An accurate waveguide port boundary condition for the time-domain finite-element method

This paper presents an accurate time-domain waveguide port boundary condition (WPBC) that can be used as a mesh truncation boundary condition to terminate a finite-element mesh. The formulation for deriving the boundary condition is based on multimodal expansion, and thus is related to the modal absorbing boundary conditions developed for the finite-difference time-domain method. The boundary condition is formulated for the general three-dimensional analysis of waveguides with an arbitrary cross section. All waveguide modes, including transverse electromagnetic, transverse electric, and transverse magnetic modes, are accounted for in the boundary condition in a unified formulation. Both propagating and evanescent modes can be properly absorbed. The proposed formulation is validated by numerical examples, and the accuracy and stability of the algorithm are investigated.