Abstract: By combining with the fast multipole expansion method (FMM), a fast and high precision multi-domain indirect boundary element method (IBEM) is developed for solving plane SH wave two-dimensional (2D) scattering by large-scale inclusions in the elastic half-space. Numerical results show that the FMM-IBEM can solve the problems of large-scale multi-domain scattering efficiently and accurately, and the storage capacity is also dramatically reduced. Then the rapid solution of millions degree-of-freedoms (DOFs) of plane SH wave scattering problem in the multi-domain is achieved on a personal computer. Finally, in the case of SH wave multiple scattering by inclusions with uniform distribution and random distribution in the half-space, the effects of stiffness and inclusion shape on plane SH wave scattering are investigated. Due to the multiple coherence scattering of elastic wave, the plane SH wave scattering by inclusion group is significantly different from that by single inclusion, and the characteristics of spatial distribution and displacement spectrum of the total wave field become complicated. The scattering properties of plane SH waves mainly depend on material hardness, geometric characteristics, the angle and frequency of incident wave. In addition, this study to some extent provides new techniques and theoretical basis for forward and inversion analysis of elastic wave scattering by complex inclusions in the half-space.

Key words: multi-domain scattering, plane SH wave, fast multipole expansion, indirect boundary element method, inclusions