Coupling of the BEM with the MFS for the numerical simulation of frequency domain 2-D elastic wave propagation in the presence of elastic inclusions and cracks

Abstract

This paper proposes a coupling formulation between the boundary element method (BEM displacement and TBEM traction formulations) and the method of fundamental solutions (MFS) for the transient analysis of elastic wave propagation in the presence of multiple elastic inclusions to overcome the specific limitations of each of these methods. The full domain of the original problem is divided into sub-domains, which are handled separately by the BEM or the MFS. The coupling is enforced by imposing the required boundary conditions.The accuracy, efficiency and stability of the proposed algorithms, using different combinations of BEM and MFS, are verified by comparing the solutions against reference solutions. The computational efficiency of the proposed coupling formulation is illustrated by computing the CPU time and the error at high frequencies.The potential of the proposed procedures is illustrated by simulating the propagation of elastic waves in the vicinity of an empty crack, with null thickness placed close to an elastic inclusion.