High-Order Symplectic Compact Finite-Different Time-Domain Algorithm for Guide-Wave Structures

Based on higher order symplectic integrator temporal derivatives and compact spatial derivatives, a new high-order symplectic compact finite-difference time-domain (FDTD) algorithm is proposed. The numerical stability criteria and dispersion relation are derived analytically. Compared with the traditional compact FDTD algorithm, the proposed algorithm can significantly reduce the numerical dispersion error and can be made nearly independent of the maximum limitation of the Courant-Friedrich-Levy law. By means of the numerical examples, the proposed algorithm has the benefit of conserving energy for long-time propagation, which can be used to enhance the computational efficiency for the full-wave-analysis of guided-wave structures.