Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395, Rheinbach, Oliver ORCID: 0000-0002-9310-8533 and Uran, Matthias (2017). NONLINEAR FETI-DP AND BDDC METHODS: A UNIFIED FRAMEWORK AND PARALLEL RESULTS. SIAM J. Sci. Comput., 39 (6). S. C417 - 35. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

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Abstract

Parallel Newton-Krylov FETI-DP (Finite Element Tearing and Interconnecting-Dual-Primal) domain decomposition methods are fast and robust solvers, e.g., for nonlinear implicit problems in structural mechanics. In these methods, the nonlinear problem is first linearized and then decomposed into loosely coupled (linear) problems, which can be solved in parallel. By changing the order of the operations, new parallel communication can be constructed, where the loosely coupled local problems are nonlinear. We discuss different nonlinear FETI-DP methods which are equivalent when applied to linear problems but which show a different performance for nonlinear problems. Moreover, a new unified framework is introduced which casts all nonlinear FETI-DP domain decomposition approaches discussed in the literature into a single algorithm. Furthermore, the equivalence of nonlinear FETI-DP methods to specific nonlinearly right-preconditioned Newton-Krylov methods is shown. For the methods using nested Newton iterations, a strategy is presented to stop the inner Newton iteration early, resulting in an approximate local nonlinear elimination. Additionally, the nonlinear BDDC (Balancing Domain Decomposition by Constraint) method is presented as a right-preconditioned Newton approach. Finally, for the first time, parallel weak scaling results for four different nonlinear FETI-DP approaches are compared to standard Newton-Krylov FETI-DP in two and three dimensions, using both exact as well as highly scalable inexact linear FETI-DP preconditioners and up to 131 072 message passing interface (MPI) ranks on the JUQUEEN supercomputer at Forschungszentrum Julich. For a model problem with nonlocal nonlinearities, nonlinear FETI-DP methods are shown to be up to five times faster than the standard Newton-Krylov FETI-DP approach.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel UNSPECIFIED orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin UNSPECIFIED orcid.org/0000-0002-4232-9395 UNSPECIFIED Rheinbach, Oliver UNSPECIFIED orcid.org/0000-0002-9310-8533 UNSPECIFIED Uran, Matthias UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-244668
DOI:	10.1137/16M1102495
Journal or Publication Title:	SIAM J. Sci. Comput.
Volume:	39
Number:	6
Page Range:	S. C417 - 35
Date:	2017
Publisher:	SIAM PUBLICATIONS
Place of Publication:	PHILADELPHIA
ISSN:	1095-7197
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language BALANCING DOMAIN DECOMPOSITION; PRECONDITIONERS; CONVERGENCE; ELIMINATION Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/24466