Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem
Type
ArticleAuthors
Chen, Meng-Huo
Greenbaum, Anne
KAUST Department
Earth Science and Engineering ProgramPhysical Science and Engineering (PSE) Division
Date
2015-03-18Online Publication Date
2015-03-18Print Publication Date
2015-08Permanent link to this record
http://hdl.handle.net/10754/594215
Metadata
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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.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.Sponsors
National Science FoundationPublisher
WileyDOI
10.1002/nla.1980ae974a485f413a2113503eed53cd6c53
10.1002/nla.1980