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

Kersten Schmidt; Sébastien Tordeux

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 45, Issue: 6, page 1115-1140
  • ISSN: 0764-583X

Abstract

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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 ε 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 ε and obtain optimal bound for the modelling error outside the sheet of order ε N + 1 for the condition of order N. We end the paper with numerical experiments involving high order finite elements for sheets with varying curvature.

How to cite

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Schmidt, Kersten, and Tordeux, Sébastien. "High order transmission conditions for thin conductive sheets in magneto-quasistatics." ESAIM: Mathematical Modelling and Numerical Analysis 45.6 (2011): 1115-1140. <http://eudml.org/doc/276350>.

@article{Schmidt2011,
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 ε 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 ε and obtain optimal bound for the modelling error outside the sheet of order $\varepsilon^\{N+1\}$ for the condition of order N. We end the paper with numerical experiments involving high order finite elements for sheets with varying curvature. },
author = {Schmidt, Kersten, Tordeux, Sébastien},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Asymptotic expansions; transmission condition; thin conducting sheets; asymptotic expansions},
language = {eng},
month = {6},
number = {6},
pages = {1115-1140},
publisher = {EDP Sciences},
title = {High order transmission conditions for thin conductive sheets in magneto-quasistatics},
url = {http://eudml.org/doc/276350},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Schmidt, Kersten
AU - Tordeux, Sébastien
TI - High order transmission conditions for thin conductive sheets in magneto-quasistatics
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/6//
PB - EDP Sciences
VL - 45
IS - 6
SP - 1115
EP - 1140
AB - 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 ε 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 ε and obtain optimal bound for the modelling error outside the sheet of order $\varepsilon^{N+1}$ for the condition of order N. We end the paper with numerical experiments involving high order finite elements for sheets with varying curvature.
LA - eng
KW - Asymptotic expansions; transmission condition; thin conducting sheets; asymptotic expansions
UR - http://eudml.org/doc/276350
ER -

References

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