辛算法及其在电磁场方程中的应用

许多基本的物理问题都可描述成Hamilton系统。Hamilton系统的主要特征是保持系统的相空间体积不变和总能量不变，因此在建立求解Hamilton系统的算法时，要力争算法能保持这些基本特征，以保证算法的逼真性。辛算法是近年来发展起来的求解Hamilton系统的新算法。本文介绍有限维和无限维Hamilton系统的辛算法的基本理论和在求解电磁场方程中的应用。

Symplectic Algorithms and Its Applications in Electromagnetic Field Equations

Most of the fundamental physical problems can be formulated as a Hamilton system. An appropriate numerical method for the solution of the Hamilton system is the symplectic integration that preserves the most important properties of the Hamilton system such as conserving phase volume and total energy. In this paper we give an introduction to the theory of symplectic geometry and then study the symplectic algorithms and their applications in electromagnetic field equations.