N. Khoromskij
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  3. Ronald Kriemann
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Additional information

Communicated by: U. Langer

Dedicated to George C. Hsiao on the occasion of his 70th birthday.

AMS Subject Classification: 65F30, 65F50, 65N35, 65F10

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Hackbusch, W., Khoromskij, B.N. & Kriemann, R. Direct Schur complement method by domain decomposition based on H-matrix approximation. Comput. Visual Sci. 8, 179–188 (2005). https://doi.org/10.1007/s00791-005-0008-3

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  • DOI: https://doi.org/10.1007/s00791-005-0008-3

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