Differential forms inspired finite element discretization for waveguide eigenvalue problems

A differential forms inspired finite element based discretization scheme for waveguide eigenvalue problems is presented. Naïve discretization of the governing variational expression involving only transverse fields with edge elements renders the discretized eigen-equation unsolvable. Motivated by differential forms, in the proposed scheme, electric and magnetic fields are discretized with curl-conforming basis functions on the primal and dual grids, respectively. Meanwhile, magnetic flux density and electric displacement fields are discretized with divergence-conforming basis functions on the primal and dual grids, respectively. Matrices in the resultant eigen-equation is well-conditioned and easy to solve, which is validated by several numerical examples.