A Fractional Boundary Placement Model Using the Transmission-Line Modeling (TLM) Method

A technique is described to allow the placement of boundaries at noninteger space step positions within the transmission-line modeling technique without compromising the simulation time step. The development of the 2-D and 3-D modeling procedure is described where the boundary is implemented in the connection process. A previously published technique based on inductive stubs is described and the failure of this model to correctly represent field propagation along the boundary and the undesirable consequences when simulating cavity resonances are demonstrated. The method described in this paper ensures that fields incident on the boundary or traveling parallel to it are modeled with the correct delay and velocity respectively. This method presents a significant advantage over currently used approaches as no significant errors or spurious cavity resonances are produced. The accuracy of the model is presented in terms of the normally incident field delay, the velocity of propagation parallel to the boundary, and the resonances of a metallic cavity with fractionally placed boundaries.

I. Introduction

This paper describes a transmission line model [1] for accurate positioning of boundaries at noninteger space steps. The transmission line modeling (TLM) method, or matrix method, in its simplest form requires that space is discretised into uniform discrete cells with equal size and the time step is chosen to allow synchronization at speed of light propagation velocities. The electromagnetic properties of cells can be modified to allow modeling of a multitude of materials, including dielectrics, metals, composites, and frequency-dependent materials. Boundaries are normally positioned at the edge of cells within the mesh and as a result their positioning is limited by the mesh spacing chosen.