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Structured adaptive mesh refinement (SAMR) methods for the numerical solution of partial differential equations yield highly advantageous ratios for cost/accuracy as compared to methods based on static uniform approximations. These techniques are being effectively used in many domains including computational fluid dynamics, numerical relativity, astrophysics, subsurface modeling, and oil reservoir simulation. Distributed implementations of these methods, however, lead to significant challenges in dynamic data-distribution, load-balancing, and runtime management. This paper presents an application-centric characterization of a suite of dynamic domain-based inverse space-filling curve partitioning techniques for the distributed adaptive grid hierarchies that underlie SAMR applications. The overall goal of this research is to formulate policies required to drive a dynamically adaptive metapartitioner for SAMR grid hierarchies capable of selecting the most appropriate partitioning strategy at runtime based on current application and system state. Such a metapartitioner can significantly reduce the execution time of SAMR applications.