论文标题
边界条件选择的选择对具有完美层的有限差频域系统的直接解决方案的数值效率
Effect of Choices of Boundary Conditions on the Numerical Efficiency of Direct Solutions of Finite Difference frequency Domain Systems with Perfectly Matched Layers
论文作者
论文摘要
直接求解器是求解在麦克斯韦方程的数值解决方案中出现的有限差频域（FDFD）系统的常见方法。在直接求解器中，一个人将系统矩阵分配。由于系统矩阵通常非常稀疏，因此在时间复杂性和内存要求方面，这些因素的填充是最重要的计算考虑因素。结果，确定可以系统地减少此填充的方法非常有趣。在本文中，我们表明，在通常使用完美匹配的边界层方法的背景下，可以利用完美匹配的边界层背后的边界条件的选择，以减少分解过程中发生的填充，从而在分解过程的有效性中高达40％的填充物。我们通过求解与FDFD方法相关的线性系统和特征值问题来说明我们的发现。
Direct solvers are a common method for solving finite difference frequency domain (FDFD) systems that arise in numerical solutions of Maxwell's equations. In a direct solver, one factorizes the system matrix. Since the system matrix is typically very sparse, the fill-in of these factors is the single most important computational consideration in terms of time complexity and memory requirements. As a result, it is of great interest to determine ways in which this fill-in can be systematically reduced. In this paper, we show that in the context of commonly used perfectly matched boundary layer methods, the choice of boundary condition behind the perfectly matched boundary layer can be exploited to reduce fill-in incurred during the factorization, leading to significant gains of up to 40 percent in the efficiency of the factorization procedure. We illustrate our findings by solving linear systems and eigenvalue problems associated with the FDFD method.
