Abstract
A mathematical model in which the antenna radiation problem is considered as the scattering problem of the incident field created by the excitation source (antenna port) on the antenna patches is developed. The problem is reduced to a hyper singular integral equation for surface currents. The solution of this integral equation (surface currents) contains also a singularity near the antenna excitation points. These surface currents are presented as the sum of an analytically extracted term, which contains the main singularity, and of unknown additional currents. The unknown additional currents are smooth functions near the excitation points. To solve the integral equation for additional currents, the finite element Galerkin method (method of the RWG type) is applied. So the problem of finding the scattered field and calculating the antenna characteristics using a surface mesh without reducing cells size in the vicinity of the excitation points is solved.
Similar content being viewed by others
REFERENCES
C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed. (Wiley, Hoboken, NJ, 2016).
W. Gibson, The Method of Moments in Electromagnetics (Chapman and Hall, CRC, Boca Raton, 2008).
S. M. Rao, D. R. Wilton, and A. W. Glisson, ‘‘Electromagnetic scattering by surfaces of arbitrary shape,’’ IEEE Trans. Antennas Propag. 30, 409–418 (1982).
Yu. G. Smirnov, ‘‘Convergence of the Galerkin methods for equations with elliptic operators on subspaces and solving the electric field equation,’’ Comput. Math. Math. Phys. 47, 126–135 (2007).
A. G. Davydov, E. V. Zakharov, and Yu. V. Pimenov, ‘‘A method for the numerical solution of problems of diffraction of electromagnetic waves by nonclosed surfaces of arbitrary shape,’’ Dokl. Akad. Nauk 276, 96–100 (1984).
E. V. Zakharov, G. V. Ryzhakov, and A. V. Setukha, ‘‘Numerical solution of 3D problems of electromagnetic wave diffraction on a system of ideally conducting surfaces by the method of hypersingular integral equations,’’ Differ. Equat. 50, 1240–1251 (2014).
A. Setukha and S. Fetisov, ‘‘The method of relocation of boundary condition for the problem of electromagnetic wave scattering by perfectly conducting thin objects,’’ J. Comput. Phys. 373, 631–647 (2018).
J. L. Volakis and K. Sertel, Integral Equation Methods for Electromagnetics (SciTech Publ., Raleigh, NC, 2012).
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, New York, 1984).
A. G. Derneryd, ‘‘A theoretical investigation of the rectangular microstrip antenna element,’’ IEEE Trans. Antenn. Propag. 26, 532–535 (1978).
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by E. E. Tyrtyshnikov)
Rights and permissions
About this article
Cite this article
Nenashev, A.S., Setukha, A.V. & Stepanishcheva, V.S. On the Patch Antennas Radiation Numerical Modeling with Boundary Integral Equation Method. Lobachevskii J Math 42, 1370–1380 (2021). https://doi.org/10.1134/S1995080221060202
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080221060202