Multilevel Di usion Schemes for Repartitioning of Adaptive Meshes

For a large class of irregular grid applications, the structure of the mesh changes from one phase of the computation to the next. Eventually, as the graph evolves, the adapted mesh has to be repartitioned to ensure good load balance. If this new graph is partitioned from scratch, it will lead to an excessive migration of data among processors. In this paper, we present two new schemes for computing repartitionings of adaptively re ned meshes. These schemes perform di usion of vertices in a multilevel framework and minimize vertex movement without signi cantly compromising the edge-cut. We present heuristics to control the tradeo between edge-cut and vertex migration costs. We also show that multilevel di usion produces results with improved edge-cuts over single-level di usion, is potentially much faster than single-level di usion in a parallel context, and is better able to make use of heuristics to control the trade-o between edge-cut and vertex migration costs than single-level di usion.