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Krylov‐accelerated algebraic multigrid for semi‐definite and nonsymmetric systems in computational fluid dynamics
Author(s) -
Emans Maximilian
Publication year - 2012
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1812
Subject(s) - multigrid method , acceleration , linear system , hierarchy , mathematics , algebraic number , computer science , positive definite matrix , grid , computational fluid dynamics , fluid dynamics , mathematical optimization , computational science , algebra over a field , partial differential equation , mathematical analysis , pure mathematics , eigenvalues and eigenvectors , physics , geometry , classical mechanics , quantum mechanics , economics , market economy , mechanics
SUMMARY This article reports on experiences with aggregation algebraic multigrid relying on Krylov acceleration on each level of the grid hierarchy as preconditioners for linear systems in general purpose fluid flow simulation software. In benchmarks that reflect the requirements of industrial simulations, it is demonstrated that for semi‐definite problems, the performance of recently published algorithms of this type is very attractive but that proposed variants of these algorithms occasionally fail for nonsymmetric problems. A modification leading to reliable solvers is suggested. Copyright © 2012 John Wiley & Sons, Ltd.