Preconditioners for the boundary element method in acoustics

We extend the preconditioning technique developed by O. Steinbach and W. L. Wendland in [8] to the Helmholtz equation in R-3 which governs time harmonic acoustic waves. Using layer potentials the scattering problem is reduced to an integral equation on the boundary of the scatterer. This equation is solved numerically with a Galerkin method. We prove that the suggested preconditioning technique yields a spectral condition number which is uniformly bounded in h for any regular family of meshes. Next we show numerical results that illustrate the efficiency of the method. The dependence upon the wavelength is discussed.