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Adaptive scientific computations require that periodic repartitioning (load balancing) occur dynamically to maintain load balance. Hypergraph partitioning is a successful model for minimizing communication volume in scientific computations, and partitioning software for the static case is widely available. In this paper, we present a new hypergraph model for the dynamic case, where we minimize the sum of communication in the application plus the migration cost to move data, thereby reducing total execution time. The new model can be solved using hypergraph partitioning with faced vertices. We describe an implementation of a parallel multilevel repartitioning algorithm within the Zoltan load-balancing toolkit, which to our knowledge is the first code for dynamic load balancing based on hypergraph partitioning. Finally, we present experimental results that demonstrate the effectiveness of our approach on a Linux cluster with up to 64 processors. Our new algorithm compares favorably to the widely used ParMETIS partitioning software in terms of quality, and would have reduced total execution time in most of our test cases.