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Discrete space-filling curves for adaptive mesh refinement

Holke, Johannes (2020) Discrete space-filling curves for adaptive mesh refinement. In: DLR-HBRS-SCAI Seminar. DLR-HBRS-SCAI Seminar, 05. March 2020, Hochschule Bonn-Rhein-Sieg, Bonn, Germany.

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For adaptive meshes that are refined and coarsened frequently partitioning according to (discrete) space-filling curves (SFCs) has been established as a fast and reliable method. Additionally to using SFCs in extreme-scale adaptive mesh refinement (AMR) codes, investigating the properties of SFCs and developing new constructions are subjects of many theoretical studies. In this talk, we provide an introduction to AMR with SFCs and develop a new self-contained mathematical framework to describe discrete SFCs. We provide definitions for the 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 a particular geometric embedding. We are certain that this definition provides the basis for new theoretical and practical insights. As a first application, we present a cross-product construction of SFCs that allows us to construct new SFCs from existing ones, e.g. a new curve for prism shaped elements.

Item URL in elib:https://elib.dlr.de/139033/
Document Type:Conference or Workshop Item (Lecture, Speech)
Title:Discrete space-filling curves for adaptive mesh refinement
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Holke, JohannesGerman Aerospace Center (DLR), Linder Höhe, 51147 Köln, Germanyhttps://orcid.org/0000-0002-2783-3286UNSPECIFIED
Date:5 March 2020
Journal or Publication Title:DLR-HBRS-SCAI Seminar
Refereed publication:No
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
Keywords:Adaptive mesh refinement Space-filling curve forest-of-trees t8code
Event Title:DLR-HBRS-SCAI Seminar
Event Location:Hochschule Bonn-Rhein-Sieg, Bonn, Germany
Event Type:Workshop
Event Dates:05. March 2020
Organizer:DLR, Hochschule Bonn Rhein-Sieg, Fraunhofer SCAI
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 11:44
Last Modified:07 Dec 2021 08:59

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