G. W. Zumbusch.
On the quality of space-filling curve induced partitions.
Z. Angew. Math. Mech., 81:25-28, 2001.
Suppl. 1, also as report SFB 256, University Bonn, no. 674, 2000.
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The solution of partial differential equations on a parallel computer is usually done by a domain decomposition approach. The mesh is split into several partitions mapped onto the processors. However, partitioning of unstructured meshes and adaptive refined meshes in general is an NP-hard problem and heuristics are used. In this paper space-filling curve based partition methods are analysed and bounds for the quality of the partitions are given. Furthermore estimates for parallel numerical algorithms such as multigrid and wavelet methods on these partitions are derived.