Quasi-Optimal Elimination Trees for 2D Grids with Singularities

Handle URI:
http://hdl.handle.net/10754/550467
Title:
Quasi-Optimal Elimination Trees for 2D Grids with Singularities
Authors:
Paszyńska, A.; Paszyński, M.; Jopek, K.; Woźniak, M.; Goik, D.; Gurgul, P.; AbouEisha, H.; Moshkov, Mikhail ( 0000-0003-0085-9483 ) ; Calo, Victor M. ( 0000-0002-1805-4045 ) ; Lenharth, A.; Nguyen, D.; Pingali, K.
Abstract:
We construct quasi-optimal elimination trees for 2D finite element meshes with singularities.These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination process model the execution of the multifrontal algorithms in serial and in parallel shared-memory executions. Since the meshes considered are a subspace of all possible mesh partitions, we call these minimizers quasi-optimal.We minimize the cost functionals using dynamic programming. Finding these minimizers is more computationally expensive than solving the original algebraic system. Nevertheless, from the insights provided by the analysis of the dynamic programming minima, we propose a heuristic construction of the elimination trees that has cost O(log(Ne log(Ne)), where N e is the number of elements in the mesh.We show that this heuristic ordering has similar computational cost to the quasi-optimal elimination trees found with dynamic programming and outperforms state-of-the-art alternatives in our numerical experiments.
KAUST Department:
Applied Mathematics and Computational Science Program; Earth Science and Engineering Program; Numerical Porous Media SRI Center (NumPor)
Citation:
Quasi-Optimal Elimination Trees for 2D Grids with Singularities 2015, 2015:1 Scientific Programming
Publisher:
Hindawi Publishing Corporation
Journal:
Scientific Programming
Issue Date:
22-Apr-2015
DOI:
10.1155/2015/303024
Type:
Article
ISSN:
1058-9244; 1875-919X
Additional Links:
http://www.hindawi.com/journals/sp/2015/303024/
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorPaszyńska, A.en
dc.contributor.authorPaszyński, M.en
dc.contributor.authorJopek, K.en
dc.contributor.authorWoźniak, M.en
dc.contributor.authorGoik, D.en
dc.contributor.authorGurgul, P.en
dc.contributor.authorAbouEisha, H.en
dc.contributor.authorMoshkov, Mikhailen
dc.contributor.authorCalo, Victor M.en
dc.contributor.authorLenharth, A.en
dc.contributor.authorNguyen, D.en
dc.contributor.authorPingali, K.en
dc.date.accessioned2015-04-22T13:55:33Zen
dc.date.available2015-04-22T13:55:33Zen
dc.date.issued2015-04-22en
dc.identifier.citationQuasi-Optimal Elimination Trees for 2D Grids with Singularities 2015, 2015:1 Scientific Programmingen
dc.identifier.issn1058-9244en
dc.identifier.issn1875-919Xen
dc.identifier.doi10.1155/2015/303024en
dc.identifier.urihttp://hdl.handle.net/10754/550467en
dc.description.abstractWe construct quasi-optimal elimination trees for 2D finite element meshes with singularities.These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination process model the execution of the multifrontal algorithms in serial and in parallel shared-memory executions. Since the meshes considered are a subspace of all possible mesh partitions, we call these minimizers quasi-optimal.We minimize the cost functionals using dynamic programming. Finding these minimizers is more computationally expensive than solving the original algebraic system. Nevertheless, from the insights provided by the analysis of the dynamic programming minima, we propose a heuristic construction of the elimination trees that has cost O(log(Ne log(Ne)), where N e is the number of elements in the mesh.We show that this heuristic ordering has similar computational cost to the quasi-optimal elimination trees found with dynamic programming and outperforms state-of-the-art alternatives in our numerical experiments.en
dc.publisherHindawi Publishing Corporationen
dc.relation.urlhttp://www.hindawi.com/journals/sp/2015/303024/en
dc.rightsThis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en
dc.titleQuasi-Optimal Elimination Trees for 2D Grids with Singularitiesen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalScientific Programmingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionJagiellonian University, 31007 Krakow, Polanden
dc.contributor.institutionAGH University of Science and Technology, 30059 Krakow, Polanden
dc.contributor.institutionInstitute for Computational Engineering and Science, University of Texas, Austin, TX 78712-1229, USAen
kaust.authorAbouEisha, Hassan M.en
kaust.authorMoshkov, Mikhailen
kaust.authorCalo, Victor M.en
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