A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements

Handle URI:
http://hdl.handle.net/10754/623778
Title:
A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements
Authors:
Chávez, Gustavo; Turkiyyah, George; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with O(Nlog2N) arithmetic complexity and O(NlogN) memory footprint. We provide a baseline for performance and applicability by comparing with well-known implementations of the $$\mathcal{H}$$ -LU factorization and algebraic multigrid within a shared-memory parallel environment that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $$\mathcal{H}$$ -LU and that it can tackle problems where algebraic multigrid fails to converge.
KAUST Department:
Extreme Computing Research Center
Citation:
Chávez G, Turkiyyah G, Keyes DE (2017) A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements. Domain Decomposition Methods in Science and Engineering XXIII: 135–143. Available: http://dx.doi.org/10.1007/978-3-319-52389-7_12.
Publisher:
Springer Nature
Journal:
Domain Decomposition Methods in Science and Engineering XXIII
Conference/Event name:
23rd International Conference on Domain Decomposition Methods, DD23
Issue Date:
17-Mar-2017
DOI:
10.1007/978-3-319-52389-7_12
Type:
Conference Paper
ISSN:
1439-7358; 2197-7100
Additional Links:
http://link.springer.com/chapter/10.1007/978-3-319-52389-7_12
Appears in Collections:
Conference Papers; Extreme Computing Research Center

Full metadata record

DC FieldValue Language
dc.contributor.authorChávez, Gustavoen
dc.contributor.authorTurkiyyah, Georgeen
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2017-05-31T11:23:04Z-
dc.date.available2017-05-31T11:23:04Z-
dc.date.issued2017-03-17en
dc.identifier.citationChávez G, Turkiyyah G, Keyes DE (2017) A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements. Domain Decomposition Methods in Science and Engineering XXIII: 135–143. Available: http://dx.doi.org/10.1007/978-3-319-52389-7_12.en
dc.identifier.issn1439-7358en
dc.identifier.issn2197-7100en
dc.identifier.doi10.1007/978-3-319-52389-7_12en
dc.identifier.urihttp://hdl.handle.net/10754/623778-
dc.description.abstractA parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with O(Nlog2N) arithmetic complexity and O(NlogN) memory footprint. We provide a baseline for performance and applicability by comparing with well-known implementations of the $$\mathcal{H}$$ -LU factorization and algebraic multigrid within a shared-memory parallel environment that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $$\mathcal{H}$$ -LU and that it can tackle problems where algebraic multigrid fails to converge.en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/chapter/10.1007/978-3-319-52389-7_12en
dc.titleA Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complementsen
dc.typeConference Paperen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalDomain Decomposition Methods in Science and Engineering XXIIIen
dc.conference.date2015-07-06 to 2015-07-10en
dc.conference.name23rd International Conference on Domain Decomposition Methods, DD23en
dc.conference.locationJeju Island, KORen
kaust.authorChávez, Gustavoen
kaust.authorTurkiyyah, Georgeen
kaust.authorKeyes, David E.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.