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A fast-multi-pole accelerated method of fundamental solutions for 2-D broadband scattering of SH waves in an infinite half space

The traditional method of fundamental solution (T-MFS) is known as an effective method for solving the scattering of elastic waves, but the T-MFS is inefficient in solving large-scale or broadband frequency problems. Therefore, in order to improve the performance in efficiency and memory requirement for treating practical complex 2-D broadband scattering problems, a new algorithm of fast multi-pole accelerated method of fundamental solution (FM-MFS) is proposed. Taking the 2-D scattering of SH waves around irregular scatterers in an elastic half-space as an example, the implementation steps are presented in detail. Based on the accuracy and efficiency verification, the FM-MFS is applied to solve the broadband frequency scattering of plane SH waves around group cavities, inclusions, a V-shaped canyon and a semi-elliptical hill. It shows that, compared with T-MFS, the FM-MFS has great advantages in reducing the consumed CPU time and memory for 2-D broadband scattering. Besides, the FM-MFS has excellent adaptability both for broad-frequency and complex-shaped scattering problems.