Diffraction at a curved grating: TM and TE cases, homogenization

Abstract

A hierarchy of effective boundary conditions is derived for a Helmholtz equation with Dirichlet or Neumann boundary conditions. These generalized impedance boundary conditions approximate the effect of thin dielectric layers with perfectly conducting inclusions covering an object. Well-posedness of the problems with these new boundary conditions is proved and optimal error estimates are given. © 1996 Academic Press, Inc.