[1094] - Recursive Algorithms for Distributed Forests of Octrees

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Isaac, T., Burstedde, C., Wilcox, L. C., Ghattas, O., 2015. Recursive Algorithms for Distributed Forests of Octrees. SIAM Journal on Scientific Computing, 37 (5), 467 - 531.
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Title(s):Main Title: Recursive Algorithms for Distributed Forests of Octrees
Description(s):Abstract: The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Efficient reference software has been made freely available to the public both in the form of the standalone p4est library and more indirectly by the general-purpose finite element library deal.II, which has been equipped with a p4est back-end. Although linear octrees, which store only leaf octants, have an underlying tree structure by definition, it is not often exploited in previously published mesh-related algorithms. This is because the branches are not explicitly stored, and because the topological relationships in meshes, such as the adjacency between cells, introduce dependencies that do not respect the octree hierarchy. In this work we combine hierarchical and topological relationships between octree branches to design efficient recursive algorithms that operate on distributed forests of octrees. We present three important algorithms with recursive implementations. The first is a parallel search for leaves matching any of a set of multiple search criteria, such as leaves that contain points or intersect polytopes. The second is a ghost layer construction algorithm that handles arbitrarily refined octrees that are not covered by previous algorithms, which require a 2:1 condition between neighboring leaves. The third is a universal mesh topology iterator. This iterator visits every cell in a domain partition, as well as every interface (face, edge and corner) between these cells. The iterator calculates the local topological information for every interface that it visits, taking into account the nonconforming interfaces that increase the complexity of describing the local topology. To demonstrate the utility of the topology iterator, we use it to compute the numbering and encoding of higher-order C0 nodal basis functions used for finite elements. We analyze the complexity of the new recursive algorithms theoretically, and assess their performance, both in terms of single-processor efficiency and in terms of parallel scalability, demonstrating good weak and strong scaling up to 458k cores of the JUQUEEN supercomputer.
Identifier(s):URL: http://arxiv.org/abs/1406.0089
Responsible Party
Creator(s):Author: Tobin Isaac
Author: Carsten Burstedde
Author: Lucas Charles Wilcox
Author: Omar Ghattas
Publisher:Society for Industrial and Applied Mathematics
TR32 Topic:Other
Related Sub-project(s):D8
Subject(s):CRC/TR32 Keywords: Adaptive mesh refinement, Parallel Computing, Numerical Methods
File Details
File Name:Isaac_et_al_2014_submitted.pdf
Data Type:Text
Size(s):35 Pages
File Size:812 kB (0.793 MB)
Date(s):Issued: 2015-09-02
Mime Type:application/pdf
Data Format:PDF
Download Permission:OnlyTR32
General Access and Use Conditions:According to the TR32DB data policy agreement.
Access Limitations:According to the TR32DB data policy agreement.
Licence:TR32DB Data policy agreement
North:-no map data
Measurement Region:None
Measurement Location:--None--
Specific Informations - Publication
Article Type:Journal
Source:SIAM Journal on Scientific Computing
Number Of Pages:35
Page Range:467 - 531
Metadata Details
Metadata Creator:Jose Fonseca
Metadata Created:2014-09-22
Metadata Last Updated:2014-09-22
Funding Phase:2
Metadata Language:English
Metadata Version:V40
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