Iterative across-time solution of linear differential equations: Krylov subspace versus waveform relaxation

Mikhail A. Bochev, I.V. Oseledets, E.E. Tyrtyshnikov

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    2 Citations (Scopus)
    41 Downloads (Pure)

    Abstract

    The aim of this paper is two-fold. First, we propose an efficient implementation of the continuous time waveform relaxation (WR) method based on block Krylov subspaces. Second, we compare this new WR-Krylov implementation against Krylov subspace methods combined with the shift and invert (SAI) technique. Some analysis and numerical experiments are presented. Since the WR-Krylov and SAI-Krylov methods build up the solution simultaneously for the whole time interval and there is no time stepping involved, both methods can be seen as iterative across-time methods. The key difference between these methods and standard time integration methods is that their accuracy is not directly related to the time step size.
    Original languageEnglish
    Pages (from-to)2088-2098
    Number of pages11
    JournalComputers and mathematics with applications
    Volume67
    Issue number12
    DOIs
    Publication statusPublished - Jul 2014

    Keywords

    • EWI-25568
    • MSC-65F60
    • MSC-65L05
    • MSC-65N22
    • MSC-65F10
    • MSC-65F30
    • Waveform relaxation
    • Residual
    • Richardson iteration
    • Low rank approximation
    • Krylov subspace methods
    • METIS-309814
    • IR-93648
    • Matrix exponential
    • Anderson acceleration

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