Finite-difference and finite-volume time-domain techniques: comparison and hybridization

Time-domain differential equation solvers, such as the finite-difference and finite-volume time-domain (FDTD and FVTD) algorithms, are receiving considerable attention as viable solution techniques for complex radiation and scattering problems. These techniques arise from using discrete approximations to the calculus operators in Maxwell´s time-domain equations. However, despite the similarities between these two algorithms, they are surprisingly different in their formulations, their implementations, and most importantly their domains of applicability. This paper compares these methodologies in terms of their development and capabilities. Numerical examples are used to demonstrate their relative accuracy and computational requirements for different problems. A novel hybrid technique which builds upon the modeling strengths of each algorithm is also proposed and demonstrated through representative numerical examples.