A short guide to exponential Krylov subspace time integration for Maxwell's equations

Mikhail A. Bochev

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.
Original languageUndefined
Place of PublicationEnschede
PublisherDepartment of Applied Mathematics, University of Twente
Number of pages27
StatePublished - Sep 2012

Publication series

NameMemorandum
PublisherDepartment of Applied Mathematics, University of Twente
No.1992
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Fingerprint

Time integration
Maxwell's equations
Numerical linear algebra
Arnoldi
Matrix exponential
Krylov subspace methods
Krylov subspace
Stopping criterion
Invert
Combined method
Exponential time
MATLAB

Keywords

  • EWI-22295
  • MSC-65N22
  • MSC-65F30
  • MSC-65F60
  • MSC-65L05
  • MSC-35Q61
  • Stopping criterion
  • IR-84360
  • Matrix exponential
  • Exponential time integration
  • Maxwell’s equations
  • Krylov subspace methods
  • Shift-and-invert
  • METIS-289707

Cite this

Bochev, M. A. (2012). A short guide to exponential Krylov subspace time integration for Maxwell's equations. (Memorandum; No. 1992). Enschede: Department of Applied Mathematics, University of Twente.

Bochev, Mikhail A. / A short guide to exponential Krylov subspace time integration for Maxwell's equations.

Enschede : Department of Applied Mathematics, University of Twente, 2012. 27 p. (Memorandum; No. 1992).

Research output: ProfessionalReport

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Bochev, MA 2012, A short guide to exponential Krylov subspace time integration for Maxwell's equations. Memorandum, no. 1992, Department of Applied Mathematics, University of Twente, Enschede.

A short guide to exponential Krylov subspace time integration for Maxwell's equations. / Bochev, Mikhail A.

Enschede : Department of Applied Mathematics, University of Twente, 2012. 27 p. (Memorandum; No. 1992).

Research output: ProfessionalReport

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AB - 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.

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Bochev MA. A short guide to exponential Krylov subspace time integration for Maxwell's equations. Enschede: Department of Applied Mathematics, University of Twente, 2012. 27 p. (Memorandum; 1992).