Space-Filling Curve Techniques for Parallel, Multiscale-Based Grid Adaptation: Concepts and Applications

Melian, Sorana; Brix, Kolja; Müller, Siegfried; Schieffer, Gero

doi:10.1007/978-3-642-17884-9_75

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2023

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“…The Hilbert space-filling curve was used in parallel codes for numerical simulations [5], and the Sierpiński curve helped to streamline finite element calculations [1]. and for loadbalancing in distributed computing [17].…”

Section: Introductionmentioning

confidence: 99%

A simple algorithm for computing a multi-dimensional the Sierpiński space-filling curve generalization

Skubalska-Rafajłowicz

2023

Annals of Computer Science and Information Systems

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Transforming multidimensional data into a onedimensional sequence using space-filling curves, such as the Hilbert curve, has been studied extensively in many papers. This work provides a systematic presentation of the construction of an arbitrarily accurate multidimensional space-filling curve approximation which is a generalization of the Sierpi ński spacefilling curve. At the same time, according to the space-filling curve construction, we present a simple algorithm for determining one of the counter-images on a unit interval of a data point lying in a multidimensional cube. The computational complexity of the algorithm depends linearly on the dimension of the cube. The paper contains numerical algorithms for local generation of the curve approximation and determination of the quasi-inverse of a data point used to transform multidimensional data into the one-dimensional form.

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Section: Introductionmentioning

confidence: 99%

A simple algorithm for computing a multi-dimensional the Sierpiński space-filling curve generalization

Skubalska-Rafajłowicz

2023

Annals of Computer Science and Information Systems

View full text Add to dashboard Cite

show abstract

Space-Filling Curve Techniques for Parallel, Multiscale-Based Grid Adaptation: Concepts and Applications

Cited by 1 publication

References 7 publications

A simple algorithm for computing a multi-dimensional the Sierpiński space-filling curve generalization

A simple algorithm for computing a multi-dimensional the Sierpiński space-filling curve generalization

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