Multilevel approximation of boundary integral operators

In this paper we consider a multilevel approximation of boundary element matrices as they arise from the discretization. of boundary integral equations by Galerkins method. Our main emphasis lies in the numerical treatment of boundary integral equations defined on complex detailed two-dimensional manifolds in the three dimensional space. Although we do not assume that the underlying discretization has any hierarchical structure we present a scheme which provides us with a suitable hierarchy. Under reasonable assumptions on the kernel of the integral operator our multilevel approximation leads to a significant compression of the stiffness matrix without loosing the asymptotic approximation property of Galerkins method. An application of this approximation is the fast matrix multiplication which is needed in an iterative solution process.