Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a new pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of non-constant coefficients in the curved space Dirac equation, convolution products usually appear when the Fourier transform is performed. To circumvent this problem, a strategy based on operator splitting and pseudodifferential operators allows for using an ordinary fast Fourier transform algorithm. The resulting numerical methods are efficient and have spectral convergence. Simultaneously, wave absorption at the boundary can be easily included using absorbing layers to cope with some potential unwanted effects of periodic conditions inherent to spectral methods. The numerical schemes are first tested on simple systems to verify the convergence and are then applied to the dynamics of charge carriers in strained graphene.

使用Dirac方程的新伪微分表示法以及简单的傅立叶基础技术，得出了用于求解一般静态弯曲空间中Dirac方程的伪谱数值方案。由于弯曲空间狄拉克方程中存在非恒定系数，因此在执行傅立叶变换时通常会出现卷积。为了解决这个问题，基于算子分裂和伪微分算子的策略允许使用普通的快速傅里叶变换算法。所得的数值方法高效且具有光谱收敛性。同时，可以使用吸收层轻松应对边界处的波吸收，以应对光谱方法固有的周期性条件的某些潜在有害影响。