ON FAST COMPUTATIONS WITH THE INVERSE TO HARMONIC POTENTIAL-OPERATORSVIA DOMAIN DECOMPOSITION

In this paper a method for fast computations with the inverse to weakl y singular, hypersingular and double layer potential boundary integral operators associated with the Laplacian on Lipschitz domains is propo sed and analyzed. It is based on the representation formulae suggested for above-mentioned boundary operators in terms of the Poincare-Stekl ov interface mappings generated by the special decompositions of the i nterior and exterior domains. Computations with the discrete counterpa rts of these formulae can be efficiently performed by iterative substr ucturing algorithms provided some asymptotically optimal techniques fo r treatment of interface operators on subdomain boundaries. For both t wo- and three-dimensional cases the computation cost and memory needs are of the order O(N log(p) N) and O(N log(2) N), respectively, with 1 less than or equal to p less than or equal to 3, where N is the numbe r of degrees of freedom on the boundary under consideration (some kind s of polygons and polyhedra). The proposed algorithms are well suited for serial and parallel computations.