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Adaptive Mesh Refinement (AMR) is a type of multiscale algorithm that achieves high resolution in localized regions of dynamic, multidimensional numerical simulations. One of the key issues related to AMR is dynamic load balancing (DLB), which allows large-scale adaptive applications to run efficiently on parallel systems. In this paper we present an efficient DLB scheme for structured AMR (SAMR) applications. Our DLB scheme combines a grid-splitting technique with direct grid movements (e.g., direct movement from an overloaded processor to an underloaded proces sor), for which the objective is to efficiently redistribute workload among all the processors so as to reduce the parallel execution time. The potential benefits of our DLB scheme are examined by incorporating our techniques into a parallel, cosmological application that uses SAMR techniques. Experiments show that by using our scheme, the parallel execution time can be reduced by up to 47% and the quality of load-balancing can be improved by a factor of four.