Solving the Helmholtz Equation for Exterior Problems with Variable Index of Refraction: I

A new technique for numerically solving the reduced wave equation on exterior domains is presented. The method is basically a relaxation scheme which exploits the limiting amplitude principle. A modified boundary condition at "infinity" is also given. The technique is tested on several model problems: the scattering of a plane wave off a metal cylinder, a metal strip, a Helmholtz resonator, an inhomogeneous cylinder (lens), and a nonlinear plasma column. The results are in good qualitative agreement with previously calculated values. In particular, the numerical solutions exhibit the correct refractive and diffractive effects at moderate frequencies.