A novel hybrid finite difference time domain-wavelet-Galerkin (FDTD-WG) technique is presented for the accurate representation of electromagnetic field solutions in regions of fast field transitions. Its fundamental concept lies in the combination of the robust FDTD method with the wavelet-Galerkin formulation, which in its turn can efficiently treat highly varying phenomena. The computational domain is, therefore, divided into regions of smooth and fast field variations. Proper determination of these two areas leads to improved simulations and significantly reduced computational burden, turning the proposed scheme into a powerful tool. Numerical results derived from the manipulation of various waveguides, proves the validity and efficacy of the new scheme
Tsiboukis et al. (Sun,) studied this question.