This paper presents bounds on the quality of partitions induced by space-filling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i. e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times worse with respect to the length of the surface. The Lebesgue indexing gives better results than the Hilbert indexing in worst case analysis. Furthermore, the surface of partitions based on the Lebesgue indexing are at most 3 times larger than the optimal in average case.

This paper presents the quality of partitions induced by the Lebesgue curve in average case. The surface that surrounds an arbitrary index range is compared with the optimal partition in the grid, i. e. the square. The upper bound on the surface is asymptotically 3 times the optimal size.

This technical report presents the definition of a circular Hilbert-like space-filling curve. Preliminary evaluations in a simulation environment have shown good locality preserving properties. The results are compared with known bounds for other indexing schemes: Hilbert-, Lebesgue-, and H-Indexing. We evaluated partitions induced by the indexing schemes and uses the diameter and the surface as measures. For both we present worst case and average case results.

In this paper we show the efficient parallelisation of an industrial finite element simulation code and the dynamic and fair management of jobs running on a multi-processor machine. We have parallelised...