Wave-number estimates for regularized combined field boundary integral operators in acoustic scattering problems with Neumann boundary conditions (Q2856617)

The authors analyse the coercivity and the wave-number dependence of the norms of the operators that enter a class of combined field regularized integral equations (CFIERs) for the solution of two- and three-dimensional acoustic scattering problems with Neumann boundary conditions. They prove that the norms grow modestly with the wave-number in the high-frequency regime for smooth boundaries. They rigorusly estblish that, for high frequencies and sufficiently large coupling constants, the CFIER operators are coercive in \(L^{2}(\Gamma )\) in the case of circular and spherical geometries \(\Gamma \), and that the coercivity constants do not depend on the wave-numbers. A fully discrete Nyström collocation method for the solution of two-dimensional acoustic scattering problems with von Neumann boundary conditions based on regularized combined field integral equations is presented. Pointwise superalgebraic convergence rates of the discrete solutions are established for analytic boundaries and boundary data.