Numerical Evaluation of High-Order Finite Element Time Domain Formulations in Electromagnetics

This paper compares three full-wave finite-element time-domain (FETD) formulations. The first is based on the vector wave equation; the others on Maxwell's equations,
viz
. the EBHD formulation that discretizes
E

^rarr
,
B

^rarr
,
H

^rarr
and D
^rarr
and the EB formulation that discretizes only
E

^rarr
and
B

^rarr
. The latter two formulations use a combination of 1- and 2-form discretization to avoid an auxiliary mesh. A novel method for making the EBHD formulation operational is presented. Conditions for finite-difference time-domain (FDTD)-like explicit operation are discussed. The formulations are compared numerically by solving a three-dimensional cavity and a rectangular waveguide using high-order field representations up to mixed fourth order. The error balance between time integration and field representation is investigated. Difficulties in making the EBHD formulation operational which have not previously been addressed in the literature are discussed and worked around. Novel numerical results show that the EBHD formulation has serious performance limitations.