The unconditionally-stable cycle-sweep method for 3D FDTD

To overcome the Courant limit in the explicit finite-difference time-domain (FDTD) methods, several unconditionally-stable methods have been proposed. This paper presents the cycle-sweep Crank-Nicolson method for solving 3D Maxwell's Equations. The cycle-sweep method is unconditionally stable and 2
^nd
order accurate in both time and space, and solves only six tridiagonal matrices instead of nine in the approximate-factorization-splitting method we reported previously. The cycle-sweep method is much more efficient than either a direct implementation of the Crank-Nicolson scheme or the approximate-factorization-splitting method.