An Unconditionally Stable Laguerre-Based S-MRTD Time-Domain Scheme

A time-domain method that combines the scaling function-based multiresolution time domain (S-MRTD) technique with a Laguerre polynomial-based time-integration scheme is formulated, applied, and evaluated in this letter. The motivation for this work stems from the fact that the disadvantages of each of these two techniques can be compensated for by the strength of the other. Namely, while S-MRTD suffers from a reduced Courant number than the finite difference time domain (FDTD), the use of the Laguerre time-integration renders it unconditionally stable. In turn, Laguerre-FDTD is an implicit method, based on matrix inversion. The coarse gridding that S-MRTD allows for leads to significant reduction in the size of this matrix. Specific numerical experiments indicate the improved performance of this Laguerre-S-MRTD approach, compared to its two constituent techniques and thus its significant potential as a novel time-domain solver.