On mesh coarsening procedures for the virtual element method

TL;DR

This paper introduces novel coarsening indicators and procedures for the virtual element method, enhancing adaptive remeshing by enabling effective mesh simplification while preserving critical geometrical features.

Contribution

It proposes new indicators and a robust coarsening procedure for the virtual element method, addressing a gap in adaptive remeshing techniques.

Findings

Effective coarsening indicators for virtual element meshes

Robust coarsening procedure applicable to structured and unstructured meshes

Mesh quality and feature preservation during coarsening

Abstract

In the context of adaptive remeshing, the virtual element method provides significant advantages over the finite element method. The attractive features of the virtual element method, such as the permission of arbitrary element geometries, and the seamless permission of 'hanging' nodes, have inspired many works concerning error estimation and adaptivity. However, these works have primarily focused on adaptive refinement techniques with little attention paid to adaptive coarsening (i.e. de-refinement) techniques that are required for the development of fully adaptive remeshing procedures. In this work novel indicators are proposed for the identification of patches/clusters of elements to be coarsened, along with a novel procedure to perform the coarsening. The indicators are computed over prospective patches of elements rather than on individual elements to identify the most suitable combinations of elements to coarsen. The coarsening procedure is robust and suitable for meshes of structured and unstructured/Voronoi elements. Numerical results demonstrate the high degree of efficacy of the proposed coarsening procedures and sensible mesh evolution during the coarsening process. It is demonstrated that critical mesh geometries, such as non-convex corners and holes, are preserved during coarsening, and that meshes remain fine in regions of interest to engineers, such as near singularities.