解Maxwell-Dirac系统的显隐数值格式

Explicit-implicit numerical scheme for the Maxwell-Dirac system

显隐数值格式能计算一般初边界条件和复杂区域的Maxwell-Dirac系统。首先对系统中的Maxwell方程组使用显式差分方法离散;为了保证波函数的守恒性,对Dirac方程应用时间分裂方法进行分裂,并对分裂后的方程使用隐式差分离散。此数值格式在时间和空间方向均能达到二阶精度,并且理论上证明了数值格式的稳定性和数值解的守恒性。最后通过实例验证了该显隐数值格式的精度及守恒性等性质。

An implicit-explicit numerical method is presented for solving the Maxwell-Dirac system with normal initial-boundary conditions and complex region. At first, the Maxwell equations are discretized by the explicit finite difference. To guarantee the conservation of wave functions, the Dirac equations are splitted by the time-splitting method and discretized by the implicit finite difference. This numerical scheme has the second-order accuracy in both time and space. Its stability and the conservation of numerical solutions are shown. Numerical results are given to test the accuracy and conservation of this scheme.