Preconditioned Krylov subspace methods for boundary element solution of the Helmholtz equation

Discretization of boundary integral equations leads, in general, to fully populated complex valued non- Hermitian systems of equations. In this paper we consider the e cient solution of these boundary element systems by preconditioned iterative methods of Krylov subspace type. We devise preconditioners based on the splitting of the boundary integral operators into smooth and non-smooth parts and show these to be extremely e cient. The methods are applied to the boundary element solution of the Burton and Miller formulation of the exterior Helmholtz problem which includes the derivative of the double layer Helmholtz potential|a hypersingular operator