Design of Least-Squares Time Integrators for Reliable FDTD Simulations

Considering the importance of providing credible discrete models for Maxwell's equations, improved time integrators are constructed in this paper for reliable time-domain simulations of wave-propagation problems. The proposed design approach results in modified versions of high-order leapfrog processes that feature error-reducing behavior, in the sense that numerically-induced flaws are efficiently dealt with. Accuracy upgrade is accomplished via proper application of the least-squares technique, whereas the incorporation of optimized spatial expressions can further improve the wideband behavior. The combination of the proposed integrators with standard as well as optimized approximations in space is examined in numerical experiments, and it is shown that our treatment of time integration can contribute decisively to the foundation of reliable and efficient computational models.