论文标题
在2D中自适应精制网格的局部粗化算法及其在MATLAB中的有效实现
Local Coarsening Algorithms on Adaptively Refined Meshes in 2D and Their Efficient Implementation in MATLAB
论文作者
论文摘要
自适应网格划分包括局部改进以及网格的粗化。通常，粗化算法基于明确的完善历史记录。在这项工作中，我们处理的是，基于AmeshRef软件包中实施的三角形和四边形网格的完善策略（Funken and Schmidt 2018，2019）实现的精炼策略。 AMESHREF软件包是用于研究和教学目的的MATLAB-TOOLBOX，可在自适应有限元方法的精炼步骤中为用户提供一定的灵活性，但也可以在其他情况下使用计算机图形。现在，通过粗化选项扩展了此工具箱。在AmeshRef中，没有存储有关改进过程的明确信息，而是隐含在数据结构中。在这项工作中，我们提出了使用易于验证的标准来通过利用数据结构来适应网格的粗俗算法。因此，保证所需的属性并保持计算效率。在本工作中讨论了MATLAB实现和一些数值示例，并包含在工具箱截肢（Funken and Schmidt 2020）中。
Adaptive meshing includes local refinement as well as coarsening of meshes. Typically, coarsening algorithms are based on an explicit refinement history. In this work, we deal with local coarsening algorithms that build on the refinement strategies for triangular and quadrilateral meshes implemented in the ameshref package (Funken and Schmidt 2018, 2019). The ameshref package is a MATLAB-toolbox for research and teaching purposes which offers the user a certain flexibility in the REFINE step of an adaptive finite element method but can also be used in other contexts like computer graphics. This toolbox is now be extended by the coarsening option. In ameshref, no explicit information about the refinement process is stored, but is instead implicit in the data structure. In this work, we present coarsening algorithms that use easy-to-verify criteria to coarsen adaptively generated meshes by exploiting the data structure. Thereby, the desired properties are guaranteed and computational efficiency is maintained. A MATLAB implementation and some numerical examples are discussed in this work and are included in full in the toolbox ameshcoars (Funken and Schmidt 2020).
