Recursive mesh refinement on hypercubes
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Adaptive methods for PDEs can be viewed as a graph problem. An efficient parallel implementation of adaptive PDE methods then requires distributing the nodes of the associated graph uniformly across the processors so that the resulting cost of communication between processors is low.
We solve this problem in two phases: labeling of graph nodes and subsequent mapping of these labels onto processors. We describe a new form of Gray-code which we call aninterleaved Gray-code that allows easy labeling of graph nodes when the maximal level of refinement is unknown, allows easy determination of nearby nodes in the graph, is completely deterministic, and often (in a well-defined sense) distributes the graph uniformly across a hypercube. The theoretical results are supported by computational experiments on the Connection Machine.
AMS classifications65N50 68P99
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- Fox, C. F., Kolawa, A. and Williams, R.,The Implementation of a Dynamic Loadbalancer, Hypercube Multiprocessors 1987, SIAM, 1987, pp. 114–21.Google Scholar
- Gilbert, E. N.,Gray codes and paths on the N-cube, The Bell System Technical Journal, (May 1958).Google Scholar
- Gropp, W. D.,Local uniform mesh refinement for elliptic partial differential equations, Research Report 278, Dept. of Computer Science, Yale University, 1983.Google Scholar
- id., Local uniform mesh refinement on loosely coupled parallel processors, Comput. Math. Appl., 15 (1988), pp. 375–387.Google Scholar
- Li, S.-X. and Loew, M. H.,The quadcode and its arithmetic, CACM, 30 (1987), pp. 621–6.Google Scholar
- Saad, Y. and Schultz, M. H.,Some topological properties of the hypercube multiprocessor, Research Report 389, Dept. Computer Science, Yale University, 1984.Google Scholar
- Wu, A. Y.,Embedding of tree networks into hypercubes, Jour. Par. Distr. Comp. 2 (1985), pp. 238–49.Google Scholar