@book{d72bda01cdbb47ba99e7a2bb676b571e,

title = "Unconditionally stable integration of Maxwell's equations",

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.",

keywords = "IR-68838, MSC-65L20, EWI-16956, MSC-65L05, MSC-65M12, METIS-264215, MSC-65M20",

author = "J.G. Verwer and Bochev, {Mikhail A.}",

note = "Please note different possible spellings of the first author name: {"}Botchev{"} or {"}Bochev{"}.",

year = "2008",

month = sep,

language = "Undefined",

series = "Modelling, Analysis and Simulation",

publisher = "Centrum voor Wiskunde en Informatica",

number = "MAS-R0806",

address = "Netherlands",

}