Frequency independent solvability of surface scattering problems

We address the problem of frequency independent solvability of high-frequency scattering problems in the exterior of two-dimensional smooth, compact, strictly convex obstacles. Precisely, we show that if the leading term in the asymptotic expansion of the surface current is incorporated into the integral equation formulations of the scattering problem, then appropriate modifications of both the “frequency-adapted Galerkin boundary element methods” and the “Galerkin boundary element methods based on frequency dependent changes of variables” we have recently developed yield frequency independent approximations. Moreover, for any direct integral equation formulation of the scattering problem, we show that the error can be tuned to decrease at any desired rate with increasing frequency, if sufficiently many terms in the aforementioned asymptotic expansion are incorporated into the solution strategy.