Acceleration of the Jacobi iterative method by factors exceeding 100 using scheduled relaxation

Xiang Yang, Rajat Mittal

    Research output: Contribution to journalArticle

    30 Citations (Scopus)

    Abstract

    We present a methodology that accelerates the classical Jacobi iterative method by factors exceeding 100 when applied to the finite-difference approximation of elliptic equations on large grids. The method is based on a schedule of over- and under-relaxations that preserves the essential simplicity of the Jacobi method. Mathematical conditions that maximize the convergence rate are derived and optimal schemes identified. The convergence rate predicted from the analysis is validated via numerical experiments. The substantial acceleration of the Jacobi method enabled by the current method has the potential to significantly accelerate large-scale simulations in computational mechanics, as well as other areas where elliptic equations are prominent.

    Original languageEnglish (US)
    Pages (from-to)695-708
    Number of pages14
    JournalJournal of Computational Physics
    Volume274
    DOIs
    StatePublished - Oct 1 2014

    Fingerprint

    Computational mechanics
    Iterative methods
    computational mechanics
    schedules
    Experiments
    grids
    methodology
    approximation
    simulation

    All Science Journal Classification (ASJC) codes

    • Numerical Analysis
    • Modeling and Simulation
    • Physics and Astronomy (miscellaneous)
    • Physics and Astronomy(all)
    • Computer Science Applications
    • Computational Mathematics
    • Applied Mathematics

    Cite this

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    Acceleration of the Jacobi iterative method by factors exceeding 100 using scheduled relaxation. / Yang, Xiang; Mittal, Rajat.

    In: Journal of Computational Physics, Vol. 274, 01.10.2014, p. 695-708.

    Research output: Contribution to journalArticle

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