Switched Huygens Subgridding for the FDTD Method

Abstract

The solution to finely detailed finite-difference time-domain (FDTD) models is often intractable due to the Courant–Friedrichs–Lewy (CFL) condition. Subgridding offers an attractive solution to this problem. In particular, the Huygens subgridding (HSG) exhibits great performance characteristics. It features high subgridding ratios and relatively small interfacing errors. However, late time instability reduces its utility. This article presents the switched Huygens subgridding (SHSG), a fundamental modification to the HSG that improves its stability. It is shown that the SHSG is at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$143 \times $ </tex-math></inline-formula> more stable than the HSG for a 3-D subgridded half-wave dipole problem and at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10 \times $ </tex-math></inline-formula> more stable for a 1-D resonant subgridding problem. The SHSG runs <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.9 \times $ </tex-math></inline-formula> faster per iteration (in the dipole experiment) since it does not require a PML in the subgrid to enhance stability. The accuracy of the SHSG is shown to be comparable with the HSG. Also, the fields in all overlapping regions are computed equal to the single space solution at all time steps simplifying the extraction of information in these regions. This new SHSG method is more straightforward to implement and optimize due to the simplicity of its proposed stabilization mechanism.