The asymptotic computational ansatz: Application to critical angle beam transmission boundary integral equation solution

Abstract

Surface wave generation arising from critical angle beam transmission at a smooth but arbitrarily curved fluid–solid interface is studied using a numerical boundary integral equation (BIE) technique that incorporates a priori field information to significantly reduce computation. The technique substitutes a GTD-type computational ansatz into the BIE, where the phase factors of the ansatz are prescribed via asymptotic analysis, thus transforming the unknown variables to slowly varying amplitude factors. In situations where the asymptotic evaluation of these amplitude factors becomes intractable or inaccurate, common numerical integral equation methods are employed to determine the amplitude factors. The technique yields exact (in the numerically convergent sense) results for high-frequency scattering problems unsolvable by prevalent analytic or numeric techniques. Numerical implementation of the technique for critical angle beam transmission is demonstrated.