Additive Schwarz preconditioners for the h-p version boundary-element approximation to the hypersingular operator in three dimensions

We study different preconditioners for the h-p version of the Galerkin boundary-element method when used to solve hypersingular integral equations of the first kind on a surface in ?³. These integral equations result from Neumann problems for the Laplace and Lamé equations in the exterior of the surface. The preconditioners are of additive Schwarz type (non-overlapping and overlapping). In all cases, we prove that the condition numbers grow at most logarithmically with the degrees of freedom.