Investigation of geometrically small features within numerical solutions to electromagnetic field problems

摘要

In this paper we consider the numerical solution of electromagnetic field problems involving geometrically small features. The numerical approaches considered are the three dimensional symmetric condensed node transmission line matrix (TLM) method, the Yee finite-difference time-domain (FD-TD) method, and lattice gas automata (LGA). The problems were selected to allow for rigorous computational investigation, and consist of perfectly conducting cavities and thin dielectric layers. The cavity results indicate the dominant error with TLM and FD-TD methods is dispersion, while dissipation is the dominant error with LGA. The ‘cursed-fin’ analysis indicates an initial estimate of the LGA to TLM (or FD-TD) mesh spacing ratio is in the range of 10:1 to 30:1. Stair-stepping errors are minimal in LGA analysis of curved conducting surfaces due to the extremely fine spatial discritization required. The accuracy of LGA and TLM approaches to the modelling of thin dielectric regions, such as the skin of a biological model, was tested through analysis of a Gaussian pulsed plane wave normally incident on a thin dielectric layer. Numerical results were compared to an analytic solution.