Simultaneous Refinement and Coarsening for Adaptive Meshing

XiangYang Li, ShangHua Teng and Alper Üngör

Journal of Engineering with Computers, (15), 280-291, 1999


Also appeared in Proc. of the 7th International Meshing Roundtable, Dearborn, Michigan, pp. 201-210,Oct26-28,1998
Download the conference version

Abstract:

In numerical simulation of the combustion process and microstructural evolution we need to consider the adaptive meshing problem for a domain that has a moving boundary. During the simulation, the region ahead of the moving boundary needs to be refined (to stisfy stonger numerical conditions), and the submesh in the region behind the moving boundary should be coarsened (to reduce the mesh size). We present a unified scheme for simulatenously refining and coarsening a mesh. Our method uses sphere packings and guarantees that the resulting mesh is well-shaped and is within a constant factor of the optimal possible in the number of mesh elements. We also present several variations of our provably good algorithm.