Abstract
For analyses of problems of three-dimensional electromagnetic fields by methods of finite elements, formulation based on hexagonal edge elements was used which also was applicable to bodies of arbitrary shape. In previous formulation, a combination of tetrahedral elements was used to construct hexagonal edge elements. This paper proposes the use of vectorial shape functions in constructing hexagonal edge elements. Their shape functions agreed with the Nedelec-type elements when a hexagonal body was reduced to a rectangular solid. However, spurious solutions were generated when the body shape deviated from the rectangular solid. Therefore, it is necessary to incorporate Lagrange multipliers as new unknowns in applying elements obtained by the authors to a general three-dimensional body model. The final discretized equation becomes a simultaneous equation and is not solved by an eigenvalue problem. As a general model, a circular cylindrical cavity was treated and the resonant frequencies and excitation responses were obtained. For the resonant frequencies, the results obtained herein are compared with those by using the Nedelec-type tetrahedral elements.
Published Version
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