快速多极边界元进行大规模数值计算  

FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR LARGE-SCALE NUMERICAL COMPUTATION

作　　者：戴呈豪[1] 何锃[1] 彭伟才[1] 吕浚潮[1] 

机构地区：[1]华中科技大学力学系,武汉430074

出　　处：《机械强度》2008年第2期229-234,共6页Journal of Mechanical Strength

基　　金：国家自然科学基金资助项目(10472035)~~

摘　　要：快速多极边界元是近些年发展起来的边界元新型算法。在保持求解精度不变的前提下,快速多极边界元的计算量和存储量都比常规边界元有数量级上的减少,从而使在普通台式机上求解大规模问题成为可能。文中采用一种新的弹性力学快速多极边界元格式,使展开系数和传递关系得以简化。通过算例将新的方法与常规边界元进行比较,验证其精确性和高效性。在普通台式机上完成了含大量随机分布孔洞的平板的大规模数值计算。Fast multipole BEM（boundary element method） is a new algorithm developed for BEM these years. The computational cost and memory requirement of fast muhipole BEM is more than an order of magnitude lower than that of traditional BEM without changing accuracy, making it possible to solve large-scale problems on a desktop. A new fast multipole BEM format for elastostatics is applied to simplify expansion coefficients and translation relationships. This new method is compared with traditional BEM to prove its accuracy and efficiency by numerical example. A large-scale numerical computation about square plate with many randomly distributed holes is finished on a desktop.

关 键 词：边界元 快速多极算法 树结构 广义极小残差法 数值计算 

分 类 号：O242.2[理学—计算数学]