### ASA 127th Meeting M.I.T. 1994 June 6-10

## 5pUW12. Single surface integral equation for penetrable wedge scattering.

**Anthony M. J. Davis
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*Math. Dept., Univ. of Alabama, Tuscaloosa, AL 35487-0350
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**Robert W. Scharstein
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*Univ. of Alabama, Tuscaloosa, AL 35487-0286
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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.]