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Low-Rank Iteration Schemes for the Multi-Frequency Solution of Acoustic Boundary Element Equations
Journal of Theoretical and Computational Acoustics ( IF 1.9 ) Pub Date : 2021-05-08 , DOI: 10.1142/s2591728521500043
Suhaib Koji Baydoun 1 , Steffen Marburg 1 , Matthias Voigt 2, 3
Affiliation  

The implicit frequency dependence of linear systems arising from the acoustic boundary element method necessitates an efficient treatment for problems in a frequency range. Instead of solving the linear systems independently at each frequency point, this paper is concerned with solving them simultaneously at multiple frequency points within a single iteration scheme. The proposed concept is based on truncation of the frequency range solution and is incorporated into two well-known iterative solvers - BiCGstab and GMRes. The proposed method is applied to two acoustic interior problems as well as to an exterior problem in order to assess the underlying approximations and to study the convergence behavior. While this paper provides the proof of concept, its application to large-scale acoustic problems necessitates efficient preconditioning for multi-frequency systems, which are yet to be developed.

中文翻译:

声边界元方程多频解的低秩迭代方案

由声学边界元法引起的线性系统的隐含频率依赖性需要对频率范围内的问题进行有效处理。本文不是在每个频率点独立求解线性系统,而是在单个迭代方案中在多个频率点同时求解它们。所提出的概念基于频率范围解的截断,并被纳入两个著名的迭代求解器——BiCGstab 和 GMRes。所提出的方法适用于两个声学内部问题以及一个外部问题,以评估潜在的近似值并研究收敛行为。虽然本文提供了概念证明,
更新日期:2021-05-08
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