Abstract: The study is devoted to mathematical modeling of magnetic fields of positioning systems, the active elements of which are made of ferromagnets with shape memory effect. The development of effective systems of mathematical modeling of three-dimensional magnetic fields, necessary at the stage of design of positioning systems with ferromagnets with shape memory as well as the identification and diagnosis of such systems is relevant. In this study, one of the ways to increase the efficiency of modeling systems is considered. This is the application of a combined method combining the finite element grid method for field analysis in nonlinear calculation subdomains (ferromagnets) and the gridless method of fundamental solutions for calculating the field in linear subdomains (surrounding ferromagnet space and coils with current). The computational algorithm is developed on the basis of the mathematical model and the results of the solution of the test problem. Examples of its application are given. A distinctive feature of the proposed approach is the creation of a mathematical model of minimum dimension which provides a significant reduction in the calculation time. For the first time, vector point fictitious magnetic moments are used for the analysis of electromagnetic systems by the method of fundamental solutions. The new point sources of the field provide higher accuracy of calculation in comparison with magnetic dipoles. This allows solving the problems of designing positioning systems, performing their diagnostics in real time.
A.L. Balaban, Yu. A. Bakhvalov and V.V. Grechikhin, 2019. Mathematical Modeling of Magnetic Fields of Actuators with Hape Memory Effect by a Combined Finite Element Method and Fundamental Solutions with Point Magnetic Moments. Journal of Engineering and Applied Sciences, 14: 5670-5677.