, Volume 16, Issue 2-3, pp 139-156

Finite Element Solution of Conical Diffraction Problems

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Abstract

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R 2 coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.