Application of the singular function expansion to an integral equation for scattering

The Dirichlet scattering problem is solved exactly for a surface of arbitrary smooth shape. The solution is given in terms of the complete, orthonormal set of functions defined on the surface and arising as singular functions of the integral operator. Since the singular values do not have a point of accumulation at zero, the method is of much greater practical value than the eigenmode expansion method (EEM). Since the terms in the infinite series are naturally ordered by size of singular value, the dominance of one or several terms in the series may be established without explicit evaluation of the coupling coefficients. Extentions of the method to other boundary value problems and applications to the singularity expansion method (SEM) are described.