An Efficient MFS Formulation for the Analysis of Acoustic Scattering by Periodic Structures

Q1 Mathematics Journal of Computational Acoustics Pub Date : 2017-09-04 DOI:10.1142/S0218396X18500030

L. Godinho, P. Amado-Mendes, A. Pereira, D. Soares

引用次数: 7

Abstract

The acoustic behavior of periodic structures has been a subject of intense study in recent years. From the computational point of view, these devices have mostly been analyzed using strategies such as the multiple scattering theory (MST) or numerical methods such as the finite element method (FEM). Some recent works propose the use of boundary methods, such as the method of fundamental solutions (MFS) or the boundary element method (BEM). However, the geometry and the large number of scatterers of these devices can lead to very large memory requirements and CPU times, which, particularly in the case of 3D problems, can be prohibitive. Here, a new numerical approach based on a frequency domain MFS formulation is proposed for 3D problems, allowing the analysis of very large problems. In this approach, the periodic character of the devices is used to define a matrix with a block structure, in which repeated blocks are only calculated once. In addition, an adaptive-cross-approximation (ACA) approach is incorp...

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一种用于周期结构声散射分析的有效MFS公式

近年来，周期结构的声学行为一直是一个研究热点。从计算的角度来看，这些器件大多是使用诸如多重散射理论（MST）的策略或诸如有限元法（FEM）的数值方法来分析的。最近的一些工作提出了使用边界方法，如基本解法（MFS）或边界元法（BEM）。然而，这些设备的几何形状和大量散射体可能会导致非常大的内存需求和CPU时间，特别是在3D问题的情况下，这可能会令人望而却步。这里，针对三维问题，提出了一种基于频域MFS公式的新的数值方法，允许分析非常大的问题。在这种方法中，设备的周期性特征用于定义具有块结构的矩阵，其中重复块只计算一次。此外，还提出了一种自适应交叉逼近（ACA）方法。。。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Acoustics 物理-声学

CiteScore

3.90

自引率

0.00%

发文量

审稿时长

4.5 months

期刊介绍： Currently known as Journal of Theoretical and Computational Acoustics (JTCA).The aim of this journal is to provide an international forum for the dissemination of the state-of-the-art information in the field of Computational Acoustics. Topics covered by this journal include research and tutorial contributions in OCEAN ACOUSTICS (a subject of active research in relation with sonar detection and the design of noiseless ships), SEISMO-ACOUSTICS (of concern to earthquake science and engineering, and also to those doing underground prospection like searching for petroleum), AEROACOUSTICS (which includes the analysis of noise created by aircraft), COMPUTATIONAL METHODS, and SUPERCOMPUTING. In addition to the traditional issues and problems in computational methods, the journal also considers theoretical research acoustics papers which lead to large-scale scientific computations. The journal strives to be flexible in the type of high quality papers it publishes and their format. Equally desirable are Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational acoustics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research in which other than strictly computational arguments may be important in establishing a basis for further developments. Tutorial review papers, covering some of the important issues in Computational Mathematical Methods, Scientific Computing, and their applications. Short notes, which present specific new results and techniques in a brief communication. The journal will occasionally publish significant contributions which are larger than the usual format for regular papers. Special issues which report results of high quality workshops in related areas and monographs of significant contributions in the Series of Computational Acoustics will also be published.