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dc.contributor.authorChavez Chavez, Gustavo Ivan
dc.contributor.authorTurkiyyah, George
dc.contributor.authorZampini, Stefano
dc.contributor.authorKeyes, David E.
dc.date.accessioned2017-12-14T12:34:04Z
dc.date.available2017-12-14T12:34:04Z
dc.date.issued2017-12-07
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.
dc.identifier.issn0377-0427
dc.identifier.doi10.1016/j.cam.2017.11.035
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.
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.
dc.publisherElsevier BV
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0377042717305952
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/
dc.subjectPreconditioning
dc.subjectCyclic reduction
dc.subjectHierarchical matrices
dc.titleParallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentComputer Science Program
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalJournal of Computational and Applied Mathematics
dc.eprint.versionPost-print
dc.contributor.institutionAmerican University of Beirut, Beirut, Lebanon
dc.identifier.arxividarXiv:1712.08872
kaust.personChavez Chavez, Gustavo Ivan
kaust.personZampini, Stefano
kaust.personKeyes, David E.
dc.date.published-online2017-12-07
dc.date.published-print2018-12


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