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An algebraic two‐level preconditioner for asymmetric, positive‐definite systems
Author(s) -
Giddings Thomas E.,
Fish Jacob
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.265
Subject(s) - preconditioner , positive definite matrix , solver , finite element method , eigenvalues and eigenvectors , mathematics , linear subspace , polygon mesh , algebraic number , linear system , condition number , pure mathematics , mathematical optimization , mathematical analysis , geometry , physics , quantum mechanics , thermodynamics
A two‐level, linear algebraic solver for asymmetric, positive‐definite systems is developed using matrices arising from stabilized finite element formulations to motivate the approach. Supported by an analysis of a representative smoother, the parent space is divided into oscillatory and smooth subspaces according to the eigenvectors of the associated normal system. Using a mesh‐based aggregation technique, which relies only on information contained in the matrix, a restriction/prolongation operator is constructed. Various numerical examples, on both structured and unstructured meshes, are performed using the two‐level cycle as the basis for a preconditioner. Results demonstrate the complementarity between the smoother and the coarse‐level correction as well as convergence rates that are nearly independent of the problem size. Copyright © 2001 John Wiley & Sons, Ltd.