  This paper presents high-order integral equation methods for evaluation of
electromagnetic wave scattering by dielectric bumps and dielectric cavities on
perfectly conducting or dielectric half-planes. In detail, the algorithms
introduced in this paper apply to eight classical scattering problems, namely:
scattering by a dielectric bump on a perfectly conducting or a dielectric
half-plane, and scattering by a filled, overfilled or void dielectric cavity on
a perfectly conducting or a dielectric half-plane. In all cases field
representations based on single-layer potentials for appropriately chosen Green
functions are used. The numerical far fields and near fields exhibit excellent
convergence as discretizations are refined--even at and around points where
singular fields and infinite currents exist.
