• Українська
  • English
ISSN 2415-3400 (Online)
ISSN 1028-821X (Print)

GENERALIZED MODE-MATCHING TECHNIQUE IN THE THEORY OF MODE DIFFRACTION. PART 4. RATE OF CONVERGENCE FOR PROJECTIVE APPROXIMATIONS

heading: 
MICROWAVE ELECTRODYNAMICS
Petrusenko, IV, Sirenko, YK
Organization: 

1University of Customs and Finance
8, Rogaleva, Dnepropetrovsk, 49000, Ukraine
E-mail: petrusigor@yahoo.com

2O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine

3L.N.Gumilyov Eurasian National University
2, Mirzoyan, Astana, 010000, Republic of Kazakhstan
E-mail: yks@bk.ru
https://doi.org/10.15407/rej2015.02.015
Language: russian
Abstract: 

In this part of the work, we continue consideration about the basics of the generalized mode-matching technique, which has recently been developed for the analysis of wave diffraction. The problem of analytical estimate of the rate of convergence of projection approximations to the operator Fresnel formulae is discussed. The unconditional strong convergence of these approximations to the true scattering operators was proved previously. For the canonical scalar problem of wave diffraction on the step discontinue in a guide a measure of inaccuracy for the approximations of scattering operators has been derived analytically. These projective approximations under consideration are the truncated Fresnel formulae for the reflection and transmission operators. It is shown that the problem can be solved by examination of strong P–convergence of projective representations of an amplitude scattering operator. An analytical estimate of the rate of convergence of approximations for the scattering operators under consideration has been obtained. The found order of approximations has been verified by numerical computation. The results obtained allow us to estimate the computational efficiency of the generalized mode-matching technique, which can be useful for numerical-analytical solution of various electromagnetic problems
Keywords: mode-matching technique, operator Fresnel formulae, rate of convergence

Manuscript submitted 19.05.2015
PACS     41.20.Jb
Radiofiz. elektron. 2015, 20(2): 15-19
Full text (PDF)

References: 
  1. Petrusenko, I. V., Sirenko, Yu. K., 2012. Generalized mode-matching technique in the theory of guided wave diffraction. Part 1. Fresnel formulas for scattering operators. Radiofizika i elektronika. 3(17)(3), pp. 8–15 (in Russian).
  2. Petrusenko, I. V., Sirenko, Yu. K., 2012. Generalized mode-matching technique in the theory of mode diffraction. Part II. Convergence of projection approximations. Radiofizika i elektronika. 3(17)(4), pp. 18–21 (in Russian).
  3. Petrusenko, I. V., Sirenko, Yu. K., 2012. Generalized mode-matching technique in the theory of mode diffraction. Part III. Resonant scattering of waves by inhomogeneities. Ibid., pp. 22–28 (in Russian).
  4. Trenogin, V. A., 2002. The functional analysis. Moscow: Fizmatlit Publ. (in Russian).
  5. Petrusenko, I. V. and Sirenko, Yu. K., 2009. Generalization of the power conservation law for scalar mode-diffraction problems. Telecommunications and Radio Engineering. 68(16), pp. 1399–1410.DOI: https://doi.org/10.1615/TelecomRadEng.v68.i16.10
  6. Mittra, R. and Lee, S. W., 1974. Analytical techniques in the theory of guided waves. Translated from English and ed. G. V. Voskresenskiy. Moscow: Mir Publ. (in Russian).