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Smoothed aggregation multigrid for incompressible flows
Author(s) -
Janka Aleš
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700457
Subject(s) - multigrid method , preconditioner , schur complement , compressibility , mathematics , black box , complement (music) , computer science , algebraic number , mathematical optimization , stability (learning theory) , iterative method , mathematical analysis , physics , mechanics , partial differential equation , chemistry , biochemistry , eigenvalues and eigenvectors , quantum mechanics , artificial intelligence , complementation , machine learning , gene , phenotype
We discuss the advantages of using algebraic multigrid based on smoothed aggregation for solving indefinite linear problems. The ingredients of smoothed aggregation are used to construct a black‐box monolithic multigrid method with indefinite coarse problems. Although we discuss some techniques for enforcing the uniform inf‐sup stability on all coarse levels, numerical experiments suggest that it is not strictly necessary. The proposed multigrid preconditioner shows robust behaviour for different time‐step parameters and even for very elongated geometries, where other techniques based on h ‐independent preconditioners of the pressure Schur complement lose their efficiency. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)