where r¼|xy| is the distance from the field point x to the source point y. Boundary-domain integral equations for boundary points can be obtained by letting y to the boundary Γ in Eq. It can be readily observed that, the two domain integrals in Eq. are related to the material inhomogeneity and the inertial effect. The two domain integrals are further transformed to boundary integrals by the radial integration method (RIM) proposed by Gao. In the RIM, the u˜i and u¨˜j in the domain integrals are approximated by a time dependent formulations which combine the radial basis function and the polynomials of the global coordinates as