Detecting Near Resonances in Acoustic Scattering

We propose and study a method for finding quasi-resonances for a linear acoustic transmission problem in frequency domain. Starting from an equivalent boundary-integral equation we perform Galerkin boundary element discretization and look for the minima of the smallest singular value of the resulting matrix as a function of the wave number k. We develop error estimates for the impact of Galerkin discretization on singular values and devise a heuristic adaptive algorithm for finding the minima in prescribed k-intervals. Our method exclusively relies on the solution of eigenvalue problems for real k, in contrast to alternative approaches that rely on extension to the complex plane.