A doubly periodic problem of magnetostatics

Integral equations are obtained for the magnetic field in a regular spatially two-dimensional heterogeneous medium. A method for the numerical solution of the basic equation is proved, and is particular, the bounds are obtained for the method of simple iteration to be applicable. The rate of convergence of the iterative process is expressed in terms of the physical properties of the medium, which in general is assumed to be non-linear, inhomogeneous, and anisotropic.