A Multilevel Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions

Journal article (2023)

Authors

A. Heinlein Numerical Analysis - EEMCS
Oliver Rheinbach University of Technology Bergakademie Freiberg
Friederike Röver University of Technology Bergakademie Freiberg
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2023 A. Heinlein, Oliver Rheinbach, Friederike Röver
DOI: https://doi.org/10.1515/cmam-2022-0168
Domain Decomposition Multilevel Overlapping Schwarz Methods Parallel Implicit Solvers
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Published Date

2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

Multilevel extensions of overlapping Schwarz domain decomposition preconditioners of Generalized Dryja-Smith-Widlund (GDSW) type are considered in this paper. The original GDSW preconditioner is a two-level overlapping Schwarz domain decomposition preconditioner, which can be constructed algebraically from the fully assembled stiffness matrix. The FROSch software, which belongs to the ShyLU package of the Trilinos software library, provides parallel implementations of different variants of GDSW preconditioners. The coarse problem can limit the parallel scalability of two-level GDSW preconditioners. As a remedy, in the past, three-level GDSW approaches have been proposed, which can significantly extend the range of scalability. Here, a multilevel extension of the GDSW preconditioner is introduced and analyzed. Finally, parallel results for the implementation in FROSch for up to 40 000 cores of the SuperMUC-NG supercomputer at Leibniz Supercomputing Centre (LRZ) and to 48 000 cores of the JUWELS supercomputer at Jülich Supercomputing Centre (JSC) are presented.