The Application Of Symplectic Schemes In The Electromagnetic Wave 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 electromagnetics computation. The main studies are as follows:In this paper, the arithmetic theory on symplectic scheme is introduced, which is constructed based on the Runge-Kutta algorithm. The constructed algorithm is applied in one-dimension Maxwell equation group in time-domain, and the emulation results shows the algorithm matches with analytical solution well and also the algorithm can be applied in electromagnetic wave calculation. And it is applied in two-dimension TM wave for the first time, the emulation analysis on the eyes which are shoot obverse by electromagnetic wave shows that the symplectic scheme is validity.