Load balancing of dynamic and adaptive mesh-based computations

One ingredient which is viewed as vital to the successful conduct of many large-scale numerical simulations is the ability to dynamically repartition the underlying adaptive finite element mesh among the processors so that the computations are balanced and interprocessor communication is minimized. We present two new schemes for adaptive repartitioning: Locally-Matched Multilevel Scratch-Remap (or LMSR) and Wavefront Diffusion. The LMSR scheme performs purely local coarsening and partition remapping in a multilevel context. In Wavefront Diffusion, the flow of vertices move in a wavefront from overbalanced to underbalanced domains. We present experimental evaluations of our LMSR and Wavefront Diffusion algorithms on synthetically generated adaptive meshes as well as on some application meshes. We show that our LMSR algorithm decreases the amount of vertex migration required to balance the graph and produces repartitionings of similar quality compared to current scratch-remap schemes. Furthermore, we show that our LMSR algorithm is more scalable in terms of execution time compared to current scratch-remap schemes. We show that our Wavefront Diffusion algorithm obtains significantly lower vertex migration requirements, while maintaining similar edge-cut results compared to current multilevel diffusion algorithms, especially for highly imbalanced graphs.