Numerical method for solving of synthesis problems of radiating systems on a prescribed power directivity pattern


  • P. O. Savenko Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of National Academy of Sciences of Ukraine, Ukraine



numerical method, synthesis problems, variational approach, power directivity pattern


A numerical solution method is presented for nonlinear problems in radiator synthesis, based on a prescribed power directivity pattern (DP). A variational problem is considered in which both mean square deviation between the prescribed and synthesized DPs and constraints imposed on the norm of excitation sources are taken into account. An existence theorem is proved for quasi-solutions, and the corresponding Euler-Lagrange equation is derived to determine them. Convergence criteria are found, and the convergence of the iterative processes employed in computing the problem is proved. For a linear radiator, the theory of branching of solutions to nonlinear equations is invoked to determine the general solution structure used in the numerical analysis of the problem.


Markov, G.T.; Petrov, B.M.; Grudinskaya, G.P. Electrodynamics and Radio Wave Propagation. Moscow: Sovetskoe Radio, 1979.

Tikhonov, A.N.; Arsenin, V.Y. Solution Methods for Ill-Posed Problems. Moscow: Nauka, 1979.

Savenko, P.A. Nonlinear Problems of Radiating Systems synthesis. Lviv: IAPMM NASU, 2002.

Savenko, P.A. Numerical Solution of Inverse Problems in the Theory of Radiator Synthesis Based on a Prescribed Power Pattern. Computational Mathematics and Mathematical Physics, 2002, Vol. 42, No. 10, p. 1495-1509.

Vainberg, M.M. Variational Method and Method of Monotone Operators. Moscow: Nauka, 1972.

Vainberg, M.M. Functional Analysis. Moscow: Prosveshchenie, 1979.

Krasnosel'kii, M.A.; Vainikko, G.M.; Zabreiko, P.P.; et. al. Approximate Solution of Operator Equations. Moscow: Nauka, 1969.

Vainberg, M.M.; Trenogin, V.A. Theory of Bifurcation of Solutions to Nonlinear Equations. Moscow: Nauka, 1972.

Minkovich, B.M.; Yakovlev, V.P. Theory of Antenna Synthesis. Moscow: Sovetskoe Radio, 1969.