The hybrid boundary node method accelerated by fast multipole expansion technique for 3D potential problems
The hybrid boundary node method accelerated by fast multipole expansion technique for 3D potential problems
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DOI：
10.1002/nme.1292
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发表时间：
2005-06
影响因子：
2.9
通讯作者：
Jianming Zhang;Masataka Tanaka;M. Endo
中科院分区：
文献类型：
--
作者：
Jianming Zhang;Masataka Tanaka;M. Endo
本文提出了一种用于求解三维拉普拉斯方程所支配问题的混合边界节点法（Hybrid BNM）的快速公式。采用预条件广义最小残差法（GMRES）来求解所得的方程组。在GMRES的每次迭代步骤中，通过快速多极子方法加速矩阵 - 向量乘法。格林核函数以球谐级数展开。使用八叉树数据结构将计算域分层细分为充分分离的单元，并调用多极展开近似。给出了局部展开和多极展开的公式，以及多极到局部展开的转换。并且应用二叉树数据结构来加速表面上的移动最小二乘近似。所有公式都在一个用C++编写的计算机代码中实现。数值例子证明了所提出方法的准确性和效率。版权所有©2005约翰威立父子有限公司
This paper presents a fast formulation of the hybrid boundary node method (Hybrid BNM) for solving problems governed by Laplace's equation in 3D. The preconditioned GMRES is employed for solving the resulting system of equations. At each iteration step of the GMRES, the matrix–vector multiplication is accelerated by the fast multipole method. Green's kernel function is expanded in terms of spherical harmonic series. An oct‐tree data structure is used to hierarchically subdivide the computational domain into well‐separated cells and to invoke the multipole expansion approximation. Formulations for the local and multipole expansions, and also conversion of multipole to local expansion are given. And a binary tree data structure is applied to accelerate the moving least square approximation on surfaces. All the formulations are implemented in a computer code written in C++. Numerical examples demonstrate the accuracy and efficiency of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.