TU Darmstadt / ULB / TUbiblio

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

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

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.

Item Type: Article
Erschienen: 2011
Creators: Schmidt, Kersten and Tordeux, Sébastien
Title: High order transmission conditions for thin conductive sheets in magneto-quasistatics
Language: English
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.

Journal or Publication Title: ESAIM: Math. Model. Numer. Anal.
Volume: 45
Number: 6
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 19 Nov 2018 21:46
DOI: 10.1051/m2an/2011009
Official URL: http://dx.doi.org/10.1051/m2an/2011009
Export:

Optionen (nur für Redakteure)

View Item View Item