Volume 41, pp. 350-375, 2014.
Convergence analysis of the FEM coupled with Fourier-mode expansion for the electromagnetic scattering by biperiodic structures
Guanghui Hu and Andreas Rathsfeld
Abstract
Scattering of time-harmonic electromagnetic plane waves
by a doubly periodic surface structure in
can be simulated by a boundary value problem of the
time-harmonic curl-curl equation. For a truncated
FEM domain, non-local boundary conditions are required
in order to satisfy the radiation conditions for the
upper and lower half spaces.
As an alternative to boundary integral formulations, to
approximate radiation conditions and absorbing boundary
methods, Huber et al. [SIAM J. Sci. Comput., 31 (2009),
pp. 1500–1517] 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.
Full Text (PDF) [312 KB],
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Key words
electromagnetic scattering, diffraction gratings, convergence analysis, finite element methods, mortar technique
AMS subject classifications
78A45, 78M10, 65N30, 35J20
