Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Uran, Matthias (2021). Adaptive Nonlinear Elimination in Nonlinear FETI-DP Methods. Technical Report.

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Abstract

Highly scalable and robust Newton-Krylov domain decomposition approaches are widely used for the solution of nonlinear implicit problems. In these methods, the nonlinear problem is first linearized and then decomposed into subdomains. By changing this order and first decomposing the nonlinear problem, many nonlinear domain decomposition methods have been designed in the last two decades. These methods often show a higher robustness compared to classical Newton-Krylov variants due to a better resolution of nonlinear effects. Additionally, the balance between local work, communication, and synchronization is usually more favorable for modern computer architectures. In all our nonlinear FETI-DP methods, we introduce a nonlinear right-preconditioner that can be interpreted as a (partial) nonlinear elimination of variables. The choice of the elimination set has a huge impact on the nonlinear convergence behavior. In order to design a nonlinear FETI-DP method that is tailored to arbitrary problems, we introduce a strategy, based on the residual of the nonlinear saddle point system, to adaptively choose sets of variables for the nonlinear elimination. The new strategy is applied to challenging distributions of nonlinearity in problems based on the p-Laplace operator. Promising numerical results are presented.

Item Type:	Preprints, Working Papers or Reports (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel axel.klawonn@uni-koeln.de orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin martin.lanser@uni-koeln.de UNSPECIFIED UNSPECIFIED Uran, Matthias m.uran@uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-377356
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2021,3
Date:	29 March 2021
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language domain decomposition methods English nonlinear domain decomposition English nonlinear FETI-DP methods English nonlinear elimination English adaptive elimination set English finite elements English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/37735