The implementation of a fast, wavelet-based Galerkin discretization of second kind integral equations on piecewise smooth surfaces ; IR 3 is described. It allows meshes consisting of triangles as well as quadrilaterals. The algorithm generates a sparse, approximate sti ness matrix with N = O(N(log N) 2 ) nonvanishing entries in O(N(log N) 4 ) operations where N is the numberof degrees of freedom on the boundary while essentially retaining the asymptotic convergence rate of the full Galerkin

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... me. A new proof of the matrix-compression estimates is given based on derivative-free kernel estimates. The condition number of the sparse sti ness matrices is bounded independently of the meshwidth. The data structure containing the compressed sti ness matrix is described in detail: it requires O(N) memory and can be set up in O(N) operations. Numerical experiments show that the asymptotic performance estimates apply for moderate N. Problems with N = 10 5 degrees of freedom were computed in core on a workstation. The impact of various parameters in the compression scheme on the performance and the accuracy of the algorithm is studied.