Department of Electrical and Electronic Engineering, University of Stellenbosch, Stellenbosch 7602, South Africa
Marais, N., Department of Electrical and Electronic Engineering, University of Stellenbosch, Stellenbosch 7602, South Africa; Davidson, D.B., Department of Electrical and Electronic Engineering, University of Stellenbosch, Stellenbosch 7602, South Africa
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, B, H and D and the EB formulation that discretizes only E and B. 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. © 2008 IEEE.
Electromagnetism; Finite difference time domain method; Maxwell equations; Numerical methods; Three dimensional; Time domain analysis; Transient analysis; Transients; Wave equations; Discretization; Electro-magnetics; Electromagnetic transient analysis; Field representations; Finite difference time domains; Finite element methods; Finite element time domains; Fourth orders; High orders; High-order methods; Maxwell's equations; Novel methods; Numerical analysis; Numerical evaluations; Numerical results; Performance limitations; Time domains; Time integrations; Vector wave equations; Finite element method