A hybrid finite element method for 3-D scattering using nodal and edge elements

Hybrid finite element methods (HFEM) as used in the present paper refer to a coupling of the finite element method (FEM) applied to Maxwell´s equations in differential form and the method of moments (MOM) applied to Maxwell´s equations in integral form. This coupling allows the strengths of each method to supplant the other. The finite element method models penetrable materials and complicated geometry, while the method of moments provides the exact radiation boundary condition where the finite element mesh is terminated. In the paper a three-dimensional HFEM implementation is presented. As in Boyse and Seidl (1991), the finite element formulation is coupled to a highly efficient BOR MOM code which provides the exact near field radiation condition. The scalar and vector potential formulation completely eliminates spurious modes when using nodal based elements, allowing iterative methods to rapidly converge and the computation of very accurate internal fields. However, calculations involving models with sharp corners initially produced very inaccurate results. A new element (Boyse et al., 1992 and Bardi et al., 1993) was used along corners and edges which combines both nodal and edge basis functions. The addition of these new elements produces very accurate results while retaining conventional nodal elements throughout most of the model.