An adaptive technique for a partial differential system automatically adjusts a computational mesh or varies the order of a numerical procedure to obtain a solution satisfying prescribed accuracy criteria in an optimal fashion. We describe data structures for distributed storage of finite element mesh data as well as software for mesh adaptation, load balancing, and solving compressible flow problems. Processor load imbalances are introduced at adaptive enrichment steps during the course of a parallel computation. To correct this, we have developed three dynamic load balancing procedures based, respectively, on load imbalance trees, moment of inertia, and octree traversal. Computational results on an IBM SP2 computer are presented for steady and transient solutions of the three-dimensional Euler equations of compressible flow.
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