Non-reflecting artificial boundaries for modelling scalar wave propagation problems in two-dimensional half space

Abstract

Using the operator splitting method, the non-reflecting artificial boundary condition, which has the same form as those originally presented by Hagstrom and Hariharan [Appl. Numer. Math. 27 (1998) 403] as well as Thompson et al. [Comput. Meth. Appl. Mech. Engrg. 191 (2001) 311], is re-derived in this paper to deal with transient scalar wave propagation problems in a two-dimensional homogeneous half space. In particular, the original non-reflecting artificial boundary condition is extended to approximately solve transient scalar wave propagation problems in a two-dimensional layered half space, which has a far field consisting of non-homogeneous materials. The proposed non-reflecting artificial boundary condition can be decomposed into three types of elements: physically meaningful springs and dashpots as well as the generalized energy absorbers, which represent the effects of incident waves at previous time instants on the truncated artificial boundary. Due to the meaningfulness in physics, the proposed non-reflecting artificial boundary is straightforwardly applied to the finite element analysis of wave propagation problems in infinite media. The related numerical results from three application examples have demonstrated the effectiveness, efficiency and usefulness of the proposed non-reflecting artificial boundary in dealing with scalar wave propagation problems in two-dimensional homogeneous and layered half spaces.