A multilevel additive Schwarz method for a hypersingular integral equation on an open curve with graded meshes

In this paper we present the additive Schwarz method for the hypersingular integral equation of the first kind in two dimensions for the h version of the Galerkin method on algebraically graded meshes. We prove that the condition number of the preconditioned system grows only polylogarithmically with respect to the number of unknowns. Our theoretical results are underlined by numerical experiments.