Extrapolation within the Time-Stepping Loop of FDTD Models

The finite-difference time-domain (FDTD) method is a popular numerical tool for predicting the time-evolution of electromagnetic field behavior. Applications of the FDTD method range from geophysics to biophotonics. However, the Courant-Friedrichs-Lewy (CFL) condition significantly limits the computational efficiency of the FDTD method (i.e., the time step increment is limited by the chosen grid resolution). As a result, it is challenging and sometimes even infeasible to apply the FDTD method to applications involving very small time step increments relative to the wavelengths of interest or when time spans involving a very large number of wavelengths are of interest. This paper proposes a technique for allowing FDTD models to periodically skip time steps during the simulation while remaining stable and providing a level of accuracy that is suitable for many applications. This method is tested and validated using FDTD models applied to the prediction of geoelectric fields. For this application, the proposed method is demonstrated to be ~3.7 times faster than a regular, brute-force FDTD model.