Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem

Handle URI:
http://hdl.handle.net/10754/594215
Title:
Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem
Authors:
Chen, Meng-Huo; Greenbaum, Anne
Abstract:
Summary: A two-grid convergence analysis based on the paper [Algebraic analysis of aggregation-based multigrid, by A. Napov and Y. Notay, Numer. Lin. Alg. Appl. 18 (2011), pp. 539-564] is derived for various aggregation schemes applied to a finite element discretization of a rotated anisotropic diffusion equation. As expected, it is shown that the best aggregation scheme is one in which aggregates are aligned with the anisotropy. In practice, however, this is not what automatic aggregation procedures do. We suggest approaches for determining appropriate aggregates based on eigenvectors associated with small eigenvalues of a block splitting matrix or based on minimizing a quantity related to the spectral radius of the iteration matrix. © 2015 John Wiley & Sons, Ltd.
KAUST Department:
Earth Science and Engineering Program
Citation:
Chen M-H, Greenbaum A (2015) Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem. Numerical Linear Algebra with Applications 22: 681–701. Available: http://dx.doi.org/10.1002/nla.1980.
Publisher:
Wiley-Blackwell
Journal:
Numerical Linear Algebra with Applications
Issue Date:
18-Mar-2015
DOI:
10.1002/nla.1980
Type:
Article
ISSN:
1070-5325
Sponsors:
National Science Foundation
Appears in Collections:
Articles; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorChen, Meng-Huoen
dc.contributor.authorGreenbaum, Anneen
dc.date.accessioned2016-01-19T14:43:27Zen
dc.date.available2016-01-19T14:43:27Zen
dc.date.issued2015-03-18en
dc.identifier.citationChen M-H, Greenbaum A (2015) Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem. Numerical Linear Algebra with Applications 22: 681–701. Available: http://dx.doi.org/10.1002/nla.1980.en
dc.identifier.issn1070-5325en
dc.identifier.doi10.1002/nla.1980en
dc.identifier.urihttp://hdl.handle.net/10754/594215en
dc.description.abstractSummary: A two-grid convergence analysis based on the paper [Algebraic analysis of aggregation-based multigrid, by A. Napov and Y. Notay, Numer. Lin. Alg. Appl. 18 (2011), pp. 539-564] is derived for various aggregation schemes applied to a finite element discretization of a rotated anisotropic diffusion equation. As expected, it is shown that the best aggregation scheme is one in which aggregates are aligned with the anisotropy. In practice, however, this is not what automatic aggregation procedures do. We suggest approaches for determining appropriate aggregates based on eigenvectors associated with small eigenvalues of a block splitting matrix or based on minimizing a quantity related to the spectral radius of the iteration matrix. © 2015 John Wiley & Sons, Ltd.en
dc.description.sponsorshipNational Science Foundationen
dc.publisherWiley-Blackwellen
dc.subjectAggregationen
dc.subjectAlgebraic multigriden
dc.subjectRotated anisotropic diffusionen
dc.titleAnalysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problemen
dc.typeArticleen
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalNumerical Linear Algebra with Applicationsen
dc.contributor.institutionDepartment of Applied Mathematics; University of Washington; Box 353925 Seattle WA 98195 USAen
kaust.authorChen, Meng-Huoen
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