基于传输线法的非线性静磁场四边形有限元加速求解方法研究

Finite element method (FEM) is the most commonly used numerical computation method. With the increasing complex solution models and the advent of multi-physics problems, the time cost using the finite element method is one of the headaches for simulation engineers. To solve the overlong solution time of finite element method and accelerate the solving process, this paper proposed a black-box circuit model based on the transmission line method (TLM) to solve the magnetostatic problem using FEM with quadrilateral shape element. Firstly, we introduced the principle of TLM and applied the traditional Galerkin method into the quadrilateral shape finite element to obtain the global stiffness matrix. Then the nonlinear finite element matrix was modelled as nonlinear circuit network according to the equivalence of admittance matrix. Finally, we solved the circuit network using TLM iteration. The distribution of an axisymmetrical contactor's magnetostatic field was obtained by the method proposed. Compared with the traditional Newton-Raphson (NR) iteration and commercial FEM software COMSOL, the feasibility and correctness of the method was verified.