Stretched coordinate PML in TLM - Odeyemi, Jomiloju (2022)
As with all differential equation based numerical methods, open boundary problems in TLM require special boundary treatments to be applied at the edges of the computational domain in order to accurately simulate the conditions of an infinite propagating medium. Particular consideration must be given to the choice of the domain truncation technique employed since this can result in the computation of inaccurate field solutions. Various techniques have been employed over the years to address this problem, where each method has shown varying degree of success depending on the nature of the problem under study. To date, the most popular methods employed are the matched boundary, analytical absorbing boundary conditions (ABCs) and the Perfectly Matched Layer (PML). Due to the low absorption capability of the matched boundary and analytical ABCs a significant distance must exist between the boundary and the features of the problem in order to ensure that an accurate solution is obtained. This substantially increases the overall computational burden. On the other hand, as extensively demonstrated in the Finite Difference Time Domain (FDTD) method, minimal reflections can be achieved with the PML over a wider frequency range and for wider angles of incidence. However, to date, only a handful of PML formulations have been demonstrated within the framework of the TLM method and, due to the instabilities observed, their application is not widely reported. The advancement of the PML theory has enabled the study of more complex geometries and media, especially within the FDTD and Finite Element (FE) methods. It can be argued that the advent of the PML within these numerical methods has contributed significantly to their overall usability since a higher accuracy can be achieved without compromising on the computational costs. It is imperative that such benefits are also realized in the TLM method.