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Author
J.G. Verwer
M.A. Botchev
Year
2009
Title
Unconditionally stable integration of Maxwell’s equations
Journal
Linear Algebra and its Applications
Volume | Issue number
431 | 3-4
Pages (from-to)
300-317
Document type
Article
Faculty
Faculty of Science (FNWI)
Institute
Korteweg-de Vries Institute for Mathematics (KdVI)
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 φ-functions. A three-space dimensional test problem is used for numerical assessment and comparison with an economical second-order implicit-explicit integrator.
URL
go to publisher's site
Language
Undefined/Unknown
Permalink
http://hdl.handle.net/11245/1.316080

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