Efficient time-stepping-free time integration of the Maxwell equations

Mikhail A. Bochev

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    Abstract

    Solution of the time dependent Maxwell equations is an important problem arising in many applications ranging from nanophotonics to geoscience and astronomy. The problem is far from trivial, and solutions typically exhibit complicated wave properties as well as damping behavior. Usually, special staggered time stepping schemes are used [Botchev,Verwer,2009]. Although their time step may be severely restricted by the CFL condition, performance of these schemes is hard to beat by modern implicit or exponential time integration schemes [Verwer,Botchev,2009]. We show that in some cases so-called time-stepping-free schemes provide a very efficient alternative to the standard schemes. These schemes employ the matrix exponential function and can be implemented by special block Krylov subspace techniques [Botchev,Grimm,Hochbruck,2013],[Botchev,2013]. Numerical examples demonstrating the efficiency of the proposed approach are presented, coming from the fields of nanophotonics and geoscience.
    Original languageUndefined
    Title of host publicationProceedings of the International Conference "Difference schemes and applications" in Honor of the 90-th Birthday of Prof. V.S. Ryaben'kii.
    EditorsK.V. Brushlinskii, M.S. Gavreeva, V.T. Zhukov, A.V. Severin, N.A. Cmykhova
    Place of PublicationMoscow
    PublisherRussian Academy of Sciences, Keldysh Institute of Applied Mathematics.
    Pages16
    Number of pages1
    ISBN (Print)978-5-98354-010-1
    Publication statusPublished - May 2013
    EventInternational Conference "Difference schemes and applications" in Honor of the 90-th Birthday of Prof. V.S. Ryaben'kii - Moscow, Russia
    Duration: 27 May 201331 May 2013

    Publication series

    Name
    PublisherRussian Academy of Sciences, Keldysh Institute of Applied Mathematics

    Conference

    ConferenceInternational Conference "Difference schemes and applications" in Honor of the 90-th Birthday of Prof. V.S. Ryaben'kii
    Period27/05/1331/05/13
    OtherMay 27-31, 2013

    Keywords

    • EWI-23476
    • Photonics
    • Time domain modeling
    • METIS-297716
    • IR-86639
    • Maxwell equations
    • Exponential time integration

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