The method of local corrections (MLC) developed by Anderson for two spatial dimensions is a particle-particle particle-mesh method, in which the calculation of the velocity field induced by a collection of vortices is split into two parts: (i) a finite difference velocity field calculation using a fast Poisson solver, the results of which are used to represent the velocity field induced by vortices far from the evaluation point; and (ii) an N-body calculation to compute the velocity field at a vortex induced by nearby vortices. We present a fast vortex method for incompressible flow in three dimensions, based on the extension of the MLC algorithm from two to three spatial dimensions and the use of adaptive mesh refinement in the finite difference calculation of the MLC. Calculations with a vortex ring in three dimensions show that the break-even point between the MLC with AMR and the direct method is at N ? 3000 on a Cray Y-MP; for N ? 64,000 MLC with AMR can be 12 times faster than the direct method. Results from calculations of two colliding inviscid vortex rings demonstrate the increased resolution which can be obtained using fast methods.
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