Pötz Walter
Institut für Physik, Karl-Franzens-Universität Graz, Universitätsplatz 5, 8010 Graz, Austria.
Phys Rev E. 2021 Jan;103(1-1):013301. doi: 10.1103/PhysRevE.103.013301.
Perfectly matched layer (PML) boundary conditions are constructed for the Dirac equation and general electromagnetic potentials. A PML extension is performed for the partial differential equation and two versions of a staggered-grid single-cone finite-difference scheme. For the latter, PML auxiliary functions are computed either within a Crank-Nicholson scheme or one derived from the formal continuum solution in integral form. Stability conditions are found to be more stringent than for the original scheme. Spectral properties under spatially uniform PML confirm damping of any out-propagating wave contributions. Numerical tests deal with static and time-dependent electromagnetic textures in the boundary regions for parameters characteristic for topological insulator surfaces. When compared to the alternative imaginary-potential method, PML offers vastly improved wave absorption owing to a more efficient suppression of back-reflection. Remarkably, this holds for time-dependent textures as well, making PML a useful approach for transient transport simulations of Dirac fermion systems.
为狄拉克方程和一般电磁势构建了完全匹配层（PML）边界条件。对偏微分方程以及交错网格单锥有限差分格式的两个版本进行了PML扩展。对于后者，PML辅助函数可在克兰克 - 尼科尔森格式内计算，也可从积分形式的形式连续解推导得出。发现稳定性条件比原格式更为严格。空间均匀PML下的频谱特性证实了对任何向外传播波分量的衰减。数值测试针对拓扑绝缘体表面特征参数的边界区域中的静态和随时间变化的电磁纹理。与替代的虚势方法相比，由于更有效地抑制了背反射，PML提供了大幅改进的波吸收。值得注意的是，这对于随时间变化的纹理也成立，使得PML成为狄拉克费米子系统瞬态输运模拟的有用方法。
