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Author: Rathsfeld, Andreas × End date: 2019 × Start date: 2010 × Subject: mortar technique × WGL Institute: WIAS ×

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    Convergence analysis of the FEM coupled with Fourier-mode expansion for the electromagnetic scattering by biperiodic structures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Rathsfeld, Andreas
    Scattering of time-harmonic electromagnetic plane waves by a doubly periodic surface structure in R3 can be simulated by a boundary value problem of the time-harmonic curl-curl equation. For a truncated FEM domain, non-local boundary value conditions are required in order to satisfy the radiation conditions for the upper and lower half spaces. Alternatively to boundary integral formulations, to approximate radiation conditions and absorbing boundary methods, Huber et al. [11] have proposed a coupling method based on an idea of Nitsche. In the case of profile gratings with perfectly conducting substrate, the authors have shown previously that a slightly modified variational equation can be proven to be equivalent to the boundary value problem and to be uniquely solvable. Now it is shown that this result can be used to prove convergence for the FEM coupled by truncated wave mode expansion. This result covers transmission gratings and gratings bounded by additional multi-layer systems.
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    Scattering of time harmonic electromagnetic plane waves by perfectly conducting diffraction gratings
    (Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Rathsfeld, Andreas
    Consider scattering of time-harmonic lectromagnetic plane waves by a doubly periodic surface in R^3. The medium above the surface is supposed to be homogeneous and isotropic with a constant dielectric coefficient, while below is a perfectly conducting material. This paper is concerned with the existence of quasiperiodic solutions for any frequency of incidence. Based on an equivalent variational formulation established by the mortar technique of Nitsche, we verify the existence of solutions for a broad class of incident waves including plane waves, under the assumption that the grating profile is a Lipschitz biperiodic surface. Our solvability result covers the resonance case where a Rayleigh frequency is allowed. Non-uniqueness examples are also presented in the resonance case and the TE or TM polarization case for classical gratings.