  High frequency integral equation methodologies display the capability of
reproducing single-scattering returns in frequency-independent computational
times and employ a Neumann series formulation to handle multiple-scattering
effects. This requires the solution of an enormously large number of
single-scattering problems to attain a reasonable numerical accuracy in
geometrically challenging configurations. Here we propose a novel and effective
Krylov subspace method suitable for the use of high frequency integral equation
techniques and significantly accelerates the convergence of Neumann series. We
additionally complement this strategy utilizing a preconditioner based upon
Kirchhoff approximations that provides a further reduction in the overall
computational cost.
