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Local Multiple Traces Formulation for Electromagnetics: Stability and Preconditioning for Smooth Geometries

Abstract : We consider the time-harmonic electromagnetic transmission problem for the unit sphere. Appealing to a vector spherical harmonics analysis, we prove the first stability result of the local multiple trace formulation (MTF) for electromagnetics, originally introduced by Hiptmair and Jerez-Hanckes [Adv. Comp. Math.37(2012), 37-91] for the acoustic case, paving the way towards an extension to general piecewise homogeneous scatterers. Moreover, we investigate preconditioning techniques for the local MTF scheme and study the accumulation points of induced operators. In particular, we propose a novel second-order inverse approximation of the operator. Numerical experiments validate our claims and confirm the relevance of the preconditioning strategies.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03137241
Contributor : Xavier Claeys <>
Submitted on : Wednesday, February 10, 2021 - 12:16:25 PM
Last modification on : Friday, February 12, 2021 - 3:32:56 AM

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2003.08330.pdf
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  • HAL Id : hal-03137241, version 1

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Alan Ayala, Xavier Claeys, Paul Escapil-Inchauspé, Carlos Jerez-Hanckes. Local Multiple Traces Formulation for Electromagnetics: Stability and Preconditioning for Smooth Geometries. 2020. ⟨hal-03137241⟩

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