Common multi-frequency solution strategies for acoustic systems are either associated with high computational costs or resort to model reduction strategies, which potentially induce considerable approximation errors. In that context, this work proposes a fast multi-frequency solver for acoustic Boundary Element Method (BEM) analyses that combines conventional preconditioners with an accelerated recycling strategy, achieving in that way a fast and accurate iterative solution. Specifically, by approximating both the system and the related preconditioner by individual affine expressions, an upfront Galerkin projection on a global deflation basis is facilitated, therefore enabling the deployment of the accelerated recycling scheme. The latter acts by accelerating the construction of the related deflation projectors, therefore leading to a significantly faster recycling procedure. Finally, the efficiency of the global deflation basis is guaranteed through an Automatic Krylov subspaces Recycling for Deflation (AKR-D) [D. Panagiotopoulos, W. Desmet and E. Deckers, An accelerated subspaces recycling strategy for the deflation of parametric linear systems based on model order reduction, Comput. Methods Appl. Mech. Eng. 403 (2023) 115765] algorithm and thus, the cumulative number of iterations required by an iterative solver within a frequency sweep is drastically decreased. The proposed multi-frequency solver is tested on two industrially relevant examples of an interior and an exterior scattering problem, benchmarked against the traditional solution strategies.

声学系统的常见多频解决策略要么与高计算成本相关，要么采用模型简化策略，这可能会导致相当大的近似误差。在此背景下，这项工作提出了一种用于声学边界元法 (BEM) 分析的快速多频求解器，它将传统预处理器与加速回收策略相结合，从而实现快速、准确的迭代解决方案。具体来说，通过通过单独的仿射表达式来近似系统和相关的预处理器，有助于在全局通货紧缩的基础上进行预先伽辽金投影，从而能够部署加速回收方案。后者通过加速相关放气投影仪的构建来发挥作用，从而显着加快回收过程。最后，通过自动克雷洛夫子空间回收通货紧缩（AKR-D）[D. Panagiotopoulos、W. Desmet 和 E. Deckers，基于模型降阶的参数线性系统紧缩的加速子空间回收策略，Comput。方法应用 机甲。工程师。 403 (2023) 115765] 算法，因此，迭代求解器在频率扫描中所需的累积迭代次数大大减少。所提出的多频求解器在内部和外部散射问题的两个工业相关示例上进行了测试，并以传统解决方案策略为基准。