Universität zu Köln

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387 and Lanser, Martin ORCID: 0000-0002-4232-9395 (2021). Adaptive Nonlinear Domain Decomposition Methods. Technical Report.

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Abstract

In this article, different nonlinear domain decomposition methods are applied to nonlinear problems with highly-heterogeneous coefficient functions with jumps. In order to obtain a robust solver with respect to nonlinear as well as linear convergence, adaptive coarse spaces are employed. First, as an example for a nonlinearly left-preconditioned domain decomposition method, the two-level restricted nonlinear Schwarz method H1-RASPEN (Hybrid Restricted Additive Schwarz Preconditioned Exact Newton) is combined with an adaptive generalized Dryja–Smith–Widlund (GDSW) coarse space. Second, as an example for a nonlinearly right-preconditioned domain decomposition method, a nonlinear FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) method is equipped with an edge-based adaptive coarse space. Both approaches are compared with the respective nonlinear domain decomposition methods with classical coarse spaces as well as with the respective Newton-Krylov methods with adaptive coarse spaces. For some two-dimensional p-Laplace model problems with different spatial coefficient distributions, it can be observed that the best linear and nonlinear convergence can only be obtained when combining the nonlinear domain decomposition methods with adaptive coarse spaces.

Item Type:	Preprints, Working Papers or Reports (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Heinlein, Alexander alexander.heinlein@uni-koeln.de orcid.org/0000-0003-1578-8104 UNSPECIFIED Klawonn, Axel axel.klawonn@uni-koeln.de orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin martin.lanser@uni-koeln.de orcid.org/0000-0002-4232-9395 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-525376
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2021,6
Date:	13 July 2021
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Natural sciences and mathematics Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language Nonlinear Domain Decomposition Methods English ASPIN English RASPEN English Nonlinear Schwarz Methods English FETI-DP English Nonlinear FETI-DP English Adaptive Coarse Spaces English AGDSW English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/52537