三维弹性问题Taylor展开多极边界元法的误差分析

Error analysis applied in Taylor expansions multipole BEM for three-dimensional elasticity problems

Taylor展开多极边界元法有效的提高了边界元法的求解效率,使之可用于大规模问题的计算。然而,由于计算中对基本解进行了Taylor级数展开,与传统边界元方法相比计算精度有所下降。本文主要针对三维弹性问题Taylor展开多极边界元法的计算精度和误差进行研究。文中对两种方法的计算精度进行了比较;研究了核函数的Taylor展开性质;推导了三维弹性问题基本解的误差估计公式;给出了Taylor展开多极边界元法中远近场的划分原则。通过具体的算例,证明了该方法的正确性和误差估计公式的有效性,说明了影响Taylor展开多极边界元法求解精度的因素。

The Taylor expansions multipole BEM （TEMBEM） is an effective method in the way of improvement computational efficiency. The memory and operations requirements of multipole BEM are proportional to the unknowns N, and it can speed up the computation and adapt to large-scale numerical computation. The precision of TEMBEM is deteriorative in comparison with conventional BEM. The error and precision of TEMBEM for 3D elasticity problems are researched. This paper presents a comparison between conventional BEM and TEMBEM, and analyzes the accuracy and error of the Taylor series. The Taylor expansions properties of kernel function r are researched and the error estimate formulas of 3D elasticity problems are deduced. The principles to partition far-field and near-field are presented, and the approaches to improving precision are specified. The numerical experiments show the validity and practicability of the error estimate formulas of TEMBEM.