Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Wasiak, Adam ORCID: 0000-0002-5705-9754 (2022). Three-level BDDC for Virtual Elements. Technical Report.

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Abstract

The Virtual Element Method (VEM) is a discretization procedure for the solution of partial differential equations that allows for the use of nearly arbitrary polygonal/polyhedral grids. For the parallel scalable and iterative solution of large scale VE problems, the FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) and BDDC (Balancing Domain Decomposition by Constraints) domain decomposition methods have recently been applied. As for the case of finite element discretizations, a large global coarse problem that usually arises in large scale applications is a parallel scaling bottleneck of FETI-DP and BDDC. Nonetheless, the coarse problem/second level is usually necessary for the numerical robustness of the method. To alleviate this difficulty and to retain the scalability, the three-level BDDC method is applied to virtual element discretizations in this article. In this approach, to allow for a parallel solution of the coarse problem, the solution of it is only approximated by applying BDDC recursively, which automatically introduces a third level. Numerical results using several different configurations of the three-level approach and different polygonal meshes are presented and additionally compared with the classical two-level BDDC approach.

Item Type:	Monograph (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel axel.klawonn@uni-koeln.de https://orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin martin.lanser@uni-koeln.de https://orcid.org/0000-0002-4232-9395 UNSPECIFIED Wasiak, Adam adam.wasiak@uni-koeln.de https://orcid.org/0000-0002-5705-9754 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-641875
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2022-05
Number of Pages:	9
Date:	24 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 BDDC English Virtual Element Method English three-level BDDC English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/64187