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

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-07-12 DOI:10.1515/cmam-2022-0168

Alexander Heinlein, O. Rheinbach, F. Röver

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引用次数: 0

Abstract

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.

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二维GDSW重叠Schwarz预条件的多级推广

摘要本文考虑了广义Dryja–Smith–Widlund（GDSW）型重叠Schwarz域分解预条件子的多级扩张。最初的GDSW预处理器是一个两级重叠的Schwarz域分解预处理器，它可以由完全组装的刚度矩阵代数构造。FROSch软件属于Trilinos软件库的ShyLU包，它提供了GDSW预处理器不同变体的并行实现。粗糙问题会限制两级GDSW预处理器的并行可扩展性。作为补救措施，过去曾提出过三级GDSW方法，它可以显著扩展可扩展性的范围。本文介绍并分析了GDSW预处理器的多级扩展。最后，在FROSch中实现多达40个并行结果 000核的超级MUC NG超级计算机，以及48 000核的JUWELS超级计算机。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.