New Scheme for Electromagnetic Simulations

✍ Scribed by K.R. Chen; J.M. Dawson

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 264 KB
• Volume: 118
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1995.1081

✦ Synopsis

A new explicit time stepping scheme for electromagnetic simulations is described, the neo-finite-difference method. This numerical method which describes the time derivative as an arc instead of a straight line is more accurate. Thus, larger time steps can be used than with the standard leapfrog method. We start by Fourier analyzing the electromagnetic field in space. The Fourier amplitudes obey harmonic oscillator equations in time. The method involves approximating the time advance of a mode's amplitude from oscillator solutions for its estimated frequencies. From a computational point of view this involves replacing (\Delta t) by (2 \sin \left[\omega^{\varepsilon}(k) \Delta t / 2\right] / \omega^{E}(k)) in the finite difference equations, where (\omega^{t}(k)) is the estimated frequency of mode (k_{\text {; that }}) that (\Delta t) is multiplied by a (k)-dependent correction constant. The method not only improves the accuracy of the time stepping algorithm, but it increases the size of (\Delta t) for which it is stable. The ion-ripple laser is used as an example of a neo-finite difference electromagnetic simulation application to ilfustrate the new scheme. The size of the time step in the new scheme may be chosen one order of magnitude larger than for the standard method. The new scheme does not change the computation time per time step and only requires slight changes to the original code. 1995 Academic Press, Inc.