A method for preconditioning matrices arising from linear integral equations for elliptic boundary value problems

The discretization of linear integral equations for elliptic boundary value problems by the boundary element method yields linear systems of simultaneous equations with filled matrices. The structure of these matrices allows Fourier methods to be used to determine preconditioning matrices such that fast iterative solution of the linear system of algebraic equations is possible. The preconditioning method is applicable to Fredholm integral equations of the first kind with non-smooth convolutional principal part as well as to Fredholm integral equations of the second kind. Numerical examples are presented.