The fast multipole boundary element method for potential problems: A tutorial
The fast multipole boundary element method for potential problems: A tutorial
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DOI：
10.1016/j.enganabound.2005.11.006
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发表时间：
2006-05-01
影响因子：
3.3
通讯作者：
Nishimura, N.
中科院分区：
文献类型：
--
作者：
Liu, Y. J.;Nishimura, N.
快速多极子方法（FMM）被视为20世纪科学计算领域十大算法之一。边界元方法（BEM）与FMM相结合，如今能够在台式计算机上于数小时内解决具有数百万自由度的大规模问题。这为边界元方法开辟了广泛的应用领域，尽管边界元方法在建模阶段被认为是卓越的，但多年来因其求解过程缺乏效率而受到阻碍。然而，与传统边界元方法相比，理解快速多极边界元方法更加困难，因为快速多极子方法在公式表述和实现方面都增加了复杂性且采用了不同的方法。本文是对用于位势问题的快速多极边界元方法的介绍，旨在为熟悉传统边界元方法且希望学习和采用快速多极方法的人克服这一障碍。以二维位势问题为例，详细描述了用于求解边界积分方程的快速多极子方法的基本概念和主要步骤。给出了一个快速多极边界元程序的结构，并且还提供了源代码，这有助于开发用于解决其他问题的快速多极边界元代码。给出了数值算例，以进一步展示快速多极边界元方法在解决大规模问题时的效率、精度和潜力。（c）2006爱思唯尔有限公司。保留所有权利。
The fast multipole method (FMM) has been regarded as one of the top 10 algorithms in scientific computing that were developed in the 20th century. Combined with the FMM, the boundary element method (BEM) can now solve large-scale problems with several million degrees of freedom on a desktop computer within hours. This opened up a wide range of applications for the BEM that has been hindered for many years by the lack of efficiencies in the solution process, although it has been regarded as superb in the modeling stage. However, understanding the fast multipole BEM is even more difficult as compared with the conventional BEM, because of the added complexities and different approaches in both FMM formulations and implementations. This paper is an introduction to the fast multipole BEM for potential problems, which is aimed to overcome this hurdle for people who are familiar with the conventional BEM and want to learn and adopt the fast multipole approach. The basic concept and main procedures in the FMM for solving boundary integral equations are described in detail using the 2D potential problem as an example. The structure of a fast multipole BEM program is presented and the source code is also made available that can help the development of fast multipole BEM codes for solving other problems. Numerical examples are presented to further demonstrate the efficiency, accuracy and potentials of the fast multipole BEM for solving large-scale problems. (c) 2006 Elsevier Ltd. All rights reserved.