Abstract
The hp-adaptive Finite Element Method (hp-FEM) generates a sequence of adaptive grids with different polynomial orders of approximation and element sizes. The hp-FEM delivers exponential convergence of the numerical error with respect to the mesh size. In this paper, we propose a heuristic algorithm to construct element partition trees. The trees can be transformed directly into the orderings, which control the execution of the multi-frontal direct solvers during the hp refined finite element method. In particular, the orderings determine the number of floating point operations performed by the solver. Thus, the quality of the orderings obtained from the element partition trees is important for good performance of the solver. Our heuristic algorithm has been implemented in 3D and tested on a sequence of hp-refined meshes. We compare the quality of the orderings found by the heuristic algorithm to those generated by alternative state-of-the-art algorithms. We show 50% reduction in flops number and execution time.
Original language | English (US) |
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Title of host publication | Computational Science – ICCS 2018 - 18th International Conference, Proceedings |
Editors | Valeria V. Krzhizhanovskaya, Michael Harold Lees, Peter M. Sloot, Jack Dongarra, Yong Shi, Yingjie Tian, Haohuan Fu |
Publisher | Springer Verlag |
Pages | 760-772 |
Number of pages | 13 |
ISBN (Print) | 9783319937007 |
DOIs | |
State | Published - 2018 |
Event | 18th International Conference on Computational Science, ICCS 2018 - Wuxi, China Duration: Jun 11 2018 → Jun 13 2018 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10861 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 18th International Conference on Computational Science, ICCS 2018 |
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Country/Territory | China |
City | Wuxi |
Period | 06/11/18 → 06/13/18 |
Bibliographical note
Funding Information:The work was supported by National Science Centre, Poland grant no. DEC-2015/17/B/ST6/01867.
Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
Keywords
- Heuristic algorithms
- Multi-frontal direct solvers
- Nested-dissections
- Ordering
- hp adaptive finite element method
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science