Adaptive Mesh Refinement in 2D – An Efficient Implementation in Matlab
Adaptive Mesh Refinement in 2D – An Efficient Implementation in Matlab
复制标题
二维自适应网格细化——Matlab 中的高效实现
DOI：
10.1515/cmam-2018-0220
复制
发表时间：
2019
影响因子：
1.3
通讯作者：
Anja Schmidt
中科院分区：
文献类型：
--
作者：
S. Funken;Anja Schmidt
摘要本文讨论了二维网格自适应加密算法在Matlab中的有效实现。我们提供了不同的自适应网格细化策略，允许三角形和四边形网格和不挂节点的见解。通过合理的数据结构、Matlab内置函数的使用以及矢量化的方法，有效地实现了该算法。本文以清晰的方式展示了从理论到实现的过渡，因此旨在服务于如何实现方法的教育目的，同时保持代码尽可能短-在Matlab的71行内实现有效的自适应网格细化是可能的。数值实验强调了代码的效率，并显示了灵活的部署在不同的情况下，自适应网格细化是在使用中。我们的实施是可访问的，易于理解，因此被认为是研究和教育的宝贵工具。
Abstract This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in functions and vectorization. This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab. Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use. Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.