Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

Handle URI:
http://hdl.handle.net/10754/626377
Title:
Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients
Authors:
Chavez Chavez, Gustavo Ivan ( 0000-0002-7593-505X ) ; Turkiyyah, George; Zampini, Stefano ( 0000-0002-0435-0433 ) ; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer Science Program; Extreme Computing Research Center; Applied Mathematics and Computational Science Program
Citation:
Chávez G, Turkiyyah G, Zampini S, Keyes D (2017) Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients. Journal of Computational and Applied Mathematics. Available: http://dx.doi.org/10.1016/j.cam.2017.11.035.
Publisher:
Elsevier BV
Journal:
Journal of Computational and Applied Mathematics
Issue Date:
7-Dec-2017
DOI:
10.1016/j.cam.2017.11.035
Type:
Article
ISSN:
0377-0427
Sponsors:
We thank the editors and the reviewers for their time and comments during the review process of this work. Support from the KAUST Supercomputing Laboratory and access to Shaheen Cray XC40 is gratefully acknowledged.
Additional Links:
http://www.sciencedirect.com/science/article/pii/S0377042717305952
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorChavez Chavez, Gustavo Ivanen
dc.contributor.authorTurkiyyah, Georgeen
dc.contributor.authorZampini, Stefanoen
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2017-12-14T12:34:04Z-
dc.date.available2017-12-14T12:34:04Z-
dc.date.issued2017-12-07en
dc.identifier.citationChávez G, Turkiyyah G, Zampini S, Keyes D (2017) Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients. Journal of Computational and Applied Mathematics. Available: http://dx.doi.org/10.1016/j.cam.2017.11.035.en
dc.identifier.issn0377-0427en
dc.identifier.doi10.1016/j.cam.2017.11.035en
dc.identifier.urihttp://hdl.handle.net/10754/626377-
dc.description.abstractWe present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.en
dc.description.sponsorshipWe thank the editors and the reviewers for their time and comments during the review process of this work. Support from the KAUST Supercomputing Laboratory and access to Shaheen Cray XC40 is gratefully acknowledged.en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0377042717305952en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, 6 December 2017. DOI: 10.1016/j.cam.2017.11.035. © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectPreconditioningen
dc.subjectCyclic reductionen
dc.subjectHierarchical matricesen
dc.titleParallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficientsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentComputer Science Programen
dc.contributor.departmentExtreme Computing Research Centeren
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalJournal of Computational and Applied Mathematicsen
dc.eprint.versionPost-printen
dc.contributor.institutionAmerican University of Beirut, Beirut, Lebanonen
kaust.authorChavez Chavez, Gustavo Ivanen
kaust.authorZampini, Stefanoen
kaust.authorKeyes, David E.en
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