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This article presents a three-dimensional formulation for the analysis of acoustic barriers over an impedance plane as infinitely thin structures. The barriers are therefore modeled as simple surfaces rather than volumetric structures. Using this approach, the problems caused by near-singular integrations and near-degenerate systems of equations are averted, and mesh generation is made easier. A dual-boundary-element method is used in the analysis, involving the simultaneous solution of standard and hypersingular boundary integral equations. An optimization procedure is used to speed up the assembling of the system of equations, increasing the applicability of the method to a wider range of frequencies.