A. M. Somov - the Academy of FSGS of the Russian Federation I. S. Polyansky - Ph.D. (Eng.), Research Scientist of the Academy of FSGS of the Russian Federation. E-mail: van341@mail.ru D. E. Stepanov - Research Scientist of the Academy of FSGS of the Russian Federation

The parameterization of the reflecting surface of the mirror-type antenna by special multivariate splines of any degree for the subse-quent effective solution of the synthesis problem of a reflector antenna in the approximation of the methods of physical optics and physical theory of diffraction has been proposed in the article. It has been proposed to carry out the formation of the spline function approximation for the entire reflective surface in the large without its sampling and (or) by coverage with excess area. This approxi-mation has been realized by performing the following steps: 1) opening of the reflector is defined by a polygon; 2) the barycentric coordinate system which determines the position of an arbitrary point in the plane of the aperture reflector is implemented for the number of vertices of the polygon; 3) a set of multi-indices, characterizing the position of the grid points based on the input order of approximation is determined for a given barycentric system; 4) with the defined anchor points and barycentric coordinates the spline function approximation is determined by a rational Bezier surface polygonal. The accuracy estimation of the proposed approximation has been performed depending on the number of nodal points defined by a spline. Numerical solution of the problem of synthesis of the reflecting surface-mirror antenna has been carried out subject to the proposed approximation to evaluate the effectiveness of the generated solution.

 

1. Reutov A.S., SHishlov A.V. Osobennosti poehtapnogo sinteza zerkalnykh antenn s konturnymi diagrammami napravlennosti pri ispolzovanii splajjnovogo predstavlenija poverkhnosti zerkala // EHlektromagnitnye volny i ehlektronnye sistemy. 2003. №2. S. 4-14.
2. Arkhipov N.S., Poljanskijj I.S., Stepanov D.E. Predstavlenie otrazhajushhikh poverkhnostejj antennojj sistemy v zadachakh analiza i sinteza zerkalnykh antenn metodami fizicheskojj optiki // Telekommunikacii. 2014. №7. S. 15-21.
3. Reutov A.S. Metody sinteza gibridnykh zerkalnykh antenn dlja radiosistem s odnomernym skanirovaniem. Diss. - kand. tekhn. nauk. M. 2003.
4. Golovanov N.N. Geometricheskoe modelirovanie. M.: FIZMATLIT. 2002.
5. Silvestr P., Ferrari R. Metod konechnykh ehlementov dlja radioinzhenerov i inzhenerov-ehnergetikov / per. s angl. M.: Mir. 1986.
6. Rodionov V.I. O primenenii specialnykh mnogomernykh splajjnov proizvolnojj stepeni v chislovom analize // Vestnik Udmurtskogo un-ta. Kompjuternye nauki. 2010. Vyp. 4. S. 146-153.
7. Meyer M., Lee H., Barr A., Desbrun M. Generalized barycentric coordinates on irregular polygons // Journal of Graphics Tools. 2002. V. 7. № 1. P. 13-22.
8. Warren J., Schaefer S., Hirani A.N., Desbrun M. Barycentric coordinates for convex sets // Advances in Computational Mathematics. 2007. V. 27. № 3. P. 319-338.
9. Wachspress E.L.A rational finite element basis. New York: Academic Press. 1975.
10. Loop C.T., DeRose T.V. A multisided generalization of Bezier surfaces // ACM Transactions on Graphics. 1989. V. 8. P. 204-234.
11. Ajjzenberg G.Z. Antenny UKV. V 2 chastjakh. CH. 1. M.: Svjaz. 1977.
12. Drabkin A.L., Zuzenko V.L., Kislov A.G. Antenno-fidernye ustrojjstva. M.: Sov. radio. 1974.
13. Kobzar A.I. Prikladnaja matematicheskaja statistika. Dlja inzhenerov i nauchnykh rabotnikov. M.: FIZMATLIT. 2006.
14. Vasilev F.P. CHislennye metody reshenija ehkstremalnykh zadach. M.: Nauka. 1980.
15. Vud P. Analiz i proektirovanie zerkalnykh antenn / per. s angl. M.: Radio i svjaz. 1984.
16. Poljanskijj I.S., Stepanov D.E., Frolov M.M. Gibridnyjj geneticheskijj metod s gradientnym obucheniem i prognozirovaniem dlja reshenija zadach globalnojj optimizacii mnogoehkstremalnykh funkcijj // Vestnik Brjanskogo gosudarstvennogo tekhnicheskogo un-ta. 2014. №3 (43). S. 138-146.
17. Poljanskijj I.S. Baricentricheskie koordinaty Puassona dlja mnogomernojj approksimacii skaljarnogo potenciala vnutri proizvolnojj oblasti (CH. 1) // Vestnik SGTU. 2015. №1 (78). S. 30-36.
18. Poljanskijj I.S. Baricentricheskie koordinaty Puassona dlja mnogomernojj approksimacii skaljarnogo potenciala vnutri proizvolnojj oblasti (CH. 2) // Vestnik SGTU. 2015. №1 (78). S. 36-42.
19. Arkhipov N.S., Poljanskijj I.S. Metody analiza i strukturno-parametricheskogo sinteza zerkalnykh antenn. Orjol: Akademija FSO Rossii. 2014.
20. Somov A.M., Arkhipov N.S., Poljanskijj I.S., Stepanov D.E. Raschet diagramm napravlennosti zerkalnykh antenn v priblizhenii metodov fizicheskojj optiki i fizicheskojj teorii difrakcii // Trudy NIIR. 2015. № 2.