# 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

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topSchmidt, 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 -

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