TY - JOUR

T1 - Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem

AU - Chen, Meng-Huo

AU - Greenbaum, Anne

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: National Science Foundation

PY - 2015/3/18

Y1 - 2015/3/18

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/594215

UR - http://doi.wiley.com/10.1002/nla.1980

UR - http://www.scopus.com/inward/record.url?scp=84935746465&partnerID=8YFLogxK

U2 - 10.1002/nla.1980

DO - 10.1002/nla.1980

M3 - Article

VL - 22

SP - 681

EP - 701

JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

SN - 1070-5325

IS - 4

ER -