Element Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming

Handle URI:
http://hdl.handle.net/10754/625277
Title:
Element Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming
Authors:
AbouEisha, Hassan M. ( 0000-0003-4560-7175 ) ; Calo, Victor Manuel; Jopek, Konrad; Moshkov, Mikhail ( 0000-0003-0085-9483 ) ; Paszyńka, Anna; Paszyński, Maciej; Skotniczny, Marcin
Abstract:
We consider a class of two-and three-dimensional h-refined meshes generated by an adaptive finite element method. We introduce an element partition tree, which controls the execution of the multi-frontal solver algorithm over these refined grids. We propose and study algorithms with polynomial computational cost for the optimization of these element partition trees. The trees provide an ordering for the elimination of unknowns. The algorithms automatically optimize the element partition trees using extensions of dynamic programming. The construction of the trees by the dynamic programming approach is expensive. These generated trees cannot be used in practice, but rather utilized as a learning tool to propose fast heuristic algorithms. In this first part of our paper we focus on the dynamic programming approach, and draw a sketch of the heuristic algorithm. The second part will be devoted to a more detailed analysis of the heuristic algorithm extended for the case of hp-adaptive
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Aboueisha H, Calo VM, Jopek K, Moshkov M, Paszyńka A, et al. (2017) Element Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming. International Journal of Applied Mathematics and Computer Science 27. Available: http://dx.doi.org/10.1515/amcs-2017-0025.
Publisher:
Walter de Gruyter GmbH
Journal:
International Journal of Applied Mathematics and Computer Science
Issue Date:
13-Jul-2017
DOI:
10.1515/amcs-2017-0025
Type:
Article
ISSN:
2083-8492
Sponsors:
The work was partially supported by the Center for Numerical Porous Media, King Abdullah University of Science and Technology (KAUST), and by the National Science Centre, Poland, grant no. DEC-2012/06/M/ST1/00363. This publication also was made possible by a National Priorities Research Program grant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation). This work was partially supported by the European Union's Horizon 2020 research and an innovation program under the Marie Sklodowska-Curie grant agreement no. 644602. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin partially supported the visits of Victor Manuel Calo to the ICES.
Additional Links:
https://www.degruyter.com/view/j/amcs.2017.27.issue-2/amcs-2017-0025/amcs-2017-0025.xml
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAbouEisha, Hassan M.en
dc.contributor.authorCalo, Victor Manuelen
dc.contributor.authorJopek, Konraden
dc.contributor.authorMoshkov, Mikhailen
dc.contributor.authorPaszyńka, Annaen
dc.contributor.authorPaszyński, Maciejen
dc.contributor.authorSkotniczny, Marcinen
dc.date.accessioned2017-07-31T12:54:35Z-
dc.date.available2017-07-31T12:54:35Z-
dc.date.issued2017-07-13en
dc.identifier.citationAboueisha H, Calo VM, Jopek K, Moshkov M, Paszyńka A, et al. (2017) Element Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming. International Journal of Applied Mathematics and Computer Science 27. Available: http://dx.doi.org/10.1515/amcs-2017-0025.en
dc.identifier.issn2083-8492en
dc.identifier.doi10.1515/amcs-2017-0025en
dc.identifier.urihttp://hdl.handle.net/10754/625277-
dc.description.abstractWe consider a class of two-and three-dimensional h-refined meshes generated by an adaptive finite element method. We introduce an element partition tree, which controls the execution of the multi-frontal solver algorithm over these refined grids. We propose and study algorithms with polynomial computational cost for the optimization of these element partition trees. The trees provide an ordering for the elimination of unknowns. The algorithms automatically optimize the element partition trees using extensions of dynamic programming. The construction of the trees by the dynamic programming approach is expensive. These generated trees cannot be used in practice, but rather utilized as a learning tool to propose fast heuristic algorithms. In this first part of our paper we focus on the dynamic programming approach, and draw a sketch of the heuristic algorithm. The second part will be devoted to a more detailed analysis of the heuristic algorithm extended for the case of hp-adaptiveen
dc.description.sponsorshipThe work was partially supported by the Center for Numerical Porous Media, King Abdullah University of Science and Technology (KAUST), and by the National Science Centre, Poland, grant no. DEC-2012/06/M/ST1/00363. This publication also was made possible by a National Priorities Research Program grant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation). This work was partially supported by the European Union's Horizon 2020 research and an innovation program under the Marie Sklodowska-Curie grant agreement no. 644602. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin partially supported the visits of Victor Manuel Calo to the ICES.en
dc.publisherWalter de Gruyter GmbHen
dc.relation.urlhttps://www.degruyter.com/view/j/amcs.2017.27.issue-2/amcs-2017-0025/amcs-2017-0025.xmlen
dc.rightsThis is an open access article distributed under the Creative Commons Attribution-NonCommercial-NoDerivs license (http://creativecommons.org/licenses/by-nc-nd/3.0/).en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/en
dc.subjecth-adaptive finite element methoden
dc.subjectorderingen
dc.subjectelement partition treeen
dc.subjectextensions of dynamic programmingen
dc.subjectmultifrontalen
dc.subjectdirect solversen
dc.titleElement Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programmingen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalInternational Journal of Applied Mathematics and Computer Scienceen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionFaculty of Science and Engineering, Western Australian School of Mines Curtin University, Kent Street, Perth, WA, , , Australiaen
dc.contributor.institutionFaculty of Computer Science, Electronics and Telecommunications AGH University of Science and Technology, al. Mickiewicza 30, Kraków, 30-059, , Polanden
dc.contributor.institutionFaculty of Physics, Astronomy and Applied Computer Science Jagiellonian University, ul Łojasiewicza 11, Kraków, 30-348, , Polanden
kaust.authorAbouEisha, Hassan M.en
kaust.authorMoshkov, Mikhailen
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