Unconditionally stable integration of Maxwell's equations

J.G. Verwer, Mikhail A. Bochev

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    18 Citations (Scopus)

    Abstract

    Numerical integration of Maxwell's equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit finite difference time domain scheme. In this paper we discuss unconditionally stable integration for a general semi-discrete Maxwell system allowing non-Cartesian space grids as encountered in finite element discretizations. Such grids exclude the alternating direction implicit approach. Particular attention is given to the second-order trapezoidal rule implemented with preconditioned conjugate gradient iteration and to second-order exponential integration using Krylov subspace iteration for evaluating the arising phi-functions. A three-space dimensional test problem is used for numerical assessment and comparison with an economical second order implicit-explicit integrator. We further pay attention to the Chebyshev series expansion for computing the exponential operator for skew-symmetric matrices.
    Original languageUndefined
    Article number10.1016/j.laa.2008.12.036
    Pages (from-to)300-317
    Number of pages26
    JournalLinear algebra and its applications
    Volume431
    Issue number3-4
    DOIs
    Publication statusPublished - Jul 2009

    Keywords

    • EWI-17315
    • MSC-65L05
    • MSC-65L20
    • MSC-65M12
    • MSC-65M20
    • IR-69760
    • Krylov subspace iteration
    • exponential integration
    • implicit integration
    • conjugate gradient iteration
    • METIS-264501
    • Maxwell's equations

    Cite this

    Verwer, J. G., & Bochev, M. A. (2009). Unconditionally stable integration of Maxwell's equations. Linear algebra and its applications, 431(3-4), 300-317. [10.1016/j.laa.2008.12.036]. https://doi.org/10.1016/j.laa.2008.12.036