The Application Of Symplectic Schemes In The Time-domain Electromagnetics Scattering Computations

The computational electromagnetics have been developed rapidly with the emergence of new schemes in numerical mathematics and physics in recent years. Various numerical methods for electromagnetics simulations are proposed, but these methods have difficulties in the aspect of simulations time, required memory and accuracy. In additional, with the depth of the knowledge of the physical characters of the problems, people realized that it is also important to keep some features of the original system while pursuing the high accuracy of the schemes. Since the electromagnetics field equations can be rewritten as an infinite dimensional Hamiltonian system, which has some insight characters, the proper solution should be obtained using symplectic schemes. The symplectic schemes have the ability to preserve the global symplectic structure of the phase space for a Hamiltonian system. They have substantial benefits in numerical computation for Hamiltonian system, especially in long-term simulations. The dissertation introduced symplectic schemes for electromagnetics simulations, mainly focus on the application of the schemes in time-domain computation.The main studies are as follows:(1).Introduced the mathematics theories foundation of the symplectic schemes, include the commonly established methods for construction symplectic schemes, which are symplectic Runge- Kutta method, symplectic propagation techniques and generating function method. A minimization of the truncation error-function and optimal Courant-Friedrichs-Levy (CFL) number schemes are well established using sympletic propagation techniques.(2).The symplectic schemes for two-dimensional electromagnetics scattering problems are well established, including the schemes for separable Hamiltonian system using symplectic propagation techniques, the symplectic partitioned Runge-Kutta(PRK) schemes for non-separable Hamiltonian system for the first time. The stability and numerical dispersion were analyzed; numerical results show the efficiency of the schemes.(3).The symplectic finite-difference time-domain (SFDTD) schemes were introduced in numerical solution of three-dimensional electromagnetics. The stability and numerical dispersion for SFDTD schemes were analyzed for the first time. Numerical results show SFDTD schemes are superior to standard FDTD and high order FDTD. Especially, the introduction of the high order SFDTD schemes provides a new way for solution of three-dimensional electric largely objects scattering problems.(4).The total field and scattered field (TF-SF) technique is derived for the SFDTD method to provide the incident wave source conditions, the absorbing boundary conditions (ABC) and the improved high order perfectly matched layers (PML) ABC, the high order near field-far field transform, are all well established. All those provided the necessary techniques for three-dimensional electric largely objects scattering computations.(5).The symplectic schemes are applied to the time-domain simulation of benchmark objects scattering problems. The stability and accuracy are compared with the commonly used methods such as FDTD and high order FDTD. The results further confirmed the accuracy and efficiently of the symplectic schemes.