A RETRACTED BOUNDARY INTEGRAL-EQUATION FOR EXTERIOR ACOUSTIC PROBLEM WITH UNIQUE SOLUTION FOR ALL WAVE NUMBERS

A regular integral equation based on the surface source distribution method is developed to solve the exterior acoustic radiation and scattering problems. This integral equation, formed by seeking the equivalent mixed-layer potential distributed over an auxiliary surface retracted from the actual boundary, is uniquely solvable and has nonsingular kernel function. Hence, it is more amenable to numerical implementation and can circumvent the difficulties of singularity, nonuniqueness, and slope discontinuity of the conventional integral equation formulations. In contrast to the behavior of Fredholm integral equations of the second kind, the discretization of a regular integral equation will not result in a diagonally dominant coefficient matrix. To overcome the undesirable numerical instability, the optimal selection of the interior source surface is investigated through error estimate of the numerical integration. The versatility and accuracy of the proposed formulation are demonstrated by numerical examples involving spheres, prolate spheroids, and finite cylinders.