The 3-D Unconditionally Stable Multisymplectic FDTD Method for the Computational Electromagnetic Simulation

This research presents a three-dimensional unconditionally stable multisymplectic finite-difference time-domain (MS-FDTD) method, marking a significant advance in computational electromagnetics. For the first time, the local one-dimensional (LOD)-FDTD method is applied to the multisymplectic Preissman scheme of Maxwell’s equations. A new grid arrangement for electric and magnetic fields is designed to meet MS-FDTD discretization requirements, differing fundamentally from the traditional Yee grid. We have derived the detailed equations and techniques for implementing various boundary conditions in the proposed method. An in-depth analysis of numerical dispersion has been conducted, demonstrating the method’s superior characteristics in this regard compared to traditional FDTD methods. Additionally, the unconditional stability of our method has been thoroughly confirmed. Comprehensive simulations, including cavity resonances, bioelectromagnetic problems, and on-chip applications, validate its accuracy, efficiency, and long-term stability. This work integrates multisymplectic theory, originating from mathematics, into computational electromagnetics, providing a novel framework for numerical algorithms.