Recursive Algorithms for Distributed Forests of Octrees
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| Title: | Main Title: Recursive Algorithms for Distributed Forests of Octrees |
| Description: | 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: | http://arxiv.org/abs/1406.0089 (URL) |
Responsible Party
| Creators: | Tobin Isaac (Author), Carsten Burstedde (Author), Lucas Charles Wilcox (Author), Omar Ghattas (Author) |
| Publisher: | Society for Industrial and Applied Mathematics |
| Publication Year: | 2014 |
Topic
| TR32 Topic: | Other |
| Related Subproject: | D8 |
| Subjects: | Keywords: Adaptive mesh refinement, Parallel Computing, Numerical Methods |
File Details
| Filename: | Isaac_et_al_2014_submitted.pdf |
| Data Type: | Text - Article |
| Size: | 35 Pages |
| File Size: | 812 KB |
| Date: | Issued: 02.09.2015 |
| Mime Type: | application/pdf |
| Data Format: | |
| Language: | English |
| Status: | Completed |
Constraints
| Download Permission: | Only Project Members |
| 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 |
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Specific Information - Publication
| Publication Status: | Published |
| Review Status: | Not peer reviewed |
| Publication Type: | Article |
| Article Type: | Journal |
| Source: | SIAM Journal on Scientific Computing |
| Source Website: | http://http://epubs.siam.org/ |
| Issue: | 5 |
| Volume: | 37 |
| Number of Pages: | 65 (467 - 531) |
Metadata Details
| Metadata Creator: | Jose Fonseca |
| Metadata Created: | 22.09.2014 |
| Metadata Last Updated: | 22.09.2014 |
| Subproject: | D8 |
| Funding Phase: | 2 |
| Metadata Language: | English |
| Metadata Version: | V50 |
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Dataset Statistics
| Page Visits: | 769 |
| Metadata Downloads: | 0 |
| Dataset Downloads: | 1 |
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