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On the Theory of Discrete, Adaptive Space Filling Curves

Holke, Johannes and Burstedde, Carsten and Knapp, David (2020) On the Theory of Discrete, Adaptive Space Filling Curves. SIAM Conference on Parallel Processing for Scientific Computing, 12. - 15. Feb 2020, Seattle, Washington, USA. (Unpublished)

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Abstract

We present a newly developed, self-contained theory for discrete space-filling curves (SFCs). Mesh partitioning according to such SFCs has been established as a fast and reliable technique, in particular when combined with frequent adaptive mesh refinement (AMR) and coarsening. SFCs map the elements of a uniform or adaptive mesh onto a finite index set, thus providing a linear order of the elements. AMR operations change this order only locally. In addition to practical use in HPC, investigating the properties of SFCs and developing new constructions are subjects of many theoretical studies. The definition for discrete SFCs is usually stated as an iteration step in a sequence that converges to an analytical SFC, or provided in the language of L-systems. Both of these definitions, however, are not ideally suited to represent the complexity of arbitrarily refined adaptive meshes. To address this issue, we provide a set of self-contained concepts and definitions, introducing new underlying structures such as refinement spaces and refinement rules. Discrete SFCs map these refinement spaces to an index set and satisfy certain locality properties. Our construction is independent of any particular geometric embedding. To demonstrate the usefulness of this approach, we present as first application the cross-product binary operation between SFCs that allows us to construct a new SFC for prism elements.

Item URL in elib:https://elib.dlr.de/139043/
Document Type:Conference or Workshop Item (Speech)
Title:On the Theory of Discrete, Adaptive Space Filling Curves
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Holke, JohannesGerman Aerospace Center (DLR), Linder Höhe, 51147 Köln, Germanyhttps://orcid.org/0000-0002-2783-3286
Burstedde, CarstenInstitut für Numerische Simulation (INS), Endenicher Allee 19b, 53115 Bonn, Germanyhttps://orcid.org/0000-0001-9843-1041
Knapp, DavidGerman Aerospace Center (DLR), Linder Höhe, 51147 Köln, GermanyUNSPECIFIED
Date:February 2020
Refereed publication:No
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Unpublished
Keywords:Adaptive mesh refinement Space-filling curves t8code High-performance computing
Event Title:SIAM Conference on Parallel Processing for Scientific Computing
Event Location:Seattle, Washington, USA
Event Type:international Conference
Event Dates:12. - 15. Feb 2020
Organizer:Society for Industrial and Applied Mathematics
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space System Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Space System Technology
DLR - Research theme (Project):R - Vorhaben SISTEC (old)
Location: Köln-Porz
Institutes and Institutions:Institute for Software Technology
Institute for Software Technology > High-Performance Computing
Deposited By: Holke, Johannes
Deposited On:07 Dec 2020 11:45
Last Modified:07 Dec 2020 11:45

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