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 引用本文: 荣俊杰, 校金友, 文立华. 弹性动力学高阶核无关快速多极边界元法[J]. 力学学报, 2014, 46(5): 776-785.
Rong Junjie, Xiao Jinyou, Wen Lihua. A HIGH ORDER KERNEL INDEPENDENT FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR ELASTODYNAMICS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5): 776-785.
 Citation: Rong Junjie, Xiao Jinyou, Wen Lihua. A HIGH ORDER KERNEL INDEPENDENT FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR ELASTODYNAMICS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5): 776-785.

## A HIGH ORDER KERNEL INDEPENDENT FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR ELASTODYNAMICS

• 摘要: 基于核无关的快速多极方法， 发展了一种弹性动力学问题的快速、高精度边界元分析方法. 采用基于二次曲面单元的Nyström 离散， 将边界积分方程转化为求和形式， 可以方便地进行加速计算；由于采用二次元， 边界元分析精度很高. 将一种新型快速多极方法用于Nyström 边界元法的加速计算， 该方法的数值实现简便、不依赖于积分方程基本解的表达式， 因此通用性很好；该方法还具有最优的计算量和存储量、精度高且可以控制. 结合Nyström 边界元系数矩阵和快速多极方法转换矩阵的特点， 提出一种大幅度降低边界元内存消耗的策略. 数值结果表明， 该方法无论在分析精度， 还是计算速度和内存消耗上， 都大大优于同类方法， 是一种快速、通用的工程弹性动力学问题大规模数值分析方法.

Abstract: In this paper, a highly accurate kernel-independent fast multipole boundary element method (BEM) is developed for solving large-scale elastodynamic problems in the frequency domain. The curved quadratic elements are employed to achieve high accuracy in BEM analysis. By using the Nystr?m discretization, the boundary integral equation is transformed into a summation, and thus the fast BEM algorithms can be applied conveniently. A newly developed kernel-independent fast multipole method (KIFMM) is used for BEM acceleration. This method is of nearly optimal computational complexity; more importantly, the numerical implementation of the method does not rely on the expression of the fundamental solutions and the accuracy is controllable and can be higher with only slight increase of the computational cost. By taking advantage of the cheap matrix assembly of Nyström discretization, the memory cost of the KIFMM accelerated BEM can be further reduced by several times. The performance of the present method in terms of accuracy and computational cost are demonstrated by numerical examples with up to 2.3 million degrees of freedom and by comparisons with existing methods.

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