哈密尔顿系统的分裂步多辛数值积分(英文)

The Splitting Multisymplectic Numerical Methods for Hamiltonian Systems

对哈密尔顿系统而言,辛或多辛积分较传统的数值方法具有优越性.然而,此类数值格式大部分都是隐式的,从而在每一个时间步需要求解一个非线性的代数方程组,这将直接导致计算效率不高.在多辛积分中引进分裂步技巧,称之为分裂步多辛积分,可以弥补这一不足之处,这一数值方法的框架将在该文中简要地讨论,其中,数值例子给出了该方法在物理问题中的应用.

For Hamiltonian systems,symplectic integrators or multisymplectic integrators are superior to traditional numerica methods for Hamiltonian systems. However,most of them are implicit and engender a coupled nonlinear algebraic system at every time step. It leads to reduce the computational efficiency directly. Splitting multisymplectic integrator which combines multisymplectic integrators with splitting technique can offset this flaw. The framework of this numerical method will be briefly reviewed. Some numerical examples are shown to illustrate the application of the methods in physics.