Compression Techniques for Boundary Integral Equations - Asymptotically Optimal Complexity Estimates

Matrix compression techniques in the context of wavelet Galerkin schemes for boundary integral equations are developed and analyzed that exhibit optimal complexity in the following sense. The fully discrete scheme produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that is proven to stay proportional to the number of unknowns. Key issues are the second compression, which reduces the near field complexity significantly, and an additional a posteriori compression. The latter is based on a general result concerning an optimal work balance that applies, in particular, to the quadrature used to compute the compressed stiffness matrix with sufficient accuracy in linear time.