Unconditionally stable integration of Maxwell's equations

J.G. Verwer, Mikhail A. Bochev

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    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
    Place of PublicationAmsterdam
    PublisherCentrum voor Wiskunde en Informatica
    Number of pages26
    Publication statusPublished - Sept 2008

    Publication series

    NameModelling, Analysis and Simulation
    ISSN (Print)1386-3703


    • IR-68838
    • MSC-65L20
    • EWI-16956
    • MSC-65L05
    • MSC-65M12
    • METIS-264215
    • MSC-65M20

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