A Nonstandard Path Integral Model for Curved Surface Analysis

Tadao Ohtani, Yasushi Kanai and Nikolaos V. Kantartzis
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Tadao Ohtani: Independent Researcher, Asahikawa 070-0841, Japan
Yasushi Kanai: Department of Engineering, Faculty of Engineering, Niigata Institute of Technology, Kashiwazaki 945-1195, Japan
Nikolaos V. Kantartzis: Department of Electrical and Computer Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece

Energies, 2022, vol. 15, issue 12, 1-21

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.

Keywords: electromagnetic analysis; finite-difference time-domain methods; integral equations; numerical analysis; radar cross section (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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