Magnetic Fields by the Combined Method of Finite Elements and Fundamental Solutions with Point Magnetic Moments

Abstract

The article is devoted to mathematical modeling of three-dimensional magnetic fields in unbounded domains containing subdomains with nonlinear dependences B(H). The method for modeling the specified fields is proposed. Its application is considered on the example of the calculation of the magnetic field and the determination of the magnetomotive force of a two-stroke actuator, the active element of which is made of a ferromagnetic shape memory alloys. The computational algorithm is based on the combined finite element method (field calculation in nonlinear subdomains) and the method of fundamental solutions (field calculation in the space surrounding the ferromagnetics). The decomposition of the field is performed in a linear subdomain into two fields – from coils with current and the magnetization of a ferromagnet, which allows scalar variables to be used instead of vector variables. For the first time in the method of fundamental solutions, point vector magnetic moments are used, allowing not only to increase the accuracy of the method, which is proved by solving the test problem, but also to eliminate the numerical instability characteristic of magnetic dipoles. The obtained results are allowed effectively solve direct and inverse problems of three-dimensional magnetic fields in the design and identification of electrical devices.