Modeling the Spatial Distribution of the Magnetic Field in Magnetic Systems of Electrical Devices Using Block Elements and Fundamental Solutions

The problem of modeling the spatial distribution of the magnetic field in a ferromagnetic medium with nonlinear characteristics is solved. For the calculation, it is proposed to use block elements in the form of polygons of arbitrary shape. Discretization of the considered boundary value problems is performed by partitioning the computational domain into block elements and linearizing the material equation within each element. The distribution of the field potential inside each block element is proposed to be specified using the fundamental solutions of the Laplace equations and their conjugate functions. The algorithm for solving the boundary condition inversion problem in each block element is given, the application of which allows to set the coupling equations for the potential and the normal derivative on the element boundary. It is proposed to replace block elements with multipoles described by equations with undefined conductance matrices. The conductance matrices that define the relations between magnetic fluxes and voltages are determined by inverting the boundary conditions in each block element by the results of solving boundary value problems formulated in a special way. The analysis procedure of the magnetic circuit formed by multipoles, the connection of which corresponds to the accepted partition of the computational domain, is described. The algorithm for numerical solving an overdetermined system of linear algebraic equations arising in the analysis of a magnetic circuit is constructed. The example of calculating the fluxes distribution is given and the error is estimated.