We discuss briefly theoretical background of FEM and WBM and mathematical description of coupled FE/WB approach.FEM and WBM show advantages in wide application and high convergence rate,respectively.A coupling of predication tools benefits from advantages of both.The basic idea is to replace parts in the finite element mode,which have simple geometrical shapes,by much smaller wave models.It results in a coupled model with less degree of freedom.This allows a further refinement of model,which leads to an improved accuracy at higher frequencies and reduces number of degree of freedom by modal reduction techniques.Numerical example indicates that the proposed method has potential in covering a range with mid-frequency.

Based on the initial FMM,an FMM algorithm is proposed to solve electrostatic field problem.The algorithm introduces diagonalization to reduce time in forming local spread coefficient and enhance the computing efficiency.The computing speed and high precision of the algorithm in dealing with large-scale issue are shown with numerical examples.