Hybrid Approximation Hierarchical Boundary Element Methods for Acoustic Problems

Q1 Mathematics

Journal of Computational Acoustics Pub Date : 2017-09-12 DOI:10.1142/S0218396X17500138

Xiujuan Liu, Haijun Wu, Weikang Jiang

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引用次数: 11

Abstract

A multipole expansion approximation boundary element method (MEA BEM) based on the hierarchical matrices (H-matrices) and the multipole expansion theory was proposed previously. Though the MEA BEM can obtain higher accuracy than the adaptive cross-approximation BEM (ACA BEM), it demands more CPU time and memory than the ACA BEM does. To alleviate this problem, in this paper, two hybrid BEMs are developed taking advantage of the high efficiency and low memory consumption property of the ACA BEM and the high accuracy advantage of the MEA BEM. Numerical examples are elaborately set up to compare the accuracy, efficiency and memory consumption of the ACA BEM, MEA BEM and hybrid methods. It is indicated that the hybrid BEMs can reach the same level of accuracy as the ACA BEM and MEA BEM. The efficiency of each hybrid BEM is higher than that of the MEA BEM but lower than that of the ACA BEM. The memory consumptions of the hybrid BEMs are larger than that of the ACA BEM but less than that of the MEA BEM. The algorithm used to approximate the far-field submatrices corresponding to the cells and their nearest interactional cells determines the accuracy, efficiency and memory consumption of the hybrid BEMs. The proposed hybrid BEMs have both operation and storage logarithmic-linear complexity. They are feasible.

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声学问题的混合逼近层次边界元方法

先前提出了一种基于层次矩阵(h矩阵)和多极展开理论的多极展开近似边界元方法。虽然MEA BEM可以获得比自适应交叉逼近BEM (ACA BEM)更高的精度，但它比ACA BEM占用更多的CPU时间和内存。为了解决这一问题，本文利用ACA边界元的高效率、低内存消耗的特性和MEA边界元的高精度优势，开发了两种混合边界元。通过数值算例比较了ACA边界元法、MEA边界元法和混合边界元法的精度、效率和内存消耗。结果表明，混合边界元可以达到与ACA边界元和MEA边界元相同的精度水平。每种混合BEM的效率都高于MEA BEM，但低于ACA BEM。混合BEM的内存消耗比ACA BEM大，但比MEA BEM小。单元及其最近的相互作用单元所对应的远场子矩阵的近似算法决定了混合bem的精度、效率和内存消耗。所提出的混合bem具有操作和存储的对数线性复杂度。它们是可行的。

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.