Abstract
Contour dynamics methods are used to evolve regions of constant vorticity moving under the Euler equations for an inviscid, incompressible fluid in two dimensions. If the induced velocity field is evaluated directly, contour dynamics methods require a CPU time per timestep proportional to $N^2 $ (N being the number of nodes used to represent the contour). The fast multipole method is used to obtain an algorithm whose CPU time is $O(N)$. This results in speedup factors of 100 to 1000 without any loss of accuracy.
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