A short guide to exponential Krylov subspace time integration for Maxwell's equations

Mikhail A. Bochev

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    Abstract

    The exponential time integration, i.e., time integration which involves the matrix exponential, is an attractive tool for solving Maxwell's equations in time. However, its application in practice often requires a substantial knowledge of numerical linear algebra algorithms, in particular, of the Krylov subspace methods. This note provides a brief guide on how to apply exponential Krylov subspace time integration in practice. Although we consider Maxwell's equations, the guide can readily be used for other similar time-dependent problems. In particular, we discuss in detail the Arnoldi shift-and-invert method combined with recently introduced residual-based stopping criterion. Two of the algorithms described here are available as MATLAB codes and can be downloaded from the website \url{http://eprints.eemcs.utwente.nl/} together with this note.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages27
    Publication statusPublished - Sep 2012

    Publication series

    NameMemorandum
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1992
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • EWI-22295
    • MSC-65N22
    • MSC-65F30
    • MSC-65F60
    • MSC-65L05
    • MSC-35Q61
    • Stopping criterion
    • IR-84360
    • Matrix exponential
    • Exponential time integration
    • Maxwell’s equations
    • Krylov subspace methods
    • Shift-and-invert
    • METIS-289707

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