A Path Integral Representation Model to Extend the Analytical Capability of the Nonstandard Finite-difference Time-domain Method

Authors

  • 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 Aristotle University of Thessaloniki, Thessaloniki GR-54124, Greece

DOI:

https://doi.org/10.13052/2024.ACES.J.390304

Keywords:

Computational electromagnetics, finite-difference time-domain methods, integral equations, radar cross section

Abstract

The nonstandard finite-difference time-domain (NS-FDTD) method is a powerful tool for solving Maxwell’s equations in their differential form on orthogonal grids. Nonetheless, to precisely treat arbitrarily shaped objects, very fine lattices should be employed, which often lead to unduly computational requirements. Evidently, such an issue hinders the applicability of the technique in realistic problems. For its alleviation, a new path integral (PI) representation model, equivalent to the NS-FDTD concept, is introduced. The proposed model uses a pair of basic and complementary path integrals for the H-nodes. To guarantee the same accuracy and stability as the NS-FDTD method, the two path integrals are combined via optimization parameters, derived from the corresponding NS-FDTD formulae. Since in the PI model, E-field computations on the complementary path are not necessary, the complexity is greatly reduced. Numerical results from various real-world problems prove that the proposed method improves notably the efficiency of the NS-FDTD scheme, even on coarse orthogonal meshes.

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Author Biographies

Tadao Ohtani, Independent Researcher, Asahikawa, 070–0841, Japan

Tadao Ohtani received the B.S. and M.S. degrees in electrical and electronic engineering from Toyohashi University of Technology, Japan, in 1983 and 1985, respectively, and received Ph.D. degree in electrical and electronic engineering from Kitami Institute of Technology, Japan, in 2005. From 1985 to 2011, he worked as a researcher at Nagoya Aerospace Systems of Mitsubishi Heavy Industries, Ltd. Currently, he is an independent researcher. His research interests include numerical analysis of the electromagnetic scattering fields for aircraft design via the FDTD and the NS-FDTD method.

Yasushi Kanai, Department of Engineering, Faculty of Engineering Niigata Institute of Technology, Kashiwazaki 945–1195, Japan

Yasushi Kanai (Fellow, ACES) received the B.S., M.S. degree in engineering, and Ph.D. degree in information engineering from Niigata University, Japan, in 1982, 1984, and 1989, respectively.

He worked as a research engineer at Alps Electric Co., Ltd., from 1984 to 1992, where he developed magnetic recording heads via numerical methods. In 1992–1995, he was an associate professor at Department of Information Engineering, Niigata University. In 1995, he joined the Engineering Department, Niigata Institute of Technology, Kashiwazaki, Japan, where he is currently a professor. In 2002–2003, he was at Florida International University, Miami, FL, as a visiting scholar. He has authored/co-authored more than 190 peer-reviewed journal papers, more than 270 international conference records, more than 260 national conference records, and several book chapters. He specializes in micromagnetic analysis both in energy-assisted magnetic recording heads and media and in wave propagation via NS-FDTD analysis.

Nikolaos V. Kantartzis, Department of Electrical and Computer Engineering Aristotle University of Thessaloniki, Thessaloniki GR-54124, Greece

Nikolaos V. Kantartzis received the Diploma and Ph.D. degrees in electrical and computer engineering from the Aristotle University of Thessaloniki, Thessaloniki, Greece, in 1994 and 1999, respectively. In 1999, he joined the Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, where he is currently a professor. He has authored/coauthored 4 books, more than 190 peer-reviewed journal papers, and more than 300 publications in conference proceedings. His main research interests include computational electromagnetics, EMC, metamaterials, graphene, antenna design, and waveguide systems.

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Published

2024-03-31

How to Cite

[1]
T. Ohtani, Y. Kanai, and N. V. Kantartzis, “A Path Integral Representation Model to Extend the Analytical Capability of the Nonstandard Finite-difference Time-domain Method”, ACES Journal, vol. 39, no. 03, pp. 189–200, Mar. 2024.

Issue

2024: Vol 39 Iss 3

Section

Special issue on Finite Difference Methodologies for Microwave, Optical .....