TY - CHAP

T1 - Analyses of time-harmonic problems

AU - Assous, Franck

AU - Ciarlet, Patrick

AU - Labrunie, Simon

N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85067996341&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-70842-3_8

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

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AN - SCOPUS:85067996341

T3 - Applied Mathematical Sciences (Switzerland)

SP - 313

EP - 346

BT - Applied Mathematical Sciences (Switzerland)

ER -