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Schur complement preconditioning for elliptic systems of partial differential equations
Author(s) -
Loghin D.,
Wathen A. J.
Publication year - 2003
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.322
Subject(s) - schur complement , mathematics , symbol of a differential operator , complement (music) , semi elliptic operator , saddle point , schur's theorem , partial differential equation , elliptic partial differential equation , symbol (formal) , operator (biology) , factorization , algebra over a field , differential equation , differential operator , mathematical analysis , pure mathematics , algorithm , computer science , differential algebraic equation , ordinary differential equation , repressor , chemistry , gegenbauer polynomials , classical orthogonal polynomials , biochemistry , geometry , quantum mechanics , transcription factor , orthogonal polynomials , programming language , eigenvalues and eigenvectors , physics , complementation , gene , phenotype
Abstract One successful approach in the design of solution methods for saddle‐point problems requires the efficient solution of the associated Schur complement problem. In the case of problems arising from partial differential equations the factorization of the symbol of the operator can often suggest useful approximations for this problem. In this work we examine examples of preconditioners for regular elliptic systems of partial differential equations based on the Schur complement of the symbol of the operator and highlight the possibilities and some of the difficulties one may encounter with this approach. Copyright © 2003 John Wiley & Sons, Ltd.