COMPUTATION OF 3-D ELECTROMAGNETIC-FIELD USING DIFFERENTIAL FORMS BASED ELEMENTS AND DUAL FORMULATIONS

The vector and scalar variables describing electromagnetic fields with different requirements of continuity can be identified to four differ ent degrees of differential forms. The association of differential for ms with finite elements leads to a set of differential forms based ele ments (Whitney elements); they are naturally adapted to the discretiza tion of different vector and scalar variables. With the help of a Tont i diagram, Maxwell equations can be classified by two dual sequences t ogether with the constitutive laws of materials. The application of Wh itney elements to the two dual sequences leads to two dual approximati on schemes. As an example, two dual formulations for eddy current comp utation using potential variables and the hybrid finite element-bounda ry element method are derived, where Whitney 3-D and 2-D elements are employed. A numerical application is given at the end of the paper, wh ere the dual features of the two formulations are reported.