M. Griebel and G. W. Zumbusch.
Hash-storage techniques for adaptive multilevel solvers and their
domain decomposition parallelization.
In J. Mandel, C. Farhat, and X.-C. Cai, editors, Proceedings of
Domain Decomposition Methods 10, DD10 (1997), number 218 in Contemporary
Mathematics, pages 271-278, Providence, Rhode Island, 1998. AMS.
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Partial differential equations can be solved efficiently by adaptive multigrid methods on a parallel computer. We report on the concepts of hash-table storage techniques and space-filling curves to set up such a code. The hash-table storage requires substantial less amount of memory and is easier to code than tree data structures used in traditional adaptive multigrid codes, already for the sequential case. The parallelization takes place by a domain decomposition by space filling curves, which are intimately connected to the hash table. The new data structure simplifies the parallel version of the code substantially and introduces a cheap way to solve the load balancing and mapping problem....