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.
翻译:这项工作涉及对多边形虚拟元素的草丝进行适应性改进程序,具体地说,以前由作者提议的对结构型金属的改进程序,对于在结构化/Voronoi离散过程中产生的任意元素几何构成的具有挑战性的情况,是普遍的,在这里,对结构化和结构化的草丝进行了考虑,并通过Voronoi分别对结构化和结构化的种子点组群进行套接,形成了结构化和结构化的草丝。结构化和结构化的草裙类新颖的网目改进程序使得能够准确和有效地应用虚拟元素方法来挑战两层的弹性问题。结果显示,如作者以前的工作所显示的那样,结构型金属元素的拟议改进程序在结构化/Voronoi meshes案例中也取得了很高的功效。在各种网目类型中展示的精细程序的多功能和功效表明,这些程序完全适合虚拟元素应用。