非连续Galerkin时域方法中光滑变系数完全匹配层的一种节省内存的实现
A Memory-efficient Implementation of Perfectly Matched Layer with Smoothly-varying Coefficients in Discontinuous Galerkin Time-Domain Method
摘要：
在Maxwell和波动方程求解器中，用完全匹配层（PML）包裹计算区域是模拟/逼近辐射边界条件的最有效方法之一。许多PML实现通常使用平滑增加的衰减系数来增加给定层厚度的吸收，并且同时减少来自计算域和PML之间的界面的数值反射。在不连续Galerkin时域（DGTD）方法中，使用在网格单元内变化的PML系数需要为每个单元存储不同的质量矩阵，因此显著增加了存储器占用。在这项工作中，这个瓶颈是通过应用权重调整近似这些质量矩阵。所得到的DGTD方案具有与存储单个质量矩阵的方案相同的优点，即更高的精度（由于减少了数值反射）和增加的网格灵活性（因为PML不必逐层定义），但它需要的内存显著减少。
英文摘要：
Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a smoothly-increasing attenuation coefficient to increase the absorption for a given layer thickness, and, at the same time, to reduce the numerical reflection from the interface between the computation domain and the PML. In discontinuous Galerkin time-domain (DGTD) methods, using a PML coefficient that varies within a mesh element requires a different mass matrix to be stored for every element and therefore significantly increases the memory footprint. In this work, this bottleneck is addressed by applying a weight-adjusted approximation to these mass matrices. The resulting DGTD scheme has the same advantages as the scheme that stores individual mass matrices, namely higher accuracy (due to reduced numerical reflection) and increased meshing flexibility (since the PML does not have to be defined layer by layer) but it requires significantly less memory.
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