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.

As an entry for the 2001 Gordon Bell Award in the special category, we describe our 3-d, hybrid, adaptive mesh refinement (AMR) code Enzo designed for high-resolution, multiphysics, cosmological structure formation simulations. Our parallel implementation places no limit on the depth or complexity of the adaptive grid hierarchy, allowing us to achieve unprecedented spatial and temporal dynamic range. We report on a simulation of primordial star formation which develops over 8000 subgrids at 34 levels of refinement to achieve a local refinement of a factor of 1012 in space and time. This allows us to resolve the properties of the first stars which form in the universe assuming standard physics and a standard cosmological model. Achieving extreme resolution requires the use of 128-bit extended precision arithmetic (EPA) to accurately specify the subgrid positions. We describe our EPA AMR implementation on the IBM SP2 Blue Horizon system at the San Diego Supercomputer Center.