Asymptotic Convergence in the FDTD and TLM Methods

Y.S. Rickard, Y. Li, and N.K. Nikolova (Canada)


Electromagnetic singularities, metal details, FDTD methods, time-domain TLM method


Here we use partially the approach proposed in [20] for use in the TLM method: to simulate model structures using progressively smaller spatial steps and to extrapolate the results in order to find the asymptotic value of the desired characteristics for an infinitesimal spatial step. We investigate the asymptotic accuracy of each of the above two techniques through the computation of the resonant frequencies of rectangular cavities, in which metallic objects with (concave and convex) 90 degree and knife edges and corners are present. The rate of convergence and the extrapolated asymptotic reference value are used to estimate the accuracy of the results at every grid cell size. Next we propose a simple post process formula to obtain the asymptotic characteristic value using two coarse-mesh simulations. This approach reduces the time and memory requirements at the expense of a negligible computational overhead. We compare the accuracy of Yee’s finite-difference time domain (FDTD) method and the time domain transmission-line matrix (TLM) method in representing internal metal details containing convex and concave edges and corners. We investigate the asymptotic convergence of both methods and propose a simple and effective post-process whereby the asymptotic estimate is obtained with only two coarse-grid simulations. The comparison shows an equivalent or better convergence of the FDTD method in comparison with the TLM method, as well as better accuracy with coarse discretizations.

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