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High order transmission conditions for thin conductive sheets in magneto-quasistatics
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 essentially smaller or at the order of the skin depth. 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 $\eps^{N+1}$ for the condition of order N. Numerical experiments with high order finite elements for sheets with varying curvature verify the theoretical findings.
https://hal.inria.fr/inria-00473213
Contributor : Sébastien Tordeux Connect in order to contact the contributor
Submitted on : Thursday, November 24, 2011 - 10:41:47 PM
Last modification on : Saturday, December 4, 2021 - 3:56:22 AM
Long-term archiving on: : Sunday, December 4, 2016 - 3:52:59 PM
Contributor : Sébastien Tordeux Connect in order to contact the contributor
Submitted on : Thursday, November 24, 2011 - 10:41:47 PM
Last modification on : Saturday, December 4, 2021 - 3:56:22 AM
Long-term archiving on: : Sunday, December 4, 2016 - 3:52:59 PM
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