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All-floating coupled data-sparse boundary and interface-concentrated finite element tearing and interconnecting methods

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Computing and Visualization in Science

Abstract

Efficient and robust tearing and interconnecting solvers for large scale systems of coupled boundary and finite element domain decomposition equations are the main topic of this paper. In order to reduce the complexity of the finite element part from \({\mathcal{O}}((H/h)^{d})\) to \({\mathcal{O}}((H/h)^{d-1})\) , we use an interface-concentrated hp finite element approximation. The complexity of the boundary element part is reduced by data-sparse approximations of the boundary element matrices. Finally, we arrive at a parallel solver whose complexity behaves like \({\mathcal{O}}((H/h)^{d-1})\) up to some polylogarithmic factor, where H, h, and d denote the usual scaling parameters of the subdomains, the minimal discretization parameter of the subdomain boundaries, and the spatial dimension, respectively.

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Authors and Affiliations

  1. Institute of Computational Mathematics, Johannes Kepler University Linz, 4040, Linz, Austria

    Ulrich Langer

  2. SFB F013, Johannes Kepler University Linz, 4040, Linz, Austria

    Ulrich Langer & Clemens Pechstein

Authors
  1. Ulrich Langer
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  2. Clemens Pechstein
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Correspondence to Ulrich Langer.

Additional information

Communicated by G. Wittum.

Dedicated to Wolfgang Hackbusch on the occasion of his 60th birthday.

Ulrich Langer has been supported in parts by the Austrian Science Fund (FWF) under the grant P19255; Clemens Pechstein was supported by the Austrian Science Fund (FWF) under the grant SFB F1306.

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Langer, U., Pechstein, C. All-floating coupled data-sparse boundary and interface-concentrated finite element tearing and interconnecting methods. Comput. Visual Sci. 11, 307–317 (2008). https://doi.org/10.1007/s00791-008-0100-6

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