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A Nonlinear FETI-DP Method with an Inexact Coarse Problem

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Domain Decomposition Methods in Science and Engineering XXII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 104))

Abstract

A new nonlinear version of the well-known FETI-DP method (Finite Element Tearing and Interconnecting Dual-Primal) is introduced. In this method, the nonlinear problem is decomposed before linearization. Nonlinear approaches to domain decomposition can be viewed as a strategy to localize computational work for the efficient use with future extreme-scale supercomputers. As opposed to known nonlinear FETI-DP algorithms, in the new method the coarse solver can be replaced by a preconditioner, i.e., the coarse solve can be inexact. It is expected that the new method can show a superior parallel scalability if the number of subdomains is large. If the coarse solver is exact and the method is applied to linear problems then the method is equivalent to the standard FETI-DP method. Numerical results for up to 32,768 cores are presented using cycles of an algebraic multigrid for the coarse problem of the new method.

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Acknowledgement

The authors would like to thank Satish Balay and Barry Smith, Argonne National Laboratory (ANL), USA, for the fruitful cooperation and the assistance on running the authors’ code on the MIRA Supercomputer (BG/P) at ANL. This work was supported in part by the German Research Foundation (DFG) through the Priority Programme 1648 “Software for Exascale Computing” (SPPEXA). The authors acknowledge the use of the Cray XT6 computer at Universität Duisburg-Essen. The authors also gratefully acknowledge the SuperMUC Supercomputer at Leibniz-Rechenzentrum (www.lrz.de).

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Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Köln, Germany

    Axel Klawonn & Martin Lanser

  2. Fakultät für Mathematik und Informatik, Institut für Numerische Mathematik und Optimierung, TU Bergakademie Freiberg, Akademiestr. 6, 09599, Freiberg, Germany

    Oliver Rheinbach

Authors
  1. Axel Klawonn
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  2. Martin Lanser
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  3. Oliver Rheinbach
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Correspondence to Oliver Rheinbach .

Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Technische Universität München, Garching, Germany

    Thomas Dickopf

  2. Section de Mathématiques, Université de Genève, Genève, Switzerland

    Martin J. Gander

  3. Laboratoire Analyse, Geométrie & Applications, Université Paris XIII, Villetaneuse, France

    Laurence Halpern

  4. Institute of Computational Science, University of Lugano, Lugano, Switzerland

    Rolf Krause

  5. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Luca F. Pavarino

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Klawonn, A., Lanser, M., Rheinbach, O. (2016). A Nonlinear FETI-DP Method with an Inexact Coarse Problem. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_4

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