The theory of a singularity-enhanced method for sharp metal edge diagonal to the cell cube in FDTD grid

The complete theory of a singularity-enhanced method for a sharp metal edge diagonal to the cell cube in finite-difference time-domain (FDTD) grid is presented in this paper. In fact, it is an extended theory of a singularity-enhanced theory for a sharp metal edge diagonal to the grid in two dimensions (metal sheet is placed in XOY plane). The singular nature of electromagnetic fields at a sharp metal edge is considered, and new FDTD equations are derived for all electric and magnetic nodes affected by the singularity near the metal edge, using a contour-path subcell approach. A dramatic improvement in computed accuracy was observed when a stripline and patch antenna with sharp metal edges diagonal to the cell cube in FDTD grid was analyzed using the new FDTD equations. This method can be adopted when sharp metal edges of various metal structures were placed in diagonal line of the cell cube in FDTD grid.