Improvement of convergence of DICCG method by Eisenstat’s trick, extension of adaptiveness

It is well-known that Conjugate Gradient (CG) method with DIC factorization can be viewed as one of useful solvers for a linear system of equations with a symmetric positive definite matrix. On the other hand, Eisenstat’s trick also can be viewed as an efficient implementation for CG methed without...

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Published inTransactions of the Japan Society for Computational Engineering and Science Vol. 2008; p. 20080004
Main Authors SOMEHARA, Kazunori, FUJINO, Seiji
Format Journal Article
LanguageJapanese
Published JAPAN SOCIETY FOR COMPUTATIONAL ENGINEERING AND SCIENCE 28.02.2008
Subjects
DIC factorization
Eisensta’s trick
ICCG method
Krylov subspace methods
preconditioning
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Summary:It is well-known that Conjugate Gradient (CG) method with DIC factorization can be viewed as one of useful solvers for a linear system of equations with a symmetric positive definite matrix. On the other hand, Eisenstat’s trick also can be viewed as an efficient implementation for CG methed without preconditioning only. However, this technique had limited effectiveness because of insufficiency and instability of DIC factorization. In this paper, we will propose a strategy for a more efficient and stable implementation combined with accelerated DIC factorization and Eisenstat’s trick and by numerical experiments we will present that this indeed may lead to faster and stable convergence.
ISSN:1347-8826
DOI:10.11421/jsces.2008.20080004