A decoupling FEM for simulating near-field wave motion in two-phase media

A decoupling technique for simulating near-field wave motions in two-phase media is introduced in this paper. First, an equivalent but direct weighted residual method is presented in this paper to solve boundary value problems more explicitly. We applied the Green's theorem for integration by parts on the equivalent integral statement of the field governing equations and then introduced the Neumann conditions directly. Using this method and considering the precision requirement in wave motion simulation, a lumped-mass FEM for two-phase media with clear physical concepts and convenient implementation is derived. Then, considering the innate attenuation character of the wave in two-phase media, an attenuation parameter is introduced into Liao's Multi-Transmitting Formula (MTF) to simulate the attenuating outgoing wave in two-phase media. At last, two numerical experiments are presented and the numerical results are compared with the analytical ones demonstrating that the lumped-mass FEM and the generalized MTF introduced in this paper have good precision.