Hierarchical template-based quadrilateral mesh generation

In the context of any domain decomposition meshing strategy, this paper describes a quadrilateral mesh generation algorithm ideally suited for subdomains in which transition of mesh refinement is required. 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. Direct use of mapping algorithms imposes 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. Some examples demonstrate that this simple idea may result in structured meshes of good quality. We also show that the quadrilateral elements can be used as input to generate hexahedral elements. Three-dimensional sweeping examples, which use the proposed meshing scheme in the source and target surfaces, are also shown.