二维新型快速多极虚边界元配点法  

A NEW FAST MULTIPOLE VIRTUAL BOUNDARY ELEMENT COLLOCATION METHOD FOR SOLVING TWO-DIMENSIONAL PROBLEMS

作　　者：司炜[1] 许强[1] 

机构地区：[1]同济大学建筑工程系,上海200092

出　　处：《工程力学》2012年第10期52-56,62,共6页Engineering Mechanics

摘　　要：以二维弹性问题为研究背景,提出了一种二维新型快速多极虚边界元配点法的求解思想,即采用新型的快速多极展开和运用广义极小残值法来求解传统的虚边界元配点法方程。相对常规快速多极展开技术,该文针对二维弹性问题在原有的快速多极虚边界元法展开格式的基础上,通过引入对角化的概念,以更新展开传递格式,欲达到进一步提高计算效率的目的。数值算例说明了该方法的可行性,计算效率和计算精度。此外,该文方法的思想具有一般性,应用上具有扩展性。Based on the research background of two dimensional elasticity problems,an idea of two-dimensional new fast multipole virtual boundary element collocation methods is proposed in this paper,in other words,a new fast multipole method（FMM） and the generalized minimal residual（GMRES） algorithm are jointly employed to solve the equations related to the virtual boundary element collocation method（VBEM）.The numerical scheme suitable for original FMM with respect to two-dimensional problems of elasticity is optimized through introducing the concept of diagonalization in order to further improve the efficiency of the problem to be solved.Then large-scale numerical simulations of elastostatics might be achieved by the method.Numerical examples have proved the feasibility,efficiency and calculating precision of the method.Moreover,this article idea has the generality and the extension in the engineering applications.

关 键 词：新型快速多极算法 广义极小残值法 虚边界元法 配点法 对角化 

分 类 号：O343.1[理学—固体力学] TB33[理学—力学]