CONTROL OF ENERGY EFFICIENCY IN INDUSTRY AND HOUSING AND COMMUNAL SERVICES
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UDC 621.396.6(07), 537.8(07)
Features of iterative regularization for inverse scattering problems
A.B. Khashimov, South Ural State University, Chelyabinsk, Russian Federation, xab@kipr.susu.ac.ru
Abstract
This paper proposes the mathematical models of restoring the current distribution on surface of perfect conducting scatterer in case inaccurate input data of the electromagnetic field. The rigorous electrodynamics formulations which lead to the ill-posed functional equations of I kind are used. It is shown that the use of iterative regularization schemes provides a stable numerical solution under the certain criteria.
Keywords
scattering problems, mathematical model, functional equations, iterative regularization schemes
References
1. Colton D., Cress R. Metody integralnikh uravneny v teorii rasseyaniya [Integral Equations Methods in Scattering Theory]. Moscow, World, 1987. 312 p.
2. Bakhrah L.D., Kurochkin A.P. Radiogolografiya v mikrovolnovoii tekhnike [Radiohologram Method in Microwave Technique]. Moscow, Soviet Radio, 1979. 320 p.
3. Salikhov R.R., Khashimov A.B. Supercomputer Simulation of the Scattered Fields on Complex Shape Objects [Superkomp’yuternoye modelirovaniye v zadachakh rasseyaniya na ob’ektakh slozhnoy formy]. Bulletin of the South Ural University, Series “Computer Technologies, Automatic Control, Radio Electronics”, 2013, vol. 13, no. 1, pp. 55–61. (in Russian)
4. Voitivich N.I., Khashimov A.B. On the Correspondence of Asymptotic Solutions to 2D and 3D Problems in Antenna Engineering [O sootvetstvii asimptoticheskikh resheniy dvumernykh i trekhmernykh zadach v antennoy tekhnike]. Journal of Communications Technology and Electronics, 2010, vol. 55, no. 12, pp. 1374–1379.
5. Galishnikova T.N., Il’insky A.S. Chislennye metody v zadachakh difraktsyi [Numerical Method for Diffraction Problems]. Moscow, Publishing Center MSU, 1987. 208 p.
6. Bakushinsky A.B., Goncharsky A.V. Iterativnyi metody resheniya necorrectnikh zadach [Iterative Methods for Ill-Posed Problems]. Moscow, Science, 1989. 128 p.
2. Bakhrah L.D., Kurochkin A.P. Radiogolografiya v mikrovolnovoii tekhnike [Radiohologram Method in Microwave Technique]. Moscow, Soviet Radio, 1979. 320 p.
3. Salikhov R.R., Khashimov A.B. Supercomputer Simulation of the Scattered Fields on Complex Shape Objects [Superkomp’yuternoye modelirovaniye v zadachakh rasseyaniya na ob’ektakh slozhnoy formy]. Bulletin of the South Ural University, Series “Computer Technologies, Automatic Control, Radio Electronics”, 2013, vol. 13, no. 1, pp. 55–61. (in Russian)
4. Voitivich N.I., Khashimov A.B. On the Correspondence of Asymptotic Solutions to 2D and 3D Problems in Antenna Engineering [O sootvetstvii asimptoticheskikh resheniy dvumernykh i trekhmernykh zadach v antennoy tekhnike]. Journal of Communications Technology and Electronics, 2010, vol. 55, no. 12, pp. 1374–1379.
5. Galishnikova T.N., Il’insky A.S. Chislennye metody v zadachakh difraktsyi [Numerical Method for Diffraction Problems]. Moscow, Publishing Center MSU, 1987. 208 p.
6. Bakushinsky A.B., Goncharsky A.V. Iterativnyi metody resheniya necorrectnikh zadach [Iterative Methods for Ill-Posed Problems]. Moscow, Science, 1989. 128 p.
Source
Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control, Radio Electronics, 2013, vol. 13, no. 4, pp. 78-85. (in Russ.) (The main)