Iterative methods of calculating statistical fields in inhomogeneous, anisotropic and nonlinear media

A general theory of iterative methods for calculating electrostatic and magnetostatic fields is developed on the basis of a physical representation of secondary sources. Methods of calculating statistical fields in piecewise-homogeneous fields, including electrostatic fields produced by charged conductors and statistical fields in piecewise-homogeneous anisotropic media, are presented. The mathematical description of the properties of a medium is considered and sufficient conditions for the convergence of iterational methods are formulated. Iterative methods based on reduction to calculations of statistical fields in infinite homogeneous, isotropic media and statistical fields in piecewise-homogeneous media are examined and Galerkin and finite element methods are developed. The application of the Newton-Kantorovich and parameter continuation methods to the calculation of a statistical magnetic field in a nonlinear ferromagnetic medium is discussed and iterative methods of modeling statistical fields in inhomogeneous, anisotropic and nonlinear media are presented.