# Unconditionally stable integration of Maxwell's equations

Verwer, J.G. and Botchev, M.A. (2009) *Unconditionally stable integration of Maxwell's equations.* Linear Algebra and its Applications, 431 (3-4). pp. 300-317. ISSN 0024-3795

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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. |

Item Type: | Article |

Copyright: | © 2009 Elsevier |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/69760 |

Official URL: | http://dx.doi.org/10.1016/j.laa.2008.12.036 |

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