Yu.P. Topolyuk

Calculation of waves scattered in irregular waveguides

Wave scattering problems in irregular waveguides are investigated. The proposed algorithm for solving such problems is based on the reduction of the scattering problem to an interior boundary value problem in the irregular section. This problem is solved in general form by the boundary integral equation method and then the solutions in regular and irregular sections are matched. The scalar Dirichlet problem with excitation by a wave, incident from infinity, is considered. The approach is applied to a test problem and numerical results are compared with the ones obtained by the cross section method.

About local properties of gradient method for free phase problem with isometric operator

Variational problem on pseudo-solutions of the free phase equation an isometric operator in Hilbert spaces is considered. Local relaxation property of the gradient method and weak convergence are proven.

Numerical comparison of two methods for irregular waveguide

Two methods of solving the problem of scattering in irregular waveguides are compared. The methods are used to calculate the field in waveguides with smooth and non-smooth irregularities. Numerical results showing the efficiency of those methods are presented.

Convergence of the consecutive approximation method of a solution of the nonlinear problems of the antennas synthesis

The weak convergence of a consecutive approximation method of a solution of the nonlinear equation is proved. The problem of searching of a pseudo-solution of the equations with a free phase is reduced to this equation. The operator of the equation is a superposition of the linear limited operator and nonlinear operator (modulus of a complex function). In this case the linear operator of the problem is completely continuous.

Stability of the solutions to synthesis problems of radiating systems according to power radiation pattern

The nonlinear synthesis problems of radiating systems with use of energy criterion is considered. Stability of the approximate pseudosolutions with respect to the right part of the equation errors are proved.

Convergence of the regularization method in free phase problem

The problem with free phase is considered. Convergence of the regularization method for approximate a pseudosolutions with respect to the operator of the equation errors are proved.

Convergence of Gradient Method for Free Phase Problem with Isometric Operator

Problem of finding pseudo-solutions of the free phase equation an isometric operator in Hilbert spaces is considered. Convergence property of the gradient method are proven

On differentiability of a functional arisen in antenna synthesis theory

A nonlinear functional which has arisen in antenna synthesis theory according to the amplitude radiation pattern, is considered. The functional contains the modulus of a complex function; it is not Gateaux differentiable in complex Hilbertian spaces. The problem is reformulated for appropriate real spaces in which the functional is Gateaux differentiable.