The discrete vortex method (DVM) is based on a Lagrangian description of the vorticity transport equation. In order to numerically solve the DVM, one can split the vorticity equation into separate diffusive and convective effects. Several formulations can be used to model the diffusive effect, e.g. The random walk method, the core spreading method and the velocity diffusion method. The convection effect can be treated using the material derivative to avoid the solution of a non-linear term; this is the major advantage of the method since each discrete vortex is convected with the fluid velocity field. However, the solution of the fluid velocity field requires the contributions from the incident flow, the perturbation due to the body and the particle interactions. The latter contribution is computationally expensive since the Biot-Savart law is used to compute the induced velocity by all discrete vortices in the cloud. The fast multipole method is an attractive algorithm used to accelerate the expensive interactions of the discrete vortices. It reduces the computational cost of the Biot-Savart law from O(N2) to O(N), where N is the number of discrete vortices in the cloud for a particular time step. The present FMM algorithm is based on the original ideas of Greengard and Rokhlin, with modifications to further accelerate the solution. In the present work, both FMM and Biot-Savart law solutions are compared by calculating the vortex-vortex interactions for different cylinder wakes, previously generated by a DVM. The present numerical tool will be used in future computational simulations of aerodynamic flows past airfoils in pitching and plunging motions and vortex induced vibration problems. 10651076Chorin, A.J., Numerical study of slightly viscous flow (1973) Journal of Fluid Mechanics, 57, pp. 785-796Rossi, L.F., Resurrecting core spreading vortex methods: A new scheme that is both deterministic and convergent (1996) SIAM J. Sci. Comput, 17, pp. 370-397Ogami, Y., Akamatsu, T., Viscous flow simulation using the discrete vortex model - The diffusion velocity method (1991) Computers & Fluids, 19 (3), pp. 433-441Lewis, R.I., (1991) Vortex Element Method for Fluid Dynamic Analysis of Engineering Systems, , Cambridge Univ. Press, Cambridge, England, U.KCipra, B.A., The best of the 20th century: Editors name top 10 algorithms (2000) SIAM News, 33, pp. 1-2Greengard, L., Rokhlin, V., A fast algorithm for particle simulations (1987) Journal of Computational Physics, 73, pp. 325-348Carrier, J., Greengard, L., Rokhlin, V., A fast adaptive multipole algorithm for particle simulations (1988) SIAM Journal on Scientific and Statistical Computing, 9 (4), pp. 669-686Bimbato, A.M., Alcantara Pereira, L.A., Hirata, M.H., Simulation of viscous flow around a circular cylinder near a moving ground (2009) J. of the Braz. Soc. of Mech. Sci & Eng, 31 (3), pp. 243-252. , July-SeptemberBimbato, A.M., Study of Turbulent Flows Around A Smooth or A Rough Bluff Body Using the Discrete Vortex Method, 165p. , Ph.D. Thesis-Mechanical Engineering Institute, Federal University of Itajubá in PortugueseWolf, W.R., Airfoil Aeroacoustics: Les and Acoustic Analogy, , Ph.D. Thesis-Aeronautics and Astronautics, Stanford University1st Pan-American Congress on Computational Mechanics, PANACM 2015 and the 11th Argentine Congress on Computational Mechanics, MECOM 201527 April 2015 through 29 April 2015