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.