Multilevel Diffusion Schemes for Repartitioning of Adaptive Meshes

For a large class of irregular mesh applications, the structure of the mesh changes from one phase of the computation to the next. Eventually, as the mesh evolves, the adapted mesh has to be repartitioned to ensure good load balance. If this new graph is partitioned from scratch, it may lead to an excessive migration of data among processors. In this paper, we present schemes for computing repartitionings of adaptively refined meshes that perform diffusion of vertices in a multilevel framework. These schemes try to minimize vertex movement without significantly compromising the edge-cut. We present heuristics to control the tradeoff between edge-cut and vertex migration costs. We also show that multilevel diffusion produces results with improved edge-cuts over single-level diffusion, and is better able to make use of heuristics to control the tradeoff between edge-cut and vertex migration costs than single-level diffusion.