Anthony M. J. Davis
Math. Dept., Univ. of Alabama, Tuscaloosa, AL 35487-0350
Robert W. Scharstein
Univ. of Alabama, Tuscaloosa, AL 35487-0286
The transmission problem of time-harmonic acoustic scattering by the velocity/density contrast wedge is formulated, through symmetry arguments and with the construction of suitable Green's functions, as a pair of uncoupled surface integral equations, each with one unknown function defined on a single wedge face. The convergent solution to the Fredholm integral equation of the first kind is expressed as a Galerkin series of Laguerre polynomials, and the development takes account of the distant behavior anticipated from the asymptotic solution to the related Sommerfeld half-space problem. The required inner products for the Galerkin projection scheme, which are integrals of products of the weighted Laguerre polynomials and the pair of Green's functions for the separate homogeneous regions, are written as Taylor series coefficients of an auxiliary function. Efficient numerical implementation of the physically based analysis produces an accurate and intuitive picture of the wave interactions with this canonical scatterer. [Work supported by the Naval Research Laboratory, Stennis Space Center.]