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We use a particle-based method to simulate incompressible flows, where the Fast Multipole Method (FMM) is used to accelerate the calculation of particle interactions. The most time-consuming kernels-the Biot-Savart equation and stretching term of the vorticity equation-are mathematically reformulated so that only two Laplace scalar potentials are used instead of six, while automatically ensuring divergencefree far-field computation. Based on this formulation, and on our previous work for adoi:10.1109/sc.companion.2012.221 dblp:conf/sc/HuGYBD12 fatcat:bo2ypvvtszbgvclpqbucgvkseu