Singularity Problem With the One-sheet Huygens Subgridding Method

The Huygens subgridding (HSG) relies on the connection of two finite-difference time-domain (FDTD) grids by means of Huygens surfaces. An earlier work has presented that the Huygens surfaces can be reduced to one sheet of current in place of the usual two sheets. This letter shows that the resulting simplified HSG may be at the origin of inaccuracy in the computed results because of the singularity of the field at the edges of perfect electric or magnetic conductors. The difficulty can be easily overcome in two dimensions but not easily in three dimensions, where it is preferable to use the one sheet implementation only for the outer Huygens surface.