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Preconditioning of matrices partitioned in 2 × 2 block form: eigenvalue estimates and Schwarz DD for mixed FEM
Author(s) -
Axelsson Owe,
Blaheta Radim
Publication year - 2010
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.728
Subject(s) - mathematics , eigenvalues and eigenvectors , saddle point , block (permutation group theory) , saddle , positive definite matrix , matrix (chemical analysis) , finite element method , eigendecomposition of a matrix , limit (mathematics) , domain decomposition methods , combinatorics , mathematical analysis , mathematical optimization , geometry , physics , materials science , quantum mechanics , composite material , thermodynamics
Abstract A general framework for constructing preconditioners for 2 × 2 block matrices is presented, and eigenvalue bounds of the preconditioned matrices are derived. The results are applied both for positive‐definite problems and for saddle point matrices of regularized forms. Eigenvalues and minimal polynomials for certain limit cases are derived. A domain decomposition method, with overlap, is used to solve the pivot block of the regularized matrix. Special attention is paid to problems with heterogeneous coefficients. Copyright © 2010 John Wiley & Sons, Ltd.