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 [7] to operators satisfying Inf-Sup conditions. Thus to the Gal erkin matrix A(h) of S(k) or N (k) we associate an implicit preconditioning matrix Z(h) such that multiplication by Z(h) is of the,Fame complexity as multiplication by A(h), and Z(h)A(h) models a compact perturbation of the i dentity operator: We prove that the spectral condition number of Z(h)A(h) i s uniformly bounded for any regular family of meshes, as h --> 0. Numerical evidence of the efficiency of the preconditioning technique. is also provi ded. Finally we adapt the method to screen problems. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.