Adaptive Three-level BDDC Using Frugal Constraints - Kölner UniversitätsPublikationsServer

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Weber, Janine ORCID: 0000-0002-6692-2230 (2022). Adaptive Three-level BDDC Using Frugal Constraints. Technical Report. Open Access

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Abstract

The highly parallel scalable three-level BDDC (Balancing Domain Decomposition by Constraints) method is a very successful approach to overcome the scaling bottleneck of directly solving a large coarse problem in classical two-level BDDC. As long as the problem is homogeneous on each subregion, three-level BDDC is also provably robust in many cases. For problems with complex microstructures, as, e.g., stationary diffusion problems with jumps in the diffusion coefficient function, in two-level BDDC methods, advanced adaptive or frugal coarse spaces have to be considered to obtain a robust preconditioner. Unfortunately, these approaches result in even larger coarse problems on the second level and, additionally, computing adaptive coarse constraints is computationally expensive. Therefore, in this article, the three-level approach is combined with a provably robust adaptive coarse space and the computationally cheaper frugal coarse space. Both coarse spaces are used on the second as well as the third level. All different possible combinations are investigated numerically for stationary diffusion problems with highly varying coefficient functions.

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