A DOMAIN DECOMPOSITION SOLVER FOR LARGE SCALE TIME-HARMONIC FLOW ACOUSTICS PROBLEMS

absorbing boundary conditions; domain decomposition; high frequency problems; high-performance computing; optimized Schwarz method; Pierce operator; Absorbing boundary condition; Acoustic problems; Domain decompositions; Flow acoustics; High frequency problems; High-performance computing; Optimized Schwarz methods; Performance computing; Time-harmonic; Computational Mathematics; Applied Mathematics

Abstract :

[en] This article is devoted to the numerical resolution of high frequency time-harmonic flow acoustic problems. We use a substructured optimized nonoverlapping Schwarz domain decomposition method as a solver in order to significantly reduce the memory footprint required by such problems. To accelerate the convergence of the iterative solver we develop suitable transmission conditions based on local approximations of the Dirichlet-to-Neumann operator, taking into account convection by strongly nonuniform mean flows. The development relies on the construction of absorbing boundary conditions through microlocal analysis and pseudodifferential calculus. We analyze the potential of the method in academic settings and subsequently propose a robust domain decomposition methodology for problems of industrial relevance modeled by the Pierce linearized acoustic operator. The algorithm is implemented in an open-source high-order finite element library. It allows solving challenging three-dimensional problems with more than one billion high-order unknowns, by taking full advantage of modern computer architectures.

Disciplines :

Mathematics
Computer science

Author, co-author :

Marchner, P. ; Siemens Industry Software SAS, Châtillon, France

Bériot, H. ; Siemens Industry Software SAS, Châtillon, France

Bras, S. Le; Siemens Industry Software SAS, Châtillon, France

Antoine, X. ; Université de Lorraine, CNRS, Inria, IECL, Nancy, France

Geuzaine, Christophe ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE)

Language :

English

Title :

A DOMAIN DECOMPOSITION SOLVER FOR LARGE SCALE TIME-HARMONIC FLOW ACOUSTICS PROBLEMS

Publication date :

2025

Journal title :

SIAM Journal on Scientific Computing

ISSN :

1064-8275

eISSN :

1095-7197

Publisher :

Society for Industrial and Applied Mathematics Publications

Volume :

Issue :

Pages :

B333 - B359

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

ANRT - Association Nationale de la Recherche et de la Technologie
Siemens
FWB - Wallonia-Brussels Federation

Funding text :

This work was performed as part of the CIFRE contract 2018/1845 funded by Siemens Industry Software SAS and Association Nationale de la Recherche et de la Technologie (ANRT). This research was also funded in part through the ARC grant for Concerted Research Actions (ARC WAVES 15/19-03), financed by the Wallonia-Brussels Federation of Belgium. The authors would like to thank the anonymous reviewers for their critical examination of the manuscript and their insightful comments. Computational resources have been provided by the Consortium des \u00C9quipements de Calcul Intensif (C\u00C9CI). The present research benefited from computational resources made available on Lucia, the Tier-1 supercomputer of the Walloon Region. We acknowledge LUMI-BE for awarding this project access to the LUMI supercomputer, owned by the EuroHPC Joint Undertaking, hosted by CSC (Finland) and the LUMI consortium through a LUMI-BE Regular Access call. LUMI-BE is a joint effort by BELSPO (federal), SPW \u00C9conomie Emploi Recherche (Wallonia), Department of Economy, Science & Innovation (Flanders), and Innoviris (Brussels). This project was provided with computer and storage resources by GENCI at IDRIS, on the supercomputer Jean Zay. The authors would like to thank Dr. J\u00E9r\u00E9mie Gaidamour for his useful guidance and help on the supercomputer Jean Zay.

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since 04 June 2025

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