Coarsening unstructured meshes by edge contraction

Abstract

SUMMARYA new unstructured mesh coarsening algorithm has been developed for use in conjunction with multilevel methods. The algorithm preserves geometrical and topological features of the domain, and retains a maximal independent set of interior vertices to produce good coarse mesh quality. In anisotropic meshes, vertex selection is designed to retain the structure of the anisotropic mesh while reducing cell aspect ratio. Vertices are removed incrementally by contracting edges to zero length. Each vertex is removed by contracting the edge that maximizes the minimum sine of the dihedral angles of cells a ected by the edge contraction. Rarely, a vertex slated for removal from the mesh cannot be removed; the success rate for vertex removal is typically 99.9% or more.For two-dimensional meshes, both isotropic and anisotropic, the new approach is an unqualiÿed success, removing all rejected vertices and producing output meshes of high quality; mesh quality degrades only when most vertices lie on the boundary. Three-dimensional isotropic meshes are also coarsened successfully, provided that there is no di culty distinguishing corners in the geometry from coarselyresolved curved surfaces; sophisticated discrete computational geometry techniques appear necessary to make that distinction. Three-dimensional anisotropic cases are still problematic because of tight constraints on legal mesh connectivity. More work is required to either improve edge contraction choices or to develop an alternative strategy for mesh coarsening for three-dimensional anisotropic meshes.

Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing

“…A subset of the mesh vertices is selected with the goal of retaining as many vertices as possible while ensuring that no two selected vertices are closer together than 0.9 times the average of their length scales. Then unwanted vertices are removed one at a time from the fine mesh [27].…”

Pre-processing parallel and orthogonally positioned structural design elements to be used within the finite element method

“…For a more fundamental approach, reference should be made to Knupp & Steinberg [52]. Currently many research projects are being carried out to optimize meshing techniques for complex geometries [53][54]. Within the research domain of mesh generation, the problem as defined in Section 1.1 and Fig.…”

Robust generation of high‐quality unstructured meshes on realistic biomedical geometry

“…To devise a mesh decimation method for CAE applications, the following additional criteria should be considered: (a) watertightness of the resulting mesh, (b) mesh quality, in terms of element geometric shape and smooth size variation, (c) local curvature on the surface and (d) volume thickness. Several mesh decimation algorithms for CAE applications have been presented in the literature [6,7]. Some of them are limited to 2D models.…”