A 3D FDTD formulation using flux-corrected transport for accurate modeling of transient electromagnetic phenomena

A technique that will allow a second-order finite-difference formulation to be used to its fullest potential in both a stability and accuracy sense. The technique, flux corrected transport (FCT), uses a first-order differencing scheme together with a second-order scheme to produce a solution free of numerically induced diffusion and dispersion. The amount of low-order solution versus high-order solution that is used is determined on a node-by-node basis in a nonlinear manner. The overriding bound on FCT is preserving the conservative nature of the equations being integrated. Results are presented for a 3-D computational domain with a pulse excitation that can be introduced from any side. The domain is truncated with a Liao absorbing boundary condition on all external boundaries. Both free space propagation through the computational space and interaction with a scatterer are investigated. Solution time and accuracy are compared with the traditional Yee (1966) formulation on a staggered grid. Stability and accuracy are improved significantly over conventional finite-difference formulations.<>