αMST: A Robust Unified Algorithm for Quadrilateral Mesh Adaptation

In this paper, we introduce a unified algorithm for all three types of mesh adaptation for quadrilateral meshes. The algorithm builds upon the Minimum Singularity Templates (MST) idea proposed by the authors for improving the topological quality of a quadrilateral mesh. The MST is extended here to define the concept of an αMST where a single parameter α controls mesh adaptation: α = 1 for mesh improvement, α > 1 for mesh refinement, and α < 1 for mesh simplification. The proposed algorithm generates mesh with high geometric and topological qualities. Further, it is non-hierarchical and stateless, and yet it provides an arbitrary level of mesh adaptation. Finally, since cyclic chords can play an important role in quadrilateral mesh adaptation, we provide a simple constructive algorithm to insert such chords using the αMST. Several examples are presented that demonstrate the robustness, efficiency, and versatility of the proposed concept and algorithm.