Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Weber, Janine ORCID: 0000-0002-6692-2230 (2022). Learning Adaptive FETI-DP Constraints for Irregular Domain Decompositions. Technical Report.

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Abstract

Adaptive coarse spaces yield a robust convergence behavior for FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) and BDDC (Balancing Domain Decomposition by Constraints) methods for highly heterogeneous problems. However, the usage of such adaptive coarse spaces can be computationally expensive since, in general, it requires the setup and the solution of a relatively high amount of local eigenvalue problems on parts of the domain decomposition interface. In earlier works, see, e.g., [2], it has been shown that it is possible to train a neural network to make an automatic decision which of the eigenvalue problems in an adaptive FETI-DP method are actually necessary for robustness with a satisfactory accuracy. Moreover, these results have been extended in [6] by directly learning an approximation of the adaptive edge constraints themselves for regular, two-dimensional domain decompositions. In particular, this does not require the setup or the solution of any eigenvalue problems at all since the FETI-DP coarse space is, in this case, exclusively enhanced by the learned constraints obtained from the regression neural networks trained in an offline phase. Here, in contrast to [6], a regression neural network is trained with both, training data resulting from straight and irregular edges. Thus, it is possible to use the trained networks also for the approximation of adaptive constraints for irregular domain decompositions. Numerical results for a heterogeneous two-dimensional stationary diffusion problem are presented using both, a decomposition into regular and irregular subdomains.

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 Weber, Janine janine.weber@uni-koeln.de orcid.org/0000-0002-6692-2230 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-641226
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2022-03
Number of Pages:	10
Date:	14 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 machine learning English domain decomposition English FETI-DP English BDDC English adaptive coarse spaces English scientific machine learning English METIS English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/64122