PRECONDITIONED KRYLOV SUBSPACE METHODS FOR BOUNDARY-ELEMENT SOLUTION OF THE HELMHOLTZ-EQUATION

Discretization of boundary integral equations:leads, in general, to fu lly-populated complex valued non-Hermitian systems of equations. In th is paper we consider the efficient solution of these boundary element systems by preconditioned iterative methods of Krylov subspace type. W e devise preconditioners based on the splitting of the boundary integr al operators into smooth and non-smooth parts and show these to be ext remely efficient. The methods are applied to the boundary element solu tion of the Burton and Miller formulation of the exterior Helmholtz pr oblem which includes the derivative of the double layer Helmholtz pote ntial-a hypersingular operator. (C) 1998 John Wiley & Sons, Ltd.