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Integral Equations for Electromagnetic Scattering at Multi-Screens

by X. Claeys and R. Hiptmair

(Report number 2015-01)

Abstract
In $[$X.~Claeys and R.~Hiptmair, Integral equations on multi-screens. Integral Equations and Operator Theory, 77(2):167--197, 2013$]$ we developed a framework for the analysis of boundary integral equations for acoustic scattering at so-called multi-screens, which are arbitrary arrangements of thin panels made of impenetrable material. In this article we extend these considerations to boundary integral equations for electromagnetic scattering. We view tangential multi-traces of vector fields from the perspective of quotient spaces and introduce the notion of single-traces and spaces of jumps. We also derive representation formulas and establish key properties of the involved potentials and related boundary operators. Their coercivity will be proved using a splitting of jump fields. Another new aspect emerges in the form of surface differential operators linking various trace spaces.

Keywords: Screens, electromagnetic scattering, trace spaces, boundary integral equations

@Techreport{CH15_591,
  author = {X. Claeys and R. Hiptmair},
  title = {Integral Equations for Electromagnetic Scattering at Multi-Screens},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2015-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-01.pdf },
  year = {2015}
}

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