Paul E. Barbone
Dept. of Aerospace and Mech. Eng., 110 Cummington St., Boston Univ., Boston, MA 02215
Expressions for diffraction coefficients for canonical shapes, joints, and discontinuities are necessary in applications of the geometrical theory of diffraction to scattering from submerged structures. In many cases of practical interest, however, the diffraction coefficients are either not available or are very difficult to evaluate. The use of perturbation theory and matched asymptotic expansions in obtaining suitable approximations of diffraction coefficients is described. These two methods can yield approximations that are simple to compute, easy to apply, and are valid in complementary parametric ranges. The perturbation method assumes that the properties of the solid or its geometry are nearly homogeneous. Matched asymptotics, on the other hand, is a useful tool when the solid is nearly hard, or the fluid is light. The accuracy of these methods is demonstrated by comparing them to the exact solution for diffraction by an impedance discontinuity. When the effort is made to obtain uniformly valid asymptotic expressions, the results prove to be remarkably accurate even at values of (epsilon)=1 (here, (epsilon) is a ``small'' parameter).