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In this paper a method for fast computations with the inverse to weakly singular, hypersingular and double layer potential boundary integral operators associated with the Laplacian on Lipschitz domains is proposed and analyzed. It is based on the representation formulae suggested for above-mentioned boundary operators in terms of the Poincare-Steklov interface mappings generated by the special decompositions of the interior and exterior domains. Computations with the discrete counterparts of these formulae can be efficiently performed by iterative substructuring algorithms provided some asymptotically optimal techniques fc>r treatment of interface operators on subdomain boundaries. For both twoand three-dimensional cases the computation cost and memory needs are of the order O(N logp N) and O(N log2 N), respectively, with 1 5 p 5 3, where N is the number of degrees of freedom on the boundary under consideration (some kinds of polygons and polyhedra). The proposed algorithms are well suited for serial and parallel computations.

On Fast Computations with the Inverse to Harmonic Potential Operators via Domain Decomposition