The Novel Mathematical Model and Methodology for Computer Simulation of Magnetic Field in a Nonlinear Medium

Abstract

Introduction. Magnetic devices of various types are used in production equipment. Designing and modernizing such equipment requires a signifi cant bulk of calculations of magnetic fi elds and parameters of magnetic devices. This task is diffi cult due to large dimensionality of the system of equations and nonlinear properties of magnetic materials.Problem Statement. Due to the nonlinearity of diff erential and integral equations on which these calculations are based, they need to be solved numerically by iterative methods, the convergence of which is often uncertain. This requires powerful computing tools and considerable time. Therefore, the problem of improving mathematical mo dels and increasing the computational effi ciency of the corresponding algorithms is relevant.Purpose. To develop a mathematical model of a magnetic fi eld in a nonlinear medium in the form of a surface integral equation for a quasilinear space and a computer modeling technique with increased computational effi ciency.Material and Methods. The material of the study is the mathematical models of the magnetic fi eld in a nonlinear medium of magnetic materials and the computational properties of the corresponding algorithms. The methods of vector analysis of diff erential operators and synthesis of modifi ed formulas in the magnetic fi eld equations have been used in the work.Results. The newest mathematical model of the magnetic fi eld in which the volumetric equation for a nonlinear medium is reduced to a surface equation in quasi-linear space, which reduces the dimensionality of data arrays by one order of magnitude and the number of computational operations by two orders of magnitude, has been substantiated. On this basis, a methodology for computer modeling of fi elds with the use of a unifi ed magnetization curve has been developed.Conclusions. The applicability of this methodology to various magnetic materials and its effi ciency have been confi rmed by the example of a model problem of practical importance for improving the algorithms for calculating and analyzing magnetic fi elds in magnetic systems with nonlinear elements.