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A domain decomposition discretization of parabolic problems

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Abstract

In recent years, domain decomposition methods have attracted much attention due to their successful application to many elliptic and parabolic problems. Domain decomposition methods treat problems based on a domain substructuring, which is attractive for parallel computation, due to the independence among the subdomains. In principle, domain decomposition methods may be applied to the system resulting from a standard discretization of the parabolic problems or, directly, be carried out through a discretization of parabolic problems. In this paper, a direct domain decomposition method is introduced to discretize the parabolic problems. The stability and convergence of this algorithm are analyzed.

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Authors and Affiliations

  1. Department of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Maksymilian Dryja

  2. Department of Mathematics, University of California, and Lawrence Berkeley National Laboratory, Berkeley, CA, 94720-3840, USA

    Xuemin Tu

Authors
  1. Maksymilian Dryja
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  2. Xuemin Tu
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Corresponding author

Correspondence to Maksymilian Dryja.

Additional information

This work was supported in part by Polish Sciences Foundation under grant 2P03A00524.

This work was supported in part by the US Department of Energy under Contracts DE-FG02-92ER25127 and by the Director, Office of Science, Advanced Scientific Computing Research, U.S. Department of Energy under contract DE-AC02-05CH11231.

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Dryja, M., Tu, X. A domain decomposition discretization of parabolic problems. Numer. Math. 107, 625–640 (2007). https://doi.org/10.1007/s00211-007-0103-0

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  • DOI: https://doi.org/10.1007/s00211-007-0103-0

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