The impact of Whitney forms on computational electromagnetics

Edge elements are now known to be appropriate basis functions for the finite element method (FEM) applied to many microwave applications. Bossavit (1988, 1989) has presented edge elements as belonging to Whitney forms. In fact, he has argued for an approach based on differential forms from which the Whitney forms come out naturally when the discretization is concerned. We emphasize the role that the Whitney forms could play in computational electromagnetics by pointing out some direct consequences of their use. Considering the Whitney forms is well beyond just providing adequate basis functions in the Galerkin procedure. It allows one to fully understand why and how edge elements work so well and further sheds light on the discretization not only of the FEM but also of other numerical methods. First, we recall the elementary properties of Whitney forms. Then the discretization of Maxwell equations is tackled in this context. A possible analogy with circuit laws and the similarity with other methods are shown.