A Hybrid ADI and SBTD Scheme for Unconditionally Stable Time-Domain Solutions of Maxwell´s Equations

Based upon the sampling bi-orthogonal algorithm and alternating direction implicit scheme, we present an unconditionally stable time-domain method, SB-ADI. Similar to the ADI scheme, this method is a second-order approximation in temporal discretization. However, theoretically, the new method produces no spatial discretization error due to the sampling property and compact support of the SBTD algorithm. Dispersion and stability analysis are presented. In a numerical example of 2-D electromagnetic bandgap structure, the new method has reduced the error by a factor of 3.5 at 16% increase of CPU time with respect to the standard ADI.