Quadrilateral Mesh Generation Using Hierarchical Templates

This paper describes a quadrilateral mesh generation algorithm ideally suited for transition subdomain meshes in the context of any domain decomposition meshing strategy. The algorithm is based on an automatic hierarchical region decomposition in which, in the last level, it is possible to generate quadrilateral elements with a conventional mapping strategy. In two dimensions, a subdomain is usually a triangle or a rectangle. In this algorithm, a subdomain with two boundary curves may also be allowed. Templates impose restrictions on the number of boundary curve segments of a subdomain to be meshed. The proposed hierarchical template scheme eliminates these restrictions, requiring only an even number of boundary segments. Other algorithms in the literature present similar characteristics. However, the implementation of the hierarchical decomposition and its templates presented here is quite simple compared to other approaches. Six high-level templates are considered for a subdomain, depending on the number of boundary curves and the number of segments on each curve. Several examples demonstrate that this simple idea may result in structured meshes of surprisingly good quality. We also show the possibility of obtaining different meshes for a subdomain with fixed boundary discretization by changing the corners between curves.