@book{319b78405a1f4b7caa7719513a0169cf,

title = "A short guide to exponential Krylov subspace time integration for Maxwell's equations",

abstract = "The exponential time integration, i.e., time integration which involves the matrix exponential, is an attractive tool for solving Maxwell's equations in time. However, its application in practice often requires a substantial knowledge of numerical linear algebra algorithms, in particular, of the Krylov subspace methods. This note provides a brief guide on how to apply exponential Krylov subspace time integration in practice. Although we consider Maxwell's equations, the guide can readily be used for other similar time-dependent problems. In particular, we discuss in detail the Arnoldi shift-and-invert method combined with recently introduced residual-based stopping criterion. Two of the algorithms described here are available as MATLAB codes and can be downloaded from the website \url{http://eprints.eemcs.utwente.nl/} together with this note.",

keywords = "EWI-22295, MSC-65N22, MSC-65F30, MSC-65F60, MSC-65L05, MSC-35Q61, Stopping criterion, IR-84360, Matrix exponential, Exponential time integration, Maxwell{\textquoteright}s equations, Krylov subspace methods, Shift-and-invert, METIS-289707",

author = "Bochev, {Mikhail A.}",

year = "2012",

month = sep,

language = "Undefined",

series = "Memorandum",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1992",

}