Cost-effective schemes for the numerical simulation of electromagnetic waves

Abstract

This paper presents a cost-effectiveness analysis of explicit Finite Difference (FD-TD) methods for the numerical integration of the Maxwell's equations. Formal notions of computational cost, expressed in floating point operations, and numerical dispersion error are introduced. Restricting the analysis to leapfrog time-marching for sake of simplicity, various spatial discrete differentiators are examined. For each scheme by minimizing the cost at a given error threshold, a cost-effective operating point, time sampling rate and number of gridpoints per shortest wavelength, is obtained, which is remarkably different from the stability limit. Different schemes, each operated at its cost-effective point, are then compared. New optimal schemes improved over the conventional ones are introduced together with accurate expansions of the differentiator weights in terms of the design error threshold. Numerical experiments illustrate the suitability of the new methods for large-scale electromagnetic modeling.