二维弹性快速多极边界元法及截断误差

Fast multipole boundary element method for 2D elasticity problem and truncation error

针对二维弹性问题的快速多极边界元法,给出复变函数形式的位移基本解的展开平移格式和主要的计算步骤.通过对计算量级的分析,得出改进"相互作用列表"以后的算法加快计算的原理,说明"相互作用列表"的改进能提高算法的计算效率.同时结合近远场划分准则具体表达了源点的近场和远场距离的点.对二维弹性力学问题快速多极边界元法的多极展开截断误差进行了分析,给出如何选取截断项数的表达式,从而说明截断误差与截断项数有关,可由截断项数控制.

In terms of the Fast Multipole Boundary Element Method（FM-BEM）, expansions and translations format and the main computational steps of the fundamental solution were presented for 2D elasticity problem. Through the analysis of operations, it can obtain a principle of an algorithm that the interaction list was modified, and it demonstrates that the interaction list is able to speed up computational efficiency. At the same time, combined with division criterion for near-far field, it shows the points of near field and far field distance of the source. Truncation error from the FM-BEM multiple expansion was analyzed for 2D elasticity problem. And a formula of number of expansion terms indicates the relation of truncation error and the number of the expansion terms.