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High order transmission conditions for thin conductive sheets in magneto-quasistatics

Schmidt, Kersten ; Tordeux, Sébastien :
High order transmission conditions for thin conductive sheets in magneto-quasistatics.
[Online-Edition: http://dx.doi.org/10.1051/m2an/2011009]
In: ESAIM: Math. Model. Numer. Anal., 45 (6) S. 1115-1140.
[Artikel] , (2011)

Offizielle URL: http://dx.doi.org/10.1051/m2an/2011009

Kurzbeschreibung (Abstract)

We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses \eps are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t.~to the small parameter \eps and obtain optimal bound for the modelling error outside the sheet of order \epsN+1 for the condition of order ℕ. We end the paper with numerical experiments involving high order finite elements for sheets with varying curvature.

Typ des Eintrags: Artikel
Erschienen: 2011
Autor(en): Schmidt, Kersten ; Tordeux, Sébastien
Titel: High order transmission conditions for thin conductive sheets in magneto-quasistatics
Sprache: Englisch
Kurzbeschreibung (Abstract):

We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses \eps are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t.~to the small parameter \eps and obtain optimal bound for the modelling error outside the sheet of order \epsN+1 for the condition of order ℕ. We end the paper with numerical experiments involving high order finite elements for sheets with varying curvature.

Titel der Zeitschrift, Zeitung oder Schriftenreihe: ESAIM: Math. Model. Numer. Anal.
Band: 45
(Heft-)Nummer: 6
Fachbereich(e)/-gebiet(e): 04 Fachbereich Mathematik
04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen
Hinterlegungsdatum: 19 Nov 2018 21:46
DOI: 10.1051/m2an/2011009
Offizielle URL: http://dx.doi.org/10.1051/m2an/2011009
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