V.M. Sveshnikov - Dr.Sc. (Phys.-Math.), Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences; Professor, Novosibirsk State University. Е-mail: victor@lapasrv.sscc.ru

Poincare-Steklov equation is known from the solution of linear problems of mathematical physics by the domain decomposition method. In this paper, this equation is proposed to use for calculating the intensive charged particle beams in nonlinear self-consistent problem of electron optics. The algorithm for solving nonlinear Poincare-Steklov equation defines iterative process for solving the nonlinear problem of electron optics. The essence of the proposed approach is as follows. The computational domain is divided into two subdomains: the near-cathode and the main. In the near-cathode subdomain analytical solution is built and in the main subdomain solution is found numerically. Central question is crosslinking subdomains. To do this, Poincare-Steklov equation is written on the boundary of subdomains that is approximated by a system of nonlinear operator equations. Its solution is carried out by Broyden method. As follows from the numerical experiment, already in the fourth iteration the Broyden process is converged with acceptable accuracy for practical purposes.

 

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