An Algorithm of ADI-FDTD and R-FDTD Based on Non-zero Divergence Relationship

In this paper, it is proven that the divergence relationship of electric-field and magnetic-field is non-zero even in charge-free regions, when the electric-field and magnetic-field are calculated with Alternating Direction Implicit Finite-Difference Time-Domain (ADI-FDTD) method, and the concrete expression of the divergence relationship is derived. Based on the non-zero divergence relationship, the ADI-FDTD which is unconditionally stable is combined with the Reduced Finite-Difference Time-Domain(R-FDTD). In the proposed method (ADI/R-FDTD), the merit of ADI-FDTD, e.g. increasing time step size and decreasing calculation time, is kept, at the same time, the memory requirement is reduced by 1/3(3-D) or 2/5(2-D) of the memory requirement of ADI-FDTD. Compare to the ADI/R-FDTD based on regular zero divergence relationship, the proposed algorithm is more stable when lager time step size is used. Wave propagation in 2-D free space and the scattered field of a 1-D Frequency Selective Surface(FSS) is simulated by the proposed hybrid method. Compared with ADI-FDTD，perfect agreement of numerical results indicates that ADI/R-FDTD method is correct and efficient.