## Absorbing Boundary Conditions for Time-Domain TLM and FDTD Analysis of Electromagnetic Structures

C. Eswarappa and W.J.R. Hoefer

Electromagnetics [ETRMDV, ISSN: 0272-6343 (Taylor & Francis)], Septmber-October 1996, Vol. 16, No. 5, pp 489-519.

## Abstract

In this paper, the absorbing boundary conditions (ABCs) most commonly used in time-domain numerical methods such as the Transmission Line Matrix (TLM) method and the Finite Difference Time Domain (FDTD) method are reviewed. Such boundary conditions are required to simulate matched loads and open surfaces. We discuss and compare ABCs based on single impulse reflection coefficients, one-way equations, diakoptics or Johns matrices, and Berenger's perfectly matched layer (PML). Even though the emphasis is on applications in the TLM method, the major differences in the performances of these ABCs in TLM and FDTD are pointed out. Two ways of applying ABCs in TLM (voltage impulses and node voltages) are discussed. It has been observed that an ABC applied directly to the TLM voltage impulses absorbs better than the same ABC applied to the TLM total node voltages or FDTD field values. Furthermore, different ways of stabilizing one-way equation ABCs, such as adding damping factors, choosing proper discretizations for the boundary operators and employing digital filters, are discussed in detail. It has been found that in FDTD, the damping factors have a greater influence on the stability than the type of discretization of the absorbing boundary operators, while in TLM the opposite is true. Also, in a TLM simulation, the absorbing boundaries can be placed closer to a scatterer than in a FDTD simulation without affecting the accuracy. Several examples such as waveguides, microstrips, and high permittivity dielectric cubes have been considered to demonstrate the above observations.