A new two-dimensional panel technique has been developed to solve Laplacian flows, which eliminates the edge effect present in traditional panel methods. Such a method is very useful for applications where the velocity induced by the panels is required at arbitrary locations. Particle based flow solvers are a prime example. The method, however, requires considerably more computational effort. In this paper the method is modified to improve computational efficiency by adapting the fast multipole algorithm for the panel method. Significant improvement in computational efficiency is obtained while ensuring that the edge effects are eliminated.