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A comparison of overlapping Schwarz methods and block preconditioners for saddle point problems
Author(s) -
Klawonn Axel,
Pavarino Luca F.
Publication year - 2000
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/(sici)1099-1506(200001/02)7:1<1::aid-nla183>3.0.co;2-j
Subject(s) - preconditioner , schwarz alternating method , saddle point , mathematics , additive schwarz method , domain decomposition methods , diagonal , block (permutation group theory) , saddle , positive definite matrix , block matrix , domain (mathematical analysis) , algorithm , mathematical optimization , mathematical analysis , iterative method , geometry , finite element method , eigenvalues and eigenvectors , physics , thermodynamics , quantum mechanics
Three domain decomposition methods for saddle point problems are introduced and compared. The first two are block‐diagonal and block‐triangular preconditioners with diagonal blocks approximated by an overlapping Schwarz technique with positive definite local and coarse problems. The third is an overlapping Schwarz preconditioner based on indefinite local and coarse problems. Numerical experiments show that while all three methods are numerically scalable, the last method is almost always the most efficient. Copyright © 2000 John Wiley & Sons, Ltd.