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Preconditioner Updates for Solving Sequences of Linear Systems in Matrix-Free Environment

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    0338823 - ÚI 2011 RIV GB eng J - Journal Article
    Duintjer Tebbens, Jurjen - Tůma, Miroslav
    Preconditioner Updates for Solving Sequences of Linear Systems in Matrix-Free Environment.
    Numerical Linear Algebra with Applications. Roč. 17, č. 6 (2010), s. 997-1019. ISSN 1070-5325
    R&D Projects: GA AV ČR IAA100300802; GA AV ČR KJB100300703
    Grant - others:GA AV ČR(CZ) M100300902
    Institutional research plan: CEZ:AV0Z10300504
    Source of funding: I
    Keywords : preconditioned iterative methods * matrix-free environment * factorization updates * inexact Newton-Krylov methods * incomplete factorizations
    Subject RIV: BA - General Mathematics
    Impact factor: 1.163, year: 2010

    We present two new ways of preconditioning sequences of nonsymmetric linear systems in the special case where the implementation is matrix free. Both approaches are based on the general updates of incomplete LU decompositions recently introduced in (SISC 2007; 29(5):1918–1941) and they may be directly embedded into nonlinear algebraic solvers. The first approach uses a new model of partial matrix estimation to compute the updates. The second approach exploits separability of function components to apply the updated preconditioner via function evaluations. Experiments with matrix-free implementations of test problems show that both techniques offer useful, robust and black-box solution strategies.
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