Automated Quadrilateral Coarsening by Ring Collapse

A uniform finite element mesh rarely provides the best discretization of a domain to accommodate a solution with both optimal efficiency and minimal error. Mesh adaptation can approach a more optimal solution by accommodating regions of the mesh with higher or lower element density. Extensive attention has been given to mesh adaptation in both computational mechanics and computer graphics to provide or improve methods for increasing the model resolution or solution accuracy. The algorithm developed in this paper, entitled Automated Quadrilateral Coarsening by Ring Collapse (AQCRC), provides a unique solution to allow mesh coarsening of both structured and unstructured quadrilateral meshes. The algorithm is based on modification and removal operations utilizing the dual description of the quadrilateral mesh. The AQCRC algorithm iterates on five steps: 1) input of a coarsening region and a coarsening factor, 2) selection of coarsening rings, 3) mesh quality improvement, 4) removal of coarsening rings, and 5) mesh clean-up. Examples are presented showing the application of the algorithm.