A Fast Method for Solving Acoustic Scattering Problems in Frequency Bands

We present a methodology for computing efficiently scattered fields in a frequency band. The main feature of this methodology is the construction of a series of discrete problems that differ only by their right-hand sides, rather than by both their left- and right-hand sides. Its key steps are (a) the reformulation of the acoustic scattering problem in a bounded domain using any preferred absorbing boundary condition, (b) the characterization of the repeated derivatives with respect to the frequency of the scattered field as solutions of scattering-type problems with different source terms and boundary conditions, and (c) the reconstruction of a scattered field by either the Padé approximants or Wynnʹs algorithm. We report on several multifrequency acoustic scattering examples that illustrate the accuracy and computational efficiency of the proposed solution methodology.