标题： Maxwell-Dirac系统的分裂谱格式 显示英文标题

标题： A time-splitting spectral scheme for the Maxwell-Dirac system

摘要： 我们提出了一个用于麦克斯韦-狄拉克系统的分裂谱格式，并为相应的半经典和非相对论极限问题提供了类似的时间分裂方法。 对于麦克斯韦-狄拉克系统，该格式保持洛伦兹规范条件，无条件稳定且高效，正如我们的数值例子所示。 特别是在半经典极限下，我们关注正电子模式的产生；在非相对论极限下，我们关注电子与正电子的相互作用。 此外，在非相对论极限下，我们的数值方法在小参数 $\dt$（即特征速度与光速之比）上表现出一致收敛性。 显示英文摘要

摘要： We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac system conserves the Lorentz gauge condition, is unconditionally stable and highly efficient as our numerical examples show. In particular we focus in our examples on the creation of positronic modes in the semi-classical regime and on the electron-positron interaction in the non-relativistic regime. Furthermore, in the non-relativistic regime, our numerical method exhibits uniform convergence in the small parameter $\dt$, which is the ratio of the characteristic speed and the speed of light.