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A space-filling curve for pyramidal adaptive mesh refinement

Knapp, David (2020) A space-filling curve for pyramidal adaptive mesh refinement. Master's, Rheinische Friedrich-Wilhems-Universität Bonn.

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Abstract

In this thesis we present a space-filling curve for pyramid elements. We use the new approach for the formulation of discrete space-filling curves presented by Holke and develop a space-filling curve for pyramids that is based on the Morton-code for tetrahedra. We prove, that our curve fits the task of adaptive mesh refinement (AMR), namely that local operations on the mesh change the curve only locally. Furthermore, we develop the algorithms to use pyramids for AMR and implement them in the t8code library. We enable the support of pyramidal elements for the New, Partition, Adapt, Ghost and Balance high-level algorithms of t8code, which also results in a modified version of t8code. Using the JUWELS Supercomputer we achieve very good to ideal scaling behaviour for adaptive mesh refinement, partitioning, computing the ghost elements and for computing a mesh that fulfils a 2:1 balance condition. We achieve fast run times for the initial refinement of a mesh. Further runtime analysis shows, that except for the initial refinement, our modified version of t8code is as fast as the state-of-the-art version of t8code without pyramids. We present runtime results for meshes with up to 5.1e10 elements, and prove that our approach scales perfectly in that case.

Item URL in elib:https://elib.dlr.de/138982/
Document Type:Thesis (Master's)
Additional Information:Erstgutachter: Prof. Dr. Reinhard Klein, Zweitgutachter: Dr. Johannes Holke
Title:A space-filling curve for pyramidal adaptive mesh refinement
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Knapp, DavidGerman Aerospace Center (DLR), Linder Höhe, 51147 Köln, GermanyUNSPECIFIED
Date:October 2020
Refereed publication:No
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Number of Pages:72
Status:Unpublished
Keywords:Adaptive Mesh Refinement Space-filling curve High-Performance Computing Forest-of-trees Pyramids
Institution:Rheinische Friedrich-Wilhems-Universität Bonn
Department:Institute of Computer Science II - Computer Graphics
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:08 Dec 2020 08:28
Last Modified:08 Dec 2020 08:28

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