Differential Forms Inspired Discretization for Finite Element Analysis of Inhomogeneous Waveguides (Invited Paper)

We present a difierential forms inspired discretization for variational flnite element analysis of inhomogeneous waveguides. The variational expression of the governing equation involves transverse flelds only. The conventional discretization with edge elements yields an unsolvable generalized eigenvalue problem since one of the sparse matrix is singular. Inspired by the difierential forms where the Hodge operator transforms 1-forms to 2-forms, we propose to discretize the electric and magnetic fleld with curl-conforming basis functions on the primal and dual grid, and discretize the magnetic ∞ux density and electric displacement fleld with the divergence-conforming basis functions on the primal and dual grid, respectively. The resultant eigenvalue problem is well-conditioned and easy to solve. The proposed scheme is validated by several numerical examples.

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