A unified framework for double sweep methods for the Helmholtz equation

被引：0

作者：

Bouziani, Nacime ^{[1
]}

Nataf, Frederic ^{[2
,3
]}

Tournier, Pierre-Henri ^{[2
,3
]}

机构：

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

[2] Univ Paris 06, Lab JL Lions, 4 Pl Jussieu, F-75005 Paris, France

[3] ALPINES INRIA, Paris, France

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2023年 / 490卷

关键词：

Domain decomposition methods; Helmholtz problem; Wave propagation phenomena; High performance computing; OPTIMIZED SCHWARZ METHODS; DECOMPOSITION METHOD; BOUNDARY-CONDITIONS; POLARIZED TRACES; DOMAIN; PRECONDITIONER; ALGORITHM; LAYER;

D O I：

10.1016/j.jcp.2023.112305

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We consider sweeping domain decomposition preconditioners to solve the Helmholtz equation in the case of stripwise domain decomposition with or without overlaps. We unify their derivation and convergence studies by expressing them as Jacobi, Gauss-Seidel, and Symmetric Gauss-Seidel methods for different numbering of the unknowns. The proposed framework enables theoretical comparisons between the double sweep methods in [30,39] and those in [34,38,35]. Additionally, it facilitates the introduction of a new sweeping algorithm. We provide numerical test cases to assess the validity of the theoretical studies.

引用

页数：21

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