Paving: A new approach to automated quadrilateral mesh generation

Abstract

SUMMARYThis paper presents a new mesh generation technique, paving, which meshes arbitrary 2-D geometries with an all-quadrilateral mesh. Paving allows varying element size distributions on the boundary as well as the interior of a region. The generated mesh is well formed (i.e. nearly square elements, elements perpendicular to boundaries, etc.) and geometrically pleasing (i.e. mesh contours tend to follow geometric contours of the boundary). In this paper we describe the theory behind this algorithmic/heuristic technique, evaluate the performance of the approach and present examples of automatically generated meshes.

Adaptive and quality quadrilateral/hexahedral meshing from volumetric data

“…Starting with an initial placement nodes on the boundary, Zhu et al [13] formed individual elements by projecting edges towards the interior. As a part of CUBIT [7], the paving algorithm places elements starting from the boundary and works in [14]. Different from the decomposition and the advancing front techniques, the dual contouring method [2] extracts uniform quadrilateral meshes from volumetric imaging data to approximate isosurfaces which can be an arbitrary geometry.…”

Unconstrained Paving and Plastering: Progress Update

“…Paving [5] has been shown to be a robust and efficient solution to the quadrilateral surface meshing problem. However, its three-dimensional extension, Plastering [6,7,8], has not done the same for hexahedral mesh generation.…”

“…The domain is then systematically partitioned through the advancement of fronts. In traditional advancing front methods [5,6,12], individual solid elements are generated by following geometric reasoning to build individual nodes, edges and faces, starting from a predefined boundary mesh and advancing inwards. In contrast, Unconstrained Paving and Plastering advance geometric layers or partitions independent of element distribution.…”

Non-Local Topological Clean-Up

“…Topological clean-up is the name given to methods aimed to improve the quality of a mesh, by changing its connectivity [1,2,3,4,6]. It is usually carried out after a mesh has been generated by some meshing algorithm.…”