Transition Problems for the Helmholtz Equation.

Abstract : The transition problem for time harmonic acoustic diffraction for two homogeneous media is considered. The source is in an infinite medium in which the second medium is immersed. The interface is either Lyapunov or piecewise Lyapunov. The problem is cast into weakly singular integral equations and regularized integral equations for the total field and its normal derivative. The Neumann series obtained by a simple iteration is shown to converge for some conditions. The iteration appears simpler than the corresponding Born Approximation method. (Modified author abstract)