Passive equivalent circuit of FDTD: An application to subgridding

The finite difference time domain (FDTD) method gives accurate results for many problems but uses a large amount of computer memory and time. This can be reduced by using subgrids (fine grids) only around critical areas in the problem domain. The fields within the coarse and fine grids are found using standard FDTD equations, while at the boundary of the subgrid, interpolation of coarse grid fields is utilised. However, a simple interpolation as reported in literature exhibits late time instability. The authors present a stable scheme of updating the subgrid boundary fields by replacing the grid discontinuity with an equivalent circuit. The stability and accuracy of this new scheme is demonstrated through calculation of the cutoff wavelength of a dielectric slab loaded waveguide for various slab thicknesses.