# 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
Appears in Collections:
Conference Papers; Extreme Computing Research Center

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.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