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A novel method for the efficient and rigorous solution of electromagnetic scattering problems from 2D-faceted conducting bodies is introduced. In particular, the electric field integral equation (EFIE) is solved by resorting to analytically-derived basis functions that preserve some of the desired features of the high-frequency solutions, The sub-domains where the basis functions are defined can be electrically large, not being bound to the typical discretization size of the conventional method of moments (MoM). By properly weighting the resulting EFIE through a Galerkin procedure, the problem is reduced to a matrix equation whose dimensions do not depend on the size of the scatterer but only on its shape. The proposed method, namely high frequency integral equation (HFIE) method, is able to handle electrically large problems in a computationally efficient manner, both in terms of time and memory. The HFIE method yields good results both for open and closed bodies.