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

FMM-MFS soluton to two-dimensinal scattering of elastic waves

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。

A new algorithm named the fast multipole fundamental solution method（ FMM-MFS） was presented for calculating two-dimensional elastic wave scattering problems. The algorithm could avoid the singularity of matrix by placing the line sources of compressional wave and shear wave on a virtual boundary based on the single layer potential theory,and avoid elements discretization on the boundary. Combined with FMM,MFS can solve large-scale problems of wave scattering with greatly reducing computation and the memory requirement. Taking the two-dimensional scattering of P and SV waves around a cavity in elastic full-space as an example,the implement procedures were presented in detail,and up to millions of DOF＇s scattering problems were solved successfully on a personal computer. Based on the tests of accuracy and efficiency of FMM-MFS,the scatterings of plane waves around a cavity and randomly distributed group cavities in full-space were solved. Several important conclusions about scattering of elastic waves around cavity（ cavities）were obtained.