This paper introduces a new Windowed Green Function (WGF) method for the
numerical integral-equation solution of problems of electromagnetic scattering
by obstacles in presence of dielectric or conducting half-planes. The WGF
method, which is based on use of smooth windowing functions and integral
kernels that can be expressed directly in terms of the free-space Green
function, does not require evaluation of expensive Sommerfeld integrals. The
proposed approach is fast, accurate, flexible and easy to implement. In
particular, straightforward modifications of existing (accelerated or
unaccelerated) solvers suffice to incorporate the WGF capability. The
mathematical basis of the method is simple: the method relies on a certain
integral equation posed on the union of the boundary of the obstacle and a
small flat section of the interface between the penetrable media. Numerical
experiments demonstrate that both the near- and far-field errors resulting from
the proposed approach decrease faster than any negative power of the window
size. In the examples considered in this paper the proposed method is up to
thousands of times faster, for a given accuracy, than a corresponding method
based on the layer-Green-function.
