Two-Dimensional Time-Domain Algorithm With Adaptive Spectral Properties

We develop a two-dimensional scheme, whose spectral properties exhibit a certain degree of controllability, as an alternative to the classic finite-difference time-domain method. The new approach adopts a nonstandard structure for the spatial operators, whose final form is determined through a consistent error-minimization procedure. It is shown that isotropic improvement of accuracy can be accomplished at a single frequency, while the case of wider bands is handled with the aid of a least-squares mechanism. Reliable performance is ensured by the proposed algorithm, without compromising the stability region or requiring excessive computational resources.