Local Multiple Traces Formulation for electromagnetics: Stability and preconditioning for smooth geometries

Alan Ayala, Xavier Claeys, Paul Escapil-Inchauspé, Carlos Jerez-Hanckes

Research output: Contribution to journalArticlepeer-review

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 traces formulation (MTF) for electromagnetics, originally introduced by Hiptmair and Jerez-Hanckes (2012) 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 proposed.

Original languageEnglish
Article number114356
JournalJournal of Computational and Applied Mathematics
Volume413
DOIs
StatePublished - 15 Oct 2022
Externally publishedYes

Keywords

  • Boundary element method
  • Maxwell scattering
  • Multiple Traces Formulation
  • Preconditioning
  • Vector spherical harmonics

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