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.
PDF
CDS_TR-2022-05.pdf Download (873kB) |
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: | Preprints, Working Papers or Reports (Technical Report) | ||||||||||||||||
Creators: |
|
||||||||||||||||
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: |
|
||||||||||||||||
Refereed: | No | ||||||||||||||||
URI: | http://kups.ub.uni-koeln.de/id/eprint/64187 |
Downloads
Downloads per month over past year
Export
Actions (login required)
View Item |