Wavefront Diiusion and Lmsr: Algorithms for Dynamic Repartitioning of Adaptive Meshes

Existing state-of-the-art schemes for dynamic repartitioning of adaptive meshes can be classiied as either diiusion-based schemes or scratch-remap schemes. We present a new scratch-remap scheme called Locally-Matched Multilevel Scratch-Remap (or simply LMSR). The LMSR scheme tries to compute a partitioning that has a high overlap with the existing partitioning. We show that LMSR decreases the amount of vertex migration required to balance the graph compared to current scratch-remap schemes, particularly for slightly imbalanced graphs. We describe a new diiusion-based scheme that we refer to as Wavefront Diiusion. In Wavefront Diiusion, the ow of vertices moves in a wavefront from overweight to underweight domains. We show that Wavefront Diiusion obtains signiicantly lower vertex migration requirements while maintaining similar or better edge-cut results compared to existing diiusion algorithms, especially for highly imbalanced graphs. Furthermore, we compare Wavefront Diiusion with LMSR and show that the former scheme results in generally lower vertex migration requirements at the cost of lower quality edge-cuts. Our experimental results on parallel computers show that both schemes are highly scalable. For example, both are capable of repartitioning an eight million node graph in under three seconds on a 128-processor Cray T3E.