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

Alan Ayala (1, 2) , Xavier Claeys (1, 2) , Paul Escapil-Inchauspé (3) , Carlos F. Jerez-Hanckes (4)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
3 UC - Pontificia Universidad Católica de Chile
4 Universidad Adolfo Ibáñez [Santiago]

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.

Keywords: Maxwell Scattering; Multiple Traces Formulation; Vector Spherical Harmonics; Preconditioning; Boundary Element Method

Domains: Mathematics [math]; Numerical Analysis [math.NA]

Alan Ayala, Xavier Claeys, Paul Escapil-Inchauspé, Carlos F. Jerez-Hanckes. Local Multiple Traces Formulation for Electromagnetics: Stability and Preconditioning for Smooth Geometries. Journal of Computational and Applied Mathematics, 2022, 413, ⟨10.1016/j.cam.2022.114356⟩. ⟨hal-03137241⟩