A 4-D Subgrid Scheme for the NS-FDTD Technique Using the CNS-FDTD Algorithm With the Shepard Method and a Gaussian Smoothing Filter

A precise subgrid technique for the nonstandard finite-difference time-domain (NS-FDTD) method in 4-D (i.e., 3-D space and 1-D time) is proposed in this paper. The novel algorithm is efficiently blended with the Shepard scheme and a Gaussian smoothing filter to minimize the error in the interpolated values used for the spatial connection process. Moreover, the required time interpolation is performed via the complex (C)NS-FDTD approach. A key advantage of the proposed formulation is its structural simplicity, due to the prior interpolation concepts and the absence of any nonphysical convention, which enables its straightforward application to a variety of realistic problems. The numerical results validate the benefits of the method by means of different subgrid simulation scenarios.