Investigation of Corner Singularity in Conformal FDTD Structured Mesh Generation Based on Ray Tracing

Corner singularity in this paper for finite-difference time-domain (FDTD) method indicates the incorrect conformal area computed from the intersection information by ray tracing for tangential situation. Tangential situation originates from a mesh line aligning on an aligned plane, which leads to the fuzzification of intersection length along Yee grid edge. The intersection position of two perpendicular aligned planes or an aligned plane with arbitrary plane is the position of possible corner singularity, from which the incorrect computed conformal area may result. A universal scheme to solve the corner singularity problem is proposed. By utilizing the in or out information normal to the tangential plane, as well as cell position relation relative to the tangential plane, we can determine whether or not to modify the length of the tangential side of Yee cell for computing the conformal area. A simple numerical example of a hollow rectangular waveguide shows the necessity for handling corner singularity.