Multidirectional sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems

Acoustic; Domain decomposition methods; Helmholtz equation; High-order finite element method; Iterative solvers; Preconditioners; Computational domains; Domain decomposition procedure; Domain decompositions; Domain-decomposition methods; Helmholtz problems; Helmholtz's equations; Higher-order finite element methods; Numerical Analysis; Modeling and Simulation; Physics and Astronomy (miscellaneous); Physics and Astronomy (all); Computer Science Applications; Computational Mathematics; Applied Mathematics; Mathematics - Numerical Analysis; Computer Science - Numerical Analysis

Abstract :

[en] This paper explores a family of generalized sweeping preconditioners for Helmholtz problems with non-overlapping checkerboard partition of the computational domain. The domain decomposition procedure relies on high-order transmission conditions and cross-point treatments, which cannot scale without an efficient preconditioning technique when the number of subdomains increases. With the proposed approach, existing sweeping preconditioners, such as the symmetric Gauss-Seidel and parallel double sweep preconditioners, can be applied to checkerboard partitions with different sweeping directions (e.g. horizontal and diagonal). Several directions can be combined thanks to the flexible version of GMRES, allowing for the rapid transfer of information in the different zones of the computational domain, then accelerating the convergence of the final iterative solution procedure. Several two-dimensional finite element results are proposed to study and to compare the sweeping preconditioners, and to illustrate the performance on cases of increasing complexity.

Disciplines :

Mathematics
Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Dai, Ruiyang ; IMMC, Université catholique de Louvain, Louvain-la-Neuve, Belgium ; Université de Liège, Institut Montefiore B28, Liège, Belgium

Modave, Axel ; POEMS, CNRS, Inria, ENSTA Paris, Institut Polytechnique de Paris, Palaiseau, France

Remacle, Jean-François; IMMC, Université catholique de Louvain, Louvain-la-Neuve, Belgium

Geuzaine, Christophe ; Université de Liège - ULiège > Montefiore Institute of Electrical Engineering and Computer Science

Language :

English

Title :

Multidirectional sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems

Publication date :

15 March 2022

Journal title :

Journal of Computational Physics

ISSN :

0021-9991

eISSN :

1090-2716

Publisher :

Academic Press Inc.

Volume :

453

Pages :

110887

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0021999121007828?httpAccept=text/xml

Funding text :

This work was funded in part by the Communauté Française de Belgique under contract ARC WAVES 15/19-03 (“Large Scale Simulation of Waves in Complex Media”) and by the F.R.S.-FNRS under grant PDR 26104939 (“Fast Helmholtz Solvers on GPUs”).This work was funded in part by the Communaut? Fran?aise de Belgique under contract ARC WAVES 15/19-03 (?Large Scale Simulation of Waves in Complex Media?) and by the F.R.S.-FNRS under grant PDR 26104939 (?Fast Helmholtz Solvers on GPUs?).

Available on ORBi :

since 25 June 2022

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