二维问题快速多极虚边界元法  

Fast multipole virtual boundary element method for solving two-dimensional problems

作　　者：许强[1] 蒋彦涛[1] 米东[1] 

机构地区：[1]同济大学建筑工程系,上海200092

出　　处：《哈尔滨工程大学学报》2008年第6期550-556,共7页Journal of Harbin Engineering University

摘　　要：将快速多极展开算法和广义极小残值法应用于虚边界元法的方程求解中.以二维弹性力学问题为研究背景,提出了二维问题快速多极虚边界元法的思想.该方法利用二维复平面上的基本解,并将其展开为适合于快速多极算法的格式,即变革计算结构(或模式),使解方程的计算量和储存量与所求问题的自由度数成线性比例.此点充分体现出该方法数值模拟大规模自由度问题的能力.数值算例说明了该方法的可行性,计算效率和计算精度,同时,该方法的思想具有一般性,应用上具有扩展性.In this paper, the generalized minimal residual （GMRES） algorithm and the fast multipole method （FMM） are jointly used to evaluate the numeric solutions of equations related to virtual boundary element method （VBEM）. The idea of fast muhipole virtual boundary element method for solving two-dimensional problems is presented in the context of 2-D elasticity mechanics. The main idea of the method is to expand the fundamental solutions in 2-D complex plane to suit the requirement of FMM scheme, i.e. a change of computational structure （or mode）, so that the computational time and memory volume for solving the equations is directly proportional to the freedoms of the problem to be solved. It is shown that the proposed method has the greater capacity to simulate the problems with much bigger degrees of freedom. Numerical examples proved the feasibility, accuracy and efficiency of this method. Moreover, the idea of this method can be generalized and extended to other applications.

关 键 词：快速多极算法 广义极小残值法 虚边界元法 弹性力学 

分 类 号：O343.1[理学—固体力学] TB33[理学—力学]