An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy

Over the past few years, a number of different finite-difference time-domain (FDTD) methods for modeling electromagnetic propagation in an isotropic cold plasma have been published. We have analyzed the accuracy and stability of these methods to determine which method provides the greatest accuracy for a given computation time. For completeness, two new FDTD methods for cold plasma, one of which is based on the concept of exponential fitting, are introduced and evaluated along with the existing methods. We also introduce the concept of cutoff modification which can be easily applied to most of the FDTD methods, and which we show can improve the accuracy of these methods with no additional computational cost. Von Neumann's stability analysis is used to evaluate the stability of the various methods, and their accuracy is determined from a straightforward time-and-space harmonic analysis of the dispersion and dissipation errors. Results of numerical experiments to verify the accuracy analysis are presented. It is found that for low-loss plasma, the piecewise linear recursive convolution method (PLRC) method is the most accurate, but the method of Young (see Radio Sci., vol.29, p.1513-22, 1994) can use less memory and is nearly as accurate. In this low-loss plasma regime, cutoff modification can significantly reduce the error near cutoff at the expense of slightly greater error at lower frequencies. For strongly collisional plasmas, the PLRC method also provides the most accurate solution.