Preconditioners for the Numerical Solution of Boundary Integral Equations from Acoustics

We extend the preconditioning technique developed by O. Steinbach and W.L. Wendland in [8] to the Helmholtz equation which governs time harmonic acoustic waves. Using layer potentials to represent the diffracted wave the scattering problem is reduced to an integral equation on the surface of the scatterer. This equation can be solved numerically with a Galerkin method. However the matrix is ill-conditioned for fine meshes and close to resonant frequencies. We describe the construction of a preconditioner such that the preconditioned matrix models a compact perturbation of the identity operator. We state the relevant theoretical estimates and show numerical results. This work was financially supported by Thomson-CSF Detexis.