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An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations

The solution of the two-dimensional scattering problem for an homogeneous dielectric cylinder of arbitrary shape is considered. The numerical approach is based on a two-field system of integral equations solved by a Krylov subspace method. To accelerate and to improve the convergence of this solver, an efficient and robust preconditioner, based on the Calderón formulae, is developed. Several numerical simulations, for a wide range of physical parameters, validating the choice of this preconditioner are presented.