Proceedings of TUSUR University / Archive / Issue of Journal № 4, t. 27, 2024 / Using Gauss Quadratures to Compute Surface Singular Integrals in the Method of Moments for Scattering Problems

Using Gauss Quadratures to Compute Surface Singular Integrals in the Method of Moments for Scattering Problems

DOI: 10.21293/1818-0442-2024-27-4-13-22

Download article in PDF format

JATS xml

Abstract: The accuracy of calculating radar cross section by the method of moments, using Gauss quadratures to eliminate singularity in the formation of the system of linear algebraic equations, has been evaluated. Calculations of the bistatic radar cross section of a perfectly conducting sphere at various combinations of integration points have been performed. Using published data, the absolute and relative deviations of the obtained results have been evaluated. Using feature selective validation method, all data sets are evaluated to confirm the results of the analysis of deviations. Evaluated the number of conditioning of the matrix of the system of linear algebraic equations. The most versatile combination of integration points for computing singular inte-grals is identified, that provides the best balance between solu-tion accuracy and computational cost. The calculation of the scattering of the slit case using this combination of points is performed. The results show a good agreement with data ob-tained in commercial software based on the finite difference time domain method.

Keywords: numerical methods, method of moments, quadrature formulas, radar cross section, feature selective validation

Funding: This work was supported by the Ministry of Education and Science of Russia 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:
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. DOI: 10.21293/1818-0442-2024-27-4-13-22

Authors and copyright holders:

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

1. Ruck G.T., Garber D.J. Radar Cross Section Handbook. New York, Plenum Press, 2001, 504 p.
2. Diao P.S., Alves T., Poussot B., Azarian S. A review of radar detection fundamentals. IEEE Aerospace and Electronic Systems Magazine, 2024, vol. 39, pp. 4–24.
3. Berdishev V.P, Garin E.N., Fomin A.N. Radiolokacionnie Systemi: Uchebnik [Radar Systems: Textbook]. Krasnoyarsk, Siberian Federal University, 2011, 400 p. (in Russ).
4. Balanis C.A. Advanced Engineering Electromagnetics. 3-rd ed. New York: John Wiley & Sons, 2023, 1136 p.
5. Grigoryev A.D. Metody Vychislitelnoy Electrodinamyki [Methods of Computational Electrodynamics]. Moscow, Physical Education Publ., 2013, 430 p. (in Russ).
6. Gibson W.C. The Method of Moments in Electromagnetics, Boca Raton, Chapman & Hall/CRC, 2021, 510 p.
7. Makarov S.N. Antenna and EM Modeling with MATLAB. New York, John Wiley & Sons Publ., 2002, 288 p.
8. Harrington R.F. Matrix methods for field problems. Proceedings of the IEEE, 1967, vol. 55, no. 2, р. 136–149.
9. Yee K.S. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media // IEEE Transaction on Antennas and Propagation, 1966, vol. AP-14, pp. 302–307.
10. Freno B.A., Johnson W.A., Zinser B.F, Wilton D.R., Vipiana F., Campione S. Characterization and integration of the singular test integrals in the method‐of‐moments implementation of the electric‐field integral equation. Engineering Analysis with Boundary Elements, 2021, vol. 124, pp. 185–193.
11. Klyukin D.V., Mochalov D.M., Kuksenko S.P. [On methods of computing surface singular integrals for formulating the matrix-vector equation of the method of moments at solution of antenna problems]. Proceedings of TUSUR University, 2024, vol. 27, no 1, pp. 23–34 (in Russ).
12. Ji J., Huang P., Series expansion feasibility of singular integral in method of moments. Journal of Systems Engineering and electronics, 2014, vol. 25, no. 3, pp. 386–392.
13. 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.
14. Mosig J.R., Itoh T. Integral equation technique. Numerical Techniques for Microwave and Millimeter-wave passive Structures, 1989, pp. 133–213.
15. Dunavant D.A. High degree efficient symmetrical Gaussian quadrature rules for the triangle. International Journal for Numerical Methods in Engineering, 1985, vol. 21, no. 6, pp. 1129–1148.
16. 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.
17. 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, pp. 177–194.
18. 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.
19. 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.
20. GMSH [web]: 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: October 08, 2024).
21. LUCERNHAMMER [web]: Official website: lucernhammer – Electromagnetic signature / radar cross section URL: https://lucernhammer.tripointindustries.com/-benchmark_.data/spheres, free (accessed: October 09, 2024).
22. IEEE STD 1597.1 – 2008. IEEE Standard for Validation of Computational Electromagnetics Computer Modeling and Simulations. New York, IEEE Inc, 2009, 41 p.
23. Shaymanov N.Yu, Avraamov V.P, Ivanov A.A, Kuksenko S.P. Applying the feature selective validation method to compare experimental or simulated datasets. Software & Systems, 2024. vol 3. pp. 310–317 (in Russ.).
24. Zajkov A.O. Analysis of resonant frequencies of shielding enclosures based on monostatic radar cross section. International scientific and technical conference of students, postgraduates and young scientists «TUSUR Scientific session 2024»: Proceedings, 2024, vol 2, pp. 74–77 (in Russ.).
25. IEEE STD 1597.2–2010. IEEE Recommended Practice for Validation of Computational Electromagnetics, Computer Modeling and Simulations. New York, IEEE Inc, 2011, 124 p.