### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | Department of Applied Mathematics, University of Twente |

Number of pages | 27 |

State | Published - Sep 2012 |

### Publication series

Name | Memorandum |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1992 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Fingerprint

### 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

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

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*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.

Research output: Professional › Report

TY - BOOK

T1 - A short guide to exponential Krylov subspace time integration for Maxwell's equations

AU - Bochev,Mikhail A.

PY - 2012/9

Y1 - 2012/9

N2 - 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.

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.

KW - EWI-22295

KW - MSC-65N22

KW - MSC-65F30

KW - MSC-65F60

KW - MSC-65L05

KW - MSC-35Q61

KW - Stopping criterion

KW - IR-84360

KW - Matrix exponential

KW - Exponential time integration

KW - Maxwell’s equations

KW - Krylov subspace methods

KW - Shift-and-invert

KW - METIS-289707

M3 - Report

T3 - Memorandum

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

PB - Department of Applied Mathematics, University of Twente

ER -