Single integral equation for wave scattering

Abstract

When a wave interacts with an obstacle, the scattered and transmitted fields can be found by solving a system of integral equations for two unknown fields defined on the surface of the body. By choosing a more appropriate unknown function, the system of equations is reduced to a single singular integral equation of the first kind. This reduction is done here for transient and monochromatic waves, for a scalar field that obeys the wave equation, and for electromagnetic fields that obey Maxwell’s equations.