The locally one-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates is extended to a frequency-dependent version. The fundamental scheme is utilized to perform matrix-operator-free formulations in the right-hand sides. For the analysis of surface plasmon polaritons propagating along a plasmonic grating, the computation time is significantly reduced to less than 10%, compared with the explicit cylindrical FDTD method.

An efficient three-dimensional (3-D) fundamental locally one-dimensional finite-difference time-domain (FLOD-FDTD) method incorporated with memristor is presented. The FLOD-FDTD method achieves higher efficiency and simplicity with matrix-operator-free right-hand sides (RHS). The updating equations of memristor-incorporated FLOD-FDTD method are derived in detail. Numerical results are provided to show the trade-off between efficiency and accuracy.