Numerical analysis of thin skin depths of 3-D eddy-current problems using a combination of finite element and meshless methods

To alleviate the difficulties encountered in the generation of meshes for the finite element method for solving thin skin depth problems involving three-dimensional (3-D) eddy-currents, particularly in cases in which the eddy-current region is only a fraction of the entire domain, a new technique based on the combination of finite element and meshless methods is proposed. The use of numerical approach to uphold the mathematical properties of the combined shape functions in terms of consistency and linear independence is also investigated. It is shown that a very coarse mesh is already sufficient to give accurate numerical results with the proposed algorithm. To validate and demonstrate the advantages of the proposed method, typical numerical results on studies of high-frequency 3-D eddy-current problems are reported.