A Three-Level Extension for Fast and Robust Overlapping Schwarz (FROSch) Preconditioners with Reduced Dimensional Coarse Space

Heinlein, Alexander; Klawonn, Axel; Rheinbach, Oliver; Röver, Friederike

doi:10.1007/978-3-030-95025-5_54

Cited by 1 publication

(3 citation statements)

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“…The results for the weak parallel scalability study show that both the two-and three-level methods show a comparable performance for the problem parameters and the number of cores considered here. For a larger number of cores, we expect the three-level method to outperform the two-level method as in [16,22].…”

Section: Two-level Gdswmentioning

confidence: 99%

“…The FROSch framework has shown good weak parallel scalability employing three levels for the Laplace and linear elasticity model problem [16,18,19,22] up to the order of 100 000 subdomains and cores. Here, we show new weak parallel scalability results in two dimensions, applying the most recent parallel implementation of the three-level method in FROSch.…”

Section: Weak Parallel Scalability Studymentioning

confidence: 99%

“…The partitioning of the coarse problem by Zoltan2 is the default procedure for the multilevel extensions in FROSch as described in [22]. For linear elasticity, good parallel scalability results have been obtained using PHG in [16,22]. In all tests, we have 200 2 nodes on each subdomain; thus the largest problem is of size 1 600 000 000 degrees of freedom.…”

Section: Weak Parallel Scalability Studymentioning

confidence: 99%

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

Heinlein

Rheinbach

Röver

2023

Computational Methods in Applied Mathematics

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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.

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Section: Two-level Gdswmentioning

confidence: 99%