A Nonstandard Path Integral Model for Curved Surface Analysis

Abstract

The nonstandard finite-difference time-domain (NS-FDTD) method is implemented in the differential form on orthogonal grids, hence the benefit of opting for very fine resolutions in order to accurately treat curved surfaces in real-world applications, which indisputably increases the overall computational burden. In particular, these issues can hinder the electromagnetic design of structures with electrically-large size, such as aircrafts. To alleviate this shortcoming, a nonstandard path integral (PI) model for the NS-FDTD method is proposed in this paper, based on the fact that the PI form of Maxwell’s equations is fairly more suitable to treat objects with smooth surfaces than the differential form. The proposed concept uses a pair of basic and complementary path integrals for H-node calculations. Moreover, to attain the desired accuracy level, compared to the NS-FDTD method on square grids, the two path integrals are combined via a set of optimization parameters, determined from the dispersion equation of the PI formula. Through the latter, numerical simulations verify that the new PI model has almost the same modeling precision as the NS-FDTD technique. The featured methodology is applied to several realistic curved structures, which promptly substantiates that the combined use of the featured PI scheme greatly improves the NS-FDTD competences in the case of arbitrarily-shaped objects, modeled by means of coarse orthogonal grids.