ADI Scheme of a Nonstandard FDTD Method and Its Numerical Properties

An alternating direction implicit (ADI) scheme for a nonstandard (NS) finite-difference time-domain (FDTD) method is proposed. The NS FDTD method is derived by analyzing the dispersion relation. Two different groups of update coefficients are used to update the electric field and magnetic field, respectively. The dispersion property of the NS method is similar with that of the standard higher order method, though it is only second order accurate in the space domain. The total number of nonzero update coefficients for this method is fewer than that of the latter. This small stencil property can be used to reduce computational burden in implicit formulation of this method. The one-step leapfrog ADI scheme is adopted to examine this idea. The detailed update equations of this ADI scheme are derived. The dispersion and stability properties are also analyzed and compared with the corresponding standard one. The results show that the computational efficiency of the proposed method is higher than that of the standard one.