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.

Xiujuan Liu

Haijun Wu

Weikang Jiang

Journal of Computational Acoustics

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.

The Journal of Computational Acoustics, currently known as the Journal of Theoretical and Computational Acoustics (JTCA), aims to provide an international forum for the dissemination of cutting-edge 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 related to sonar detection and the design of noiseless ships), SEISMO-ACOUSTICS (pertinent to earthquake science and engineering, as well as underground prospection such as petroleum searching), AEROACOUSTICS (which involves the analysis of noise generated by aircraft), COMPUTATIONAL METHODS, and SUPERCOMPUTING. In addition to traditional issues and problems in computational methods, the journal also considers theoretical research papers in acoustics that lead to large-scale scientific computations. The journal strives to be flexible in the types and formats of high-quality papers it publishes. We welcome full papers that are complete and relatively self-contained original contributions, with introductions that can be understood by the broader computational acoustics community. Both rigorous and heuristic writing styles are acceptable. Of particular interest are papers addressing new areas of research where arguments beyond strictly computational ones may be significant in establishing a foundation for further developments. Tutorial review papers covering important issues in Computational Mathematical Methods, Scientific Computing, and their applications are also desirable. Short notes presenting specific new results and techniques in brief communications will be accepted. The journal will occasionally publish significant contributions that exceed the usual format for regular papers. Special issues reporting results from high-quality workshops in related areas and monographs of significant contributions in the Series of Computational Acoustics will also be published.

《Journal of Computational Acoustics》目前被称为《Journal of Theoretical and Computational Acoustics (JTCA)》。该期刊旨在为计算声学领域的最新研究成果提供一个国际交流平台。期刊涵盖的主题包括海洋声学（与声纳探测和无声船设计相关的活跃研究领域）、地震声学（与地震科学和工程相关，以及地下勘探如石油搜索）、气动声学（包括飞机噪声分析）、计算方法和超级计算等。除了传统的计算方法问题外，期刊还考虑那些能够促进大规模科学计算的理论声学研究论文。期刊力求在发表高质量论文的类型和格式上保持灵活性。我们欢迎完整且相对自成体系的原创论文，其引言应能被广泛的计算声学社区理解。无论是严谨的还是启发式的写作风格都是可接受的。特别感兴趣的是那些涉及新研究领域的论文，其中除了严格的计算论据外，其他论据可能在进一步发展的基础上也很重要。我们还欢迎关于计算数学方法、科学计算及其应用的重要问题的教程评述论文。简短的笔记也会被接受，旨在简要传达具体的新结果和技术。期刊偶尔会发表超出常规论文格式的重大贡献。还将出版与相关领域高质量研讨会结果相关的特刊以及计算声学系列中的重要贡献专著。

Hybrid Approximation Hierarchical Boundary Element Methods for Acoustic Problems

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