Boundary constrained quadrilateral mesh generation based on domain decomposition and templates

Abstract

Compared to triangular or mixed meshes, pure quadrilateral meshes generally offer higher accuracy and computational efficiency in numerical simulations. Recently, the main obstacles in the generation of quadrilateral meshes have revolved around the identification of mesh singularities and the subsequent decomposition of the domain. In this study, a novel quadrilateral mesh generation method based on domain decomposition and templates is presented. The basic idea is to decompose the domain by separating the mesh singularities rather than identifying their precise locations. Surfaces composed of a set of surface patches are meshed independently. For each surface patch, the problem domain is divided into several simple polygonal subregions, including quadrangles, triangles, and pentagons, using constrained Delaunay triangulation (CDT) and recursive bisections. Subsequently, mesh templates with a limited number of singularities are employed to rapidly generate high-quality quadrilateral meshes over those subregions. By constraining the boundary discretization of each surface patch, mesh conformability is automatically achieved. An integer linear programming equation is presented to ensure that the total number of boundary nodes on each surface is an even value. Several experimental results are presented and discussed, demonstrating the reliability and efficiency of the proposed method.