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The analysis of electrically large objects can be unaffordable due to memory and CPU time requirements. The application of the fast multipole method (FMM) to the analysis of 2D perfectly conducting (PEC) cylinders of arbitrary cross-section reduces the cost from O(N2) operations, when the method of moments (MOM) is used, to O(N1.5). For a complete analysis of the 2D scatterer, both TMz and TEz incident polarizations must be considered. FMM has been widely used for the analysis of TMz incidence, but little research has been devoted to the analysis of the TEz polarized incidence. The FMM is applied to the acceleration of the point-matching MOM discretization of the MFIE (magnetic field integral equation) obtained when the incident field is a TEz polarized wave. The results are compared, in terms of precision and efficiency, to those obtained applying MOM uniquely.