A Hybrid Indirect–Direct Coupling Method for Strongly Coupled Nonlinear Magnetic Problems

Numerical simulations of nonlinear magnetic problems incorporating interactions of electromagnetics with material properties, thermal issues, and other physical fields, have recently attracted great interest among researchers. In this paper, the coupling strength of these interaction processes is defined. Based on this quantitative definition, we demonstrate that for strongly coupled magnetic problems a conventional indirect coupling scheme is likely to diverge. To overcome this difficulty, a hybrid indirect-direct coupling method is developed. The proposed method is a synergistic combination of a direct coupling scheme-for dealing with the nonlinearity of the coupled systems-and an indirect coupling scheme for preconditioning the heterogeneous systems. To improve the performance of the proposed method for strongly coupled systems, a parametric continuation strategy is introduced. The efficiency of the proposed method is validated through numerical tests.