Non-reflecting artificial boundaries for transient scalar wave propagation in a two-dimensional infinite homogeneous layer

This paper presents an exact non-re ecting boundary condition for dealing with transient scalar wave propagation problems in a two-dimensional in nite homogeneous layer. In order to model the complicated geometry and material properties in the near eld, two vertical arti cial boundaries are considered in the in nite layer so as to truncate the in nite domain into a nite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the arti cial boundary conditions, to be applied on the truncated boundaries. Since the in nite extension direction is di erent for these two truncated vertical boundaries, namely one extends toward x→∞ and another extends toward x →−∞, the non-re ecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time-dependent partial di erential equation with only one spatial variable, can be further changed into a linear rst-order ordinary di erential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non-re ecting arti cial boundary condition can be obtained by solving the ordinary di erential equation whose stability is ensured. Some numerical examples have demonstrated that the non-re ecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in in nite and semi-in nite media