Dirac方程的紧致分裂多辛格式

Compact Splitting Multisymplectic Scheme for Dirac Equation

把非线性Dirac方程分裂成线性和非线性子问题,这些子问题都具有辛或者多辛结构,可以构造它们的辛格式.对于非线性问题,利用点点守恒律可以精确求解.至于线性问题,在空间方向用高阶紧致格式离散,在时间方向用辛欧拉法进一步离散,此格式半显式的.与传统的多辛格式相比,这种格式有计算效率高、计算时间少等优点.

The nonlinear Dirac equation can be split into a linear subproblem and a nonlinear subproblem,and these problems have symplectic or multisymplectic structure,symplectic scheme for them is constructed,then discrete calculation is made by symplectic Euler method in time and the high order compact scheme in space. Compared with the traditional multisymplectic scheme,this scheme has high computation efficiency,fast calculation and so on.