Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In this work we use Perfectly Matched Layers (PML) to increase this efficiency. PML have been widely used to truncate numerical simulations of wave equations due to improving the accuracy of the solution instead of using absorbing boundary conditions (ABCs). Here, we will develop an efficient solver by providing an alternative use of PML as transmission conditions at the interfaces between subdomains in our domain decomposition method. We solve Maxwell's equations and assess the convergence rate of our solutions compared to the situation where absorbing boundary conditions are chosen as transmission conditions.

翻译：大规模Maxwell方程的数值离散会导致病态线性系统，求解极具挑战性。对该线性系统进行连续求解的关键在于选择高效的求解器。本文采用完美匹配层（PML）来提高求解效率。PML因能提升解精度而取代吸收边界条件（ABCs），已被广泛用于波动方程数值模拟的截断处理。本研究通过创新性地将PML作为区域分解方法中子域间传输条件，开发了一种高效求解器。我们求解了Maxwell方程，并与选择吸收边界条件作为传输条件的情况进行了收敛速度对比评估。