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Global Convergence Rates of Some Multilevel Methods for Variational and Quasi-Variational Inequalities Read chapter Read first chapter

2017 | OriginalPaper | Chapter

New Nonlinear FETI-DP Methods Based on a Partial Nonlinear Elimination of Variables

Authors : Axel Klawonn, Martin Lanser, Oliver Rheinbach, Matthias Uran

Published in: Domain Decomposition Methods in Science and Engineering XXIII

Publisher: Springer International Publishing

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Abstract

We introduce two new nonlinear FETI-DP (Finite Element Tearing and Interconnecting—Dual-Primal) methods based on a partial nonlinear elimination of variables and provide a comparison to Newton-Krylov-FETI-DP, Nonlinear-FETI-DP-1, and Nonlinear-FETI-DP-2, which have already been described earlier. In contrast to classical Newton-Krylov-FETI-DP methods, where a geometrical decomposition after a Newton linearization is performed, in nonlinear FETI-DP methods, the discretized nonlinear problem is decomposed before linearization. The approaches helps to localize work and reduce communication and thus are better suited for modern computer architectures.

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previous chapter Newton-Krylov-FETI-DP with Adaptive Coarse Spaces
next chapter Direct and Iterative Methods for Numerical Homogenization
Literature
C. Farhat, M. Lesoinne, P. LeTallec, K. Pierson, D. Rixen, FETI-DP: a dual-primal unified FETI method - part I: a faster alternative to the two-level FETI method. Int. J. Numer. Methods Eng. 50, 1523–1544 (2001)CrossRefMATH
G.A. Holzapfel, Nonlinear Solid Mechanics. A Continuum Approach for Engineering (Wiley, Chichester, 2000)
A. Klawonn, O. Rheinbach, Highly scalable parallel domain decomposition methods with an application to biomechanics. ZAMM Z. Angew. Math. Mech. 90 (1), 5–32 (2010)MathSciNetCrossRefMATH
A. Klawonn, M. Lanser, P. Radtke, O. Rheinbach, On an adaptive coarse space and on nonlinear domain decomposition, in Domain Decomposition Methods in Science and Engineering XXI, ed. by J. Erhel, M.J. Gander, L. Halpern, G. Pichot, T. Sassi, O.B. Widlund. Lecture Notes in Computational Science and Engineering, vol. 98 (Springer, Berlin, 2014a), pp. 71–83
A. Klawonn, M. Lanser, O. Rheinbach, Toward extremely scalable nonlinear domain decomposition methods for elliptic partial differential equations. SIAM J. Sci. Comput. 37 (6), C667–C696 (2015)MathSciNetCrossRefMATH
Metadata
Title
New Nonlinear FETI-DP Methods Based on a Partial Nonlinear Elimination of Variables
Authors
Axel Klawonn
Martin Lanser
Oliver Rheinbach
Matthias Uran
Copyright Year
2017
Book
Domain Decomposition Methods in Science and Engineering XXIII

Print ISBN: 978-3-319-52388-0

Electronic ISBN: 978-3-319-52389-7

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-52389-7_20

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