A Comparison of Some 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 discretises Eoarr, Boarr, Hoarr and Doarr and the EB formulation that discretises only Eoarr and Boarr. The latter two formulations use a combination of 1-form and 2-form discretisation to avoid an auxiliary mesh. A method for making the EBHD formulation operational is presented and conditions for finite difference time domain (FDTD)-like explicit operation are discussed. Numerical results for a three dimensional cavity and a coaxial transmission line show that the EBHD formulation has serious performance limitations.