Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387 and Lanser, Martin ORCID: 0000-0002-4232-9395 (2022). Efficient Adaptive Elimination Strategies in Nonlinear FETI-DP Methods in Combination with Adaptive Spectral Coarse Spaces. Technical Report.

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Abstract

Nonlinear FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) is a nonlinear nonoverlapping domain decomposition method (DDM) which has a superior nonlinear convergence behavior compared with classical Newton-Krylov-DDMs - at least for many problems. Its fast and robust nonlinear convergence is strongly influenced by the choice of the second level or, in other words, the choice of the coarse constraints. Additionally, the convergence is also affected by the choice of an elimination set, that is, a set of degrees of freedom which are eliminated nonlinearly before linearization. In this article, an adaptive coarse space is combined with a problem-dependent and residual-based choice of the elimination set. An efficient implementation exploiting sparse local saddle point problems instead of an explicit transformation of basis is used. Unfortunately, this approach makes a further adaption of the elimination sets necessary, that is, edges and faces with coarse constraints have to be either included in the elimination set completely or not at all. Different strategies to fulfill this additional constraint are discussed and compared with a solely residual-based approach. The latter approach has to be implemented with an explicit transformation of basis. In general, the residual which is used to choose the elimination set has to be transformed to a space which basis functions explicitly contain the coarse constraints. This is computationally expensive. Here, for the first time, it is suggested to use an approximation of the transformed residual instead to compute the elimination set.

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 orcid.org/0000-0002-4232-9395 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-641880
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2022-06
Number of Pages:	10
Date:	25 November 2022
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Center for Data and Simulation Science
Subjects:	Natural sciences and mathematics Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language Nonlinear FETI-DP English nonlinear elimination English adaptive coarse spaces English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/64188