FDTD analysis of nonlinear magnetic diffusion by reduced c

The finite-difference time-domain (FDTD) approach is a particularly useful method for investigating nonlinear electromagnetics because the nonlinear relationships may be directly incorporated into the equation for advancing the electromagnetic fields. This approach is applicable to nonlinear magnetic materials with or without hysteresis (i.e. time dependence). Problems with geometric details that are very small compared to signal wavelengths, however, stress FDTD techniques. This occurs because the Courant-limited Δt can become small enough to require the use of >10¹¹ time steps unless one is tricky. Tricky means observing that this sort of problem has a solution which seldom depends on the speed of light c. Here, we demonstrate a procedure to elude the Courant stability condition by defining c to be 100 m/s. The present problem arose out of a magnetic diffusion FDTD application. The “reduced-c” technique should work, however, for any problem where Δt is limited by Δx/c which, in turn, is limited by the smallness of the problem geometry, not by a need for extremely fine temporal electromagnetic resolution