Higher-order (LT/QN) vector finite elements for waveguide analysis - Davidson, David B. (Applied Computational Electromagnetics Society Journal (ACES), 2022)
The finite element (FE) formulation for waveguide discontinuity analysis is reviewed and extended to multiple, arbitrarily-oriented ports. Several higher-order vector elements - specifically hierarchal linear tangential/quadratic normal (LT/QN) - are compared, and the extensions required to incorporate LT/QN elements in the formulation are presented. The improved accuracy afforded by LT/QN elements compared to constant tangential/linear normal (CT/LN) elements is investigated by considering energy conservation in an empty waveguide. Results obtained using both CT/LN and LT/QN elements are also shown for a problem of engineering interest: an E-plane bend. Results for the LT/QN elements compare especially well to approximate analytical results using quite coarse meshes. The paper concludes with a discussion of the use of iterative solvers and possible convergence problems encountered when using higher-order elements.