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Efficient analysis of sound propagation in sonic crystals using an ACA-MFS approach

机译：使用ACA-MFS方法对声晶体中的声音传播进行有效分析

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摘要

Sonic crystals have been analysed making use of a variety of strategies, such as those based in the multiple-scattering theory (MST) or in the Finite Element Method (FEM). Recently, some works have proposed the use of the Method of Fundamental Solutions (MFS) and of the Boundary Element Method (BEM). However, considering these numerical techniques, the associated memory requirements and CPU times are usually prohibitive when problems with a large number of scatterers are considered, particularly when 3D problems are addressed. A new strategy for the solution of 3D configurations of sonic crystals is proposed here, based on the use of the MFS (formulated in the frequency domain), considering a 2.5D approach to describe the 3D model. The sound field is synthesised as a summation of much simpler 2D problems, drastically reducing the memory requirements and computational effort of the analysis. To allow the solution of very large-scale problems, with a great amount of scatterers, an Adaptive-Cross-Approximation (ACA) approach is incorporated into the MFS algorithm, rendering faster calculations and significant savings in terms of computational requirements. Examples are presented illustrating the good performance of the proposed methodology and its capacity to properly handle complex large-scale models.
机译：已经使用多种策略对声波晶体进行了分析，例如基于多重散射理论（MST）或有限元方法（FEM）的那些。最近，一些工作提出了使用基本解法（MFS）和边界元法（BEM）的建议。但是，考虑到这些数值技术，当考虑到具有大量散射体的问题时，尤其是在解决3D问题时，相关的内存要求和CPU时间通常是禁止的。考虑到使用2.5D方法描述3D模型，在此基于MFS（在频域中制定）的基础上，提出了一种解决声波晶体3D构造的新策略。声场被合成为许多更简单的2D问题的总和，从而大大降低了内存需求和分析的计算量。为了解决带有大量散射体的非常大规模的问题，MFS算法中采用了自适应交叉近似（ACA）方法，可加快计算速度并显着节省计算需求。给出的示例说明了所提出方法的良好性能及其正确处理复杂大规模模型的能力。

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