弹性波三维散射快速多极子间接边界元法求解

边界元方法对于无限域中弹性波散射求解具有独特优势，但求解矩阵的非对称稠密特征极大限制了该方法在大规模实际工程中的应用。为此，基于单层位势理论，结合快速多极子展开技术，通过对球面压缩波和剪切波势函数的泰勒级数展开，建立一种新的快速多极间接边界元方法，以实现大规模弹性波三维散射的精确高效模拟。算例分析表明所提方法能够大幅度降低计算时间和存储量，可在目前普通计算机上快速实现上百万自由度弹性波三维散射问题的快速精确求解。最后以全空间椭球形孔洞群对平面P波、SV波的散射为例，揭示了三维孔洞群周围稳态位移场和应力场的若干分布规律。该文方法对低无量纲频率（ka<5.0）的大规模多体散射问题尤为适合。

THE FMM-IBEM SOLUTION OF THREE-DIMENSIONAL SCATTERING OF ELASTIC WAVES

Boundary element method has unique advantages to solve elastic wave scattering problems, while the asymmetric and dense matrix equation greatly restrict the application of traditional boundary element in practical engineering. Therefore, based on the single-layer potential theory, combined with the fast multipole expansion technique, a new rapid indirect boundary element method is developed by using the Taylor series expansion of compressible and shear wave potential function for solving large scale elastic wave scattering problems efficiently and accurately. It is verified that this method greatly improves the computing speed and reduces the calculation storage. Then the elastic wave scattering problem for millions of DOFs can be solved effectively and accurately on an ordinary personal workstation. Finally, the scattering problem of P wave by ellipsoidal cavities group in elastic full-space is solved, and some important characteristics for the displacement and stress fields in steady state are discussed based on the numerical results. This method is especially suitable for solving the multiple scattering problems at low dimensionless frequency (ka<5.0).