Study of Corner Singularity in Conformal Structured Mesh Generation for the Finite-Difference Time-Domain Method Based on Ray Tracing

We investigate the problem of erroneous conformal area extracted by ray tracing in conformal structured mesh generation for the finite-difference time-domain method when tangential situations arise, referred to as corner singularity. The erroneous conformal area results from the fuzzification of intersecting length for tangential situations. Here, an effective mesh scheme to solve the corner singularity is proposed. In this scheme, additional degrees of freedom for mesh flags of vertexes and generalized consistency modification are proposed to solve the fuzzification of intersecting length, leading to accurate extraction of the conformal area. Furthermore, the scheme can tackle the convex and concave points uniformly without leading to possible breakdown of the conventional parity-number-based method. Rigorous and less rigorous staircase criteria are proposed to classify the cells accurately and effectively. The difficulties of concave point combined with the tangential situation are also successfully solved. Numerical examples of several microwave devices are given to show the validity of the proposed mesh scheme.