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The method of moments (MoM) has been successfully applied to all types of electromagnetic scattering and radiation problems. As is well known, conventional MoM techniques lead to fully populated interaction matrices. This aspect limits the electrical size of the problem that can be solved on a given computer with limited memory. Previously introduced fast methods, such as the adaptive integral method (AIM) and fast multipole method (FMM), provide for reduced memory and CPU requirements. In this paper we consider the implementation of FMM to MoM matrices associated with 2nd order curvilinear elements. Particular emphasis is given on the convergence properties and accuracy of FMM acceleration schemes. It is demonstrated that preconditioning is often essential when dealing with FMM matrices generated from curvilinear element implementations. Also, choices of lower order multipole expansions can lead to much faster speeds but lower accuracy.