Discrete artificial boundary conditions for transient scalar wave propagation in a 2D unbounded layered media Original Research Article

This paper presents an efficient numerical method for direct time-domain solution of the transient scalar wave propagation in a two-dimensional unbounded multi-layer soil. The unbounded domain is truncated by an artificial boundary which demands the corresponding boundary conditions. In the new approach, only the artificial boundary is discretized into one-dimensional finite elements, yielding a new time-dependent partial differential equation (PDE) for displacements with respect to only one spatial coordinate. Factorization of the PDE and introduction of the residual radiation functions, there results a linear first-order ordinary differential equation (ODE). Its stability is ensured. The time-dependent discrete artificial boundary conditions are determined by the solution of the ODE. In general, it is local in time, but it is non-local in space. Several numerical examples are given to verify the superiority of the proposed method.