特征网格的自适应网格加密
Adaptive Mesh Refinement for Characteristic Grids
摘要：
我认为技术的Berger-Oliger自适应网格细化（AMR）数值求解偏微分方程与波浪形的解决方案时，使用特征（双零）网格。这样的AMR算法是自然递归的，并且过去最著名的Berger-Oliger特征AMR算法，Pretorius & Lehner（J.Comp.Phys.198（2004），10）的算法，在各个“菱形”特征网格单元上递归。这导致了细粒度内存管理的使用，在每个细化级别上，单个网格单元保持在二维链表中。这使实现复杂化，并在空间和时间上增加了开销。在这里，我描述了一个Berger-Oliger特征AMR算法，而不是在空\emph{slices}上递归。该算法与通常的Cauchy Berger-Oliger算法非常相似，并且使用相对粗粒度的内存管理，允许将整个空切片存储在内存中的连续数组中。该算法在空间和时间上都是非常有效的。我描述的离散产生的第二和第四阶的全球精度。我实现这里描述的算法的代码包含在本文附带的电子补充材料中，并且根据GNU通用公共许可证的条款，其他研究人员可以免费获得。
英文摘要：
I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive, and the best-known past Berger-Oliger characteristic AMR algorithm, that of Pretorius & Lehner (J. Comp. Phys. 198 (2004), 10), recurses on individual "diamond" characteristic grid cells. This leads to the use of fine-grained memory management, with individual grid cells kept in 2-dimensional linked lists at each refinement level. This complicates the implementation and adds overhead in both space and time. Here I describe a Berger-Oliger characteristic AMR algorithm which instead recurses on null \emph{slices}. This algorithm is very similar to the usual Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory management, allowing entire null slices to be stored in contiguous arrays in memory. The algorithm is very efficient in both space and time. I describe discretizations yielding both 2nd and 4th order global accuracy. My code implementing the algorithm described here is included in the electronic supplementary materials accompanying this paper, and is freely available to other researchers under the terms of the GNU general public license.
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