基于快速多极子基本解方法(FMM-MFS)的弹性波二维散射模拟研究

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (5) : 102-109.

论文

针对弹性波二维散射问题，发展一种新的快速多极子基本解方法（FMM-MFS）。方法基于单层位势理论，通过在虚边界上设置膨胀波线源和剪切波线源以构造散射波场，从而避免了奇异性的处理和边界单元离散；结合快速多极子展开技术（FMM），大幅度降低了计算量和存储量，突破了传统方法难以处理大规模散射问题的瓶颈。以全空间孔洞对P、SV波的二维散射为例，给出了具体求解步骤，并在个人计算机上实现了上百万自由度问题的快速精确计算。在方法效率和精度检验基础上，分别以单孔洞和随机孔洞群对平面波（P、SV波）的散射为例进行计算模拟，揭示了孔洞（群）周围弹性波散射的若干重要规律。

作者信息 +

THE FMM-MFS SOLUTON TO TWO-DIMENSINAL SCATTERING OF ELASTIC WAVES

This paper presents a new algorithm of the fast multipole fundamental solution method（FMM-MFS）for calculating two-dimensional elastic wave scattering problems. It avoids the singularity of the matrix by placing the line sources of compressional wave and shear wave on a virtual boundary based on single layer potential theory. Additionally, there is no need of elements discretization on the boundary. Combining with the FMM, MFS can solve large-scale problems of wave scattering by greatly reducing the computation and the memory requirement. Taking the two-dimensional scattering of P, SV waves around a cavity in elastic full-space as an example, the implement procedure are presented in detail, and up to millions DOF’s scattering problem are solved successfully on a personal computer. Based on the test of accuracy and efficiency of FMM-MFS, the scattering of plane waves by a cavity as well as random distributed group cavities in full-space are solved. Finally, several important conclusions about scattering of elastic waves around cavity(cavities) are obtained.

Author information +

文章历史 +

摘要

针对弹性波二维散射问题，发展一种新的快速多极子基本解方法（FMM-MFS）。方法基于单层位势理论，通过在虚边界上设置膨胀波线源和剪切波线源以构造散射波场，从而避免了奇异性的处理和边界单元离散；结合快速多极子展开技术（FMM），大幅度降低了计算量和存储量，突破了传统方法难以处理大规模散射问题的瓶颈。以全空间孔洞对P、SV波的二维散射为例，给出了具体求解步骤，并在个人计算机上实现了上百万自由度问题的快速精确计算。在方法效率和精度检验基础上，分别以单孔洞和随机孔洞群对平面波（P、SV波）的散射为例进行计算模拟，揭示了孔洞（群）周围弹性波散射的若干重要规律。

Abstract

This paper presents a new algorithm of the fast multipole fundamental solution method（FMM-MFS）for calculating two-dimensional elastic wave scattering problems. It avoids the singularity of the matrix by placing the line sources of compressional wave and shear wave on a virtual boundary based on single layer potential theory. Additionally, there is no need of elements discretization on the boundary. Combining with the FMM, MFS can solve large-scale problems of wave scattering by greatly reducing the computation and the memory requirement. Taking the two-dimensional scattering of P, SV waves around a cavity in elastic full-space as an example, the implement procedure are presented in detail, and up to millions DOF’s scattering problem are solved successfully on a personal computer. Based on the test of accuracy and efficiency of FMM-MFS, the scattering of plane waves by a cavity as well as random distributed group cavities in full-space are solved. Finally, several important conclusions about scattering of elastic waves around cavity(cavities) are obtained.

导出引用

刘中宪1,2，王冬1,2，梁建文3. 基于快速多极子基本解方法(FMM-MFS)的弹性波二维散射模拟研究[J]. 振动与冲击, 2015, 34(5): 102-109

LIU Zhong-xian1,2,WANG Dong1,2 Liang Jian-wen3. THE FMM-MFS SOLUTON TO TWO-DIMENSINAL SCATTERING OF ELASTIC WAVES[J]. Journal of Vibration and Shock, 2015, 34(5): 102-109

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