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Domain Decomposition Methods in Science and Engineering XVI pp 357–364Cite as

Neumann-Neumann Algorithms (Two and Three Levels) for Finite Element Elliptic Problems with Discontinuous Coefficients on Fine Triangulation ki

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 55))

Abstract

We design and analyze Neumann-Neumann (N-N) algorithms for elliptic problems imposed in the 2-D polygonal region Ω with discontinuous coefficients on fine triangulation. We first discuss the two-level N-N algorithm and then we extend it to three levels.

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References

  1. M. Dryja and O. B. Widlund, Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems, Comm. Pure Appl. Math., 48 (1995), pp. 121–155.

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  2. J. Mandel and M. Brezina, Balancing domain decomposition for problems with large jumps in coeffcients, Math. Comp., 65 (1996), pp. 1387–1401.

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  3. B. F. Smith, P. E. Bjørstad, and W. Gropp, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, 1996.

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  4. A. Toselli and O. B. Widlund, Domain Decomposition Methods - Algorithms and Theory, vol. 34 of Series in Computational Mathematics, Springer, 2005.

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Author information

Authors and Affiliations

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

    Maksymilian Dryja

  2. Courant Institute of Mathematical Sciences, New York University, 252 Mercer Street, New York, NY 10012, USA

    Olof Widlund

Authors
  1. Maksymilian Dryja
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  2. Olof Widlund
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Editor information

Editors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012-1185, New York, NY, USA

    Olof B. Widlund

  2. Department of Applied Physics & Mathematics, Columbia University, 500 W. 120th Street, MC 4701, 10027, New York, NY, USA

    David E. Keyes

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Dryja, M., Widlund, O. (2007). Neumann-Neumann Algorithms (Two and Three Levels) for Finite Element Elliptic Problems with Discontinuous Coefficients on Fine Triangulation ki. In: Widlund, O.B., Keyes, D.E. (eds) Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34469-8_44

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