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" Asymptotically optimal BEM solvers based on Variable Order Wavelets " The talk will discuss a variable order wavelet method for boundary integral formulations of elliptic boundary value problems. The wavelets are restrictions of piecewise polynomial functions in three variables on the boundary manifold. This construction is especially suited to obtain sparse approximate representations of integral operators on complicated geometries. For integral equations of the second kind, the non-standard form can be compressed to contain only $O(N)$ non-vanishing entries while retaining the asymptotic convergence of the full Galerkin scheme. For first-kind equations, there are logarithmic terms in the complexity estimates. We will illustrate efficiency, accuracy and preconditioning of this approach on 3D example domains and compare the results with those obtained by the Fast Multipole Method. |