论文标题
关于多边形虚拟元素的网状细化程序
On mesh refinement procedures for polygonal virtual elements
论文作者
论文摘要
这项工作涉及多边形虚拟元素网格的适应性完善程序。具体而言，作者先前针对结构化网格提出的改进程序是针对在非结构化/沃罗诺伊离散化中引起的任意元素几何形状的具有挑战性的案例的概括的。在这里，考虑了结构化和非结构化的网格，并通过分别对结构化和非结构化种子点的伏罗尼元进行镶嵌来创建。结构化和非结构化网格的新型网格完善程序允许将虚拟元素方法准确地应用于二维中挑战弹性问题。结果表明，如作者先前的工作所示，在非结构化/voronoi网格中，提出的对结构化网格的高疗效也可以实现。在各种网格类型上证明了改进程序的多功能性和功效，表明该过程非常适合虚拟元素应用程序。
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary element geometries arising in unstructured/Voronoi discretizations. Here, structured and unstructured meshes are considered and are created via Voronoi tessellation of sets of structured and unstructured seed points respectively. The novel mesh refinement procedures for both structured and unstructured meshes allow for accurate and efficient application of the virtual element method to challenging elastic problems in two-dimensions. The results demonstrate that the high efficacy of the proposed refinement procedures on structured meshes, as seen in previous work by the authors, is also achieved in the case of unstructured/Voronoi meshes. The versatility and efficacy of the refinement procedures demonstrated over a variety of mesh types indicates that the procedures are well-suited to virtual element applications.
