Least Squares Finite-Difference Time-Domain

A central least-squares spatial derivative procedure is developed. It provides simple formulas, similar to finite differences, to approximate spatial derivatives. In addition, a least-squares finite-difference time-domain (LS-FDTD) method is formulated for attenuating high-frequency nonphysical modes, superimposed to physical solution, produced by Yee's space discretization when the time step is larger than Courant-Friedrichs-Lewy (CFL) limit. The proposed method is successfully validated by solving 1-D and 2-D problems with time steps beyond the FDTD CFL limit. Accuracy and stability conditions are analytically obtained for LS-FDTD.