Proceedings of TUSUR University / Archive / Issue of Journal № 4, t. 28, 2025 / An Integration Scheme with a Variable Number of Quadrature Points for Method-of-Moments Modeling of Antennas and Scatterers

An Integration Scheme with a Variable Number of Quadrature Points for Method-of-Moments Modeling of Antennas and Scatterers

DOI: 10.21293/1818-0442-2025-28-4-27-36

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Abstract: This paper presents an integration scheme with a variable number of quadrature points for assembling the interaction matrix during the electrodynamic modeling of antennas and scatterers using the method of moments. Several examples are used to analyze the deviations in the calculated parameters and characteristics for different combinations of integration points. It is established that the proposed integration scheme accelerates the formation of the interaction by matrix up to two times on average while maintaining an acceptable accuracy of the results. The proposed integration scheme is verified and validated using analytical solutions, data obtained from third-party commercial software, and published experimental results.

Keywords: integration scheme, surface singular integral equations, gaussian quadrature formulas, method of moments, scatterer, antenna

Authors and copyright holders:

Mochalov D. M. , Tomsk State University of Control Systems and Radioelectronics (Tomsk, Russia)
Klyukin D. V. , Tomsk State University of Control Systems and Radioelectronics (Tomsk, Russia)
Zaykov A. O. , Tomsk State University of Control Systems and Radioelectronics (Tomsk, Russia)
Kuksenko S. P. , Tomsk State University of Control Systems and Radioelectronics (Tomsk, Russia)

1. Balanis C.A. Advanced engineering electromagnetics. 2rd ed. New York, John Wiley & Sons, 2012, 1045 p.
2. Grigoryev A.D. Metody vychislitelnoi electrodinamyki [Methods of computational electrodynamics]. Moscow, Physical education Publ., 2013, 430 p. (in Russ).
3. Makarov S.N. Antenna and EM modeling with MatLab. New York, John Wiley & Sons, 2002, 288 p.
4. Harrington R.F. Matrix methods for field problems. Proceedings of the IEEE, 1967, vol. 55, no. 2, pp. 136–149.
5. Mavrikakis P.S., Martin O.J.F. Surface Integral Equations in Computational Electromagnetics: A Comprehensive Overview of Theory, Formulations, Discretization Schemes and Implementations. ACES Journal, 2025, vol. 40, no. 4, pp. 279–301.
6. Klyukin D.V., Mochalov D.M., Kuksenko S.P. [On techniques to compute surface singular integrals for formulating the matrix-vector equation of the moment method when solving antenna problems]. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2024, vol. 27, no. 1, pp. 23–34 (in Russ).
7. Klyukin D.V., Zaykov A.O., Mochalov D.M., Ivanov A.A., Kuksenko S.P. [Using Gauss Quadratures to Compute Surface Singular Integrals in the Method of Moments for Scattering Problems] // Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2024, vol. 27, no. 4, pp. 13–22 (in Russ).
8. Mosig J.R. Rao–Wilton–Glisson Basis Functions and the Electrostatics of Triangles and Polygons: A tutorial. IEEE Antennas and Propagation Magazine, 2025, pp. 2–12. DOI: 10.1109/MAP.2025.3606371.
9. Rao S., Wilton D., Glisson A. Electromagnetic scattering by surfaces of arbitrary shape. IEEE Transactions on antennas and propagation, 1982, vol. 30, no. 3, pp. 409–418.
10. Umashankar K., Taflove A., Rao S.M. Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric bodies. IEEE Transactions on Antennas and Propagation, 1986, vol. 34, no. 6, pp. 758–766.
11. Rao S.M., Cha C.C., Cravey R.L., Wilkes D.L. Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness. IEEE Transactions on Antennas and Propagation, 1991, vol. 39, no. 5, pp. 627–631.
12. Gibson W.C. The Method of Moments in Electromagnetics. 3rd ed. Boca Raton, Chapman & Hall/CRC, 2021, 479 p.
13. Bourlier C. Scattering from quasi-planar and moderate rough surfaces: Efficient method to fill the EFIE-Galerkin MoM impedance matrix and to solve the linear system. IEEE Transactions on Antennas and Propagation, 2021, Vol. 69, No. 9, pp. 5761–5770.
14. Bourlier C. Characteristic Basic Function Method Accelerated by a New Physical Optics Approximation for the Scattering from a Dielectric Object. Progress in Electromagnetics Research B, 2023, vol. 103, p. 177–194.
15. Huang S., Xiao G., Hu Y., Liu R., Mao J. Multibranch Rao-Wilton-Glisson basis functions for electromagnetic scattering problems. IEEE Transactions on Antennas and Propagation, 2021, vol. 69, no. 10, pp. 6624–6634.
16. Bourlier C. Acceleration of the primary basic functions calculation from the EFIE-characteristic basis function method (CBFM) combined with a new physical optics approximation. Progress in Electromagnetics Research B, 2023, vol. 99, pp. 179–195.
17. GMSH. Official website: Gmsh – A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Available at: https://gmsh.info, free (Accessed: 15 January 2026).
18. Lucernhammer. Official website: lucernhammer – Electromagnetic signature / radar cross section. Available at: https://lucernhammer.tripointindustries.com/-benchmark_ .data/ spheres (Accessed: 15 January 2026).
19. Brown G.H., Woodward O.M. Experimentally determined radiation characteristics of conical and triangular antennas. RCA Review, 1952, vol. 13, no. 4, pp. 425–452.

Funding: This work was supported by the Ministry of Education and Science of the Russian Federation under project FEWM-2024-0005 and the Russian Science Foundation under project No. 23-79-10165, https://rscf.ru/project/23-79-10165/.

For citation:
Mochalov D. M., Klyukin D. V., Zaykov A. O., Kuksenko S. P. An Integration Scheme with a Variable Number of Quadrature Points for Method-of-Moments Modeling of Antennas and Scatterers. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2025, vol. 28, no. 4, pp. 27–36. DOI: 10.21293/1818-0442-2025-28-4-27-36

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