Integral Equations for Electromagnetic Scattering at Multi-Screens

Xavier Claeys 1, 2 Ralf Hiptmair 3
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
Inria de Paris, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, LJLL - Laboratoire Jacques-Louis Lions
Abstract : In [X. Claeys and R. Hiptmair, Integral equations on multi-screens. Integral Equ Oper 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.
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Xavier Claeys, Ralf Hiptmair. Integral Equations for Electromagnetic Scattering at Multi-Screens. Integral Equations and Operator Theory, Springer Verlag, 2016, 84 (1), pp.36. ⟨http://link.springer.com/article/10.1007%2Fs00020-015-2242-5⟩. ⟨10.1007/s00020-015-2242-5⟩. ⟨hal-01251236⟩

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