Analyses of time-harmonic problems

Franck Assous; Patrick Ciarlet; Simon Labrunie

doi:10.1007/978-3-319-70842-3_8

Analyses of time-harmonic problems

Franck Assous, Patrick Ciarlet, Simon Labrunie

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this chapter, we specifically study the time-harmonic Maxwell equations. They derive from the time-dependent equations by assuming that the time dependence of the data and fields is proportional to exp (− ıωt), for a pulsation ω ≥ 0 (the frequency is equal to ω∕(2π)). When the pulsation ω is not known, the time-harmonic problem models free vibrations of the electromagnetic fields. One has to solve an eigenproblem, for which both the fields and the pulsation are unknowns. On the other hand, when ω is part of the data, the time-harmonic problem models sustained vibrations. Generally speaking, we refer to this problem as a Helmholtz-like problem, for which the only unknown is the fields.

Original language	English
Title of host publication	Applied Mathematical Sciences (Switzerland)
Publisher	Springer
Pages	313-346
Number of pages	34
DOIs	https://doi.org/10.1007/978-3-319-70842-3_8
State	Published - 2018
Externally published	Yes

Publication series

Name	Applied Mathematical Sciences (Switzerland)
Volume	198
ISSN (Print)	0066-5452
ISSN (Electronic)	2196-968X

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© Springer International Publishing AG, part of Springer Nature 2018.

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10.1007/978-3-319-70842-3_8

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Analyses of time-harmonic problems

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