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On the performance of the algebraic optimized Schwarz methods with applications

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Abstract

We investigate the performance of algebraic optimized Schwarz methods used as preconditioners for the solution of discretized differential equations. These methods consist on modifying the so-called transmission blocks. The transmission blocks are replaced by new blocks in order to improve the convergence of the corresponding iterative algorithms. In the optimal case, convergence in two iterations can be achieved. We are also interested in the behavior of the algebraic optimized Schwarz methods with respect to changes in the problems parameters. We focus on constructing preconditioners for different numerically challenging differential problems such as: Periodic and Torus problems; Meshfree problems; Three-dimensional problems. We present different numerical simulations corresponding to different type of problems in two- and three-dimensions.

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Authors and Affiliations

  1. School of Science and Engineering, Al Akhawayn University, Avenue Hassan II, 53000, P.O. Box 1630, Ifrane, Morocco

    Lahcen Laayouni

  2. Department of Mathematics (038-16), Temple University, 1805 N Broad Street, Philadelphia, PA, 19122-6094, USA

    Daniel B. Szyld

Authors
  1. Lahcen Laayouni
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  2. Daniel B. Szyld
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Correspondence to Daniel B. Szyld.

Additional information

Part of this research was performed during a visit of the first author to Temple University which was supported by a Fulbright fellowship. The second author was supported in part by the U.S. Department of Energy under grant DE-FG02-05ER25672 and the U.S. National Science Foundation under grant DMS-1115520.

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Laayouni, L., Szyld, D.B. On the performance of the algebraic optimized Schwarz methods with applications. Numer Algor 67, 889–916 (2014). https://doi.org/10.1007/s11075-014-9831-2

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  • DOI: https://doi.org/10.1007/s11075-014-9831-2

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