TY - JOUR
T1 - Switched Huygens Subgridding for the FDTD Method
AU - Hartley, John
AU - Giannopoulos, Antonios
AU - Davidson, Nigel
N1 - Funding Information:
This work was supported in part by the U.K. Engineering and Physical Sciences Research Council (EPSRC) and in part by the Defence Science and Technology Laboratory (Dstl).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2022/8/11
Y1 - 2022/8/11
N2 - 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 143 × more stable than the HSG for a 3-D subgridded half-wave dipole problem and at least 10 × more stable for a 1-D resonant subgridding problem. The SHSG runs 1.9 × 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.
AB - 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 143 × more stable than the HSG for a 3-D subgridded half-wave dipole problem and at least 10 × more stable for a 1-D resonant subgridding problem. The SHSG runs 1.9 × 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.
KW - Finite-difference time-domain (FDTD)
KW - Huygens subgridding (HSG)
KW - Huygens surfaces
KW - subgridding
KW - switched Huygens subgridding (SHSG)
UR - http://www.scopus.com/inward/record.url?scp=85128295010&partnerID=8YFLogxK
U2 - 10.1109/TAP.2022.3161371
DO - 10.1109/TAP.2022.3161371
M3 - Article
AN - SCOPUS:85128295010
SN - 0018-926X
VL - 70
SP - 6872
EP - 6882
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 8
ER -