Journal of Applied & Computational Mathematics

On the Validity of Modal Expansion in Pekeris Waveguide with PML

Abstract

Jianxin Zhu and Zengsi Chen

The perfectly matched layer (PML) is a widely used tool to truncate the infinite domain in numerical computations. It can also be used in the modal expansion of an open Pekeris waveguide. In a bounded waveguide with PML, the modal expansion consists of three kinds of modes. They are propagation modes, leaky modes and PML modes. The PML modes are introduced by the utilization of PML, and depend on the parameters of the PML. The validity of the modal expansion of the PML-truncated waveguide is discussed in this paper. It is proved that the expansion coefficient tends to zero when the index of modes tends to infinity, thus the truncation of the infinite sum is reasonable. Moreover, it is also proved that the numerical computation of the coefficients is stable.