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22295 A short guide to exponential Krylov subspace time integration for Maxwell's equations
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Botchev, M.A. (2012) A short guide to exponential Krylov subspace time integration for Maxwell's equations. Memorandum 1992, Department of Applied Mathematics, University of Twente, Enschede. ISSN 1874-4850

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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.

Item Type:Internal Report (Memorandum)
Research Group:EWI-MACS: Mathematics of Computational Science
Research Program:MESA-APS: Advanced Photonic Structures
Research Project:BRICKS/MSV1: Scientific computing
Uncontrolled Keywords:Matrix exponential, Maxwell’s equations, Krylov subspace methods, Exponential time integration, Shift-and-invert, Stopping criterion
ID Code:22295
Deposited On:28 September 2012
More Information:statisticsmetis

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