3-D nonlinear magnetic field analysis with a novel adaptive finite element method

In this paper, an adaptive degrees-of-freedom finite element method is extended to three-dimensional (3-D) nonlinear magnetic field analysis. The error distribution of the discrete solution changes along with the iterative process, and mesh coarsening or other operations with the same effect is needed to keep the scale of the problem small. In this proposed adaptive method, dispensable degrees of freedom (DoFs) are eliminated from the unknown list by constraining them with supplementary interpolation functions, which are formulated with master DoFs. Compared with mesh coarsening, the administration of DoFs and geometric data are no longer required, while the topology of the mesh is maintained. To extend to 3-D problems, a novel constraint, which produces accurate coefficients for an alterable number of master DoFs, is presented. The constraint is integrated into the element algebraic equation, followed by a conventional assembly. Other techniques for the adaptive algorithm are also included in this method. Several numerical examples are tested to showcase the effectiveness of this method in 3-D problems.