Fast, adaptive summation of point forces in the two-dimensional Poisson equation

Authors:
Leon van Dommelen;Elke A. Rundensteiner
Affiliations:
Department of Mechanical Engineering, FAMU/FSU College of Engineering & Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306, USA;Department of Computer Science, Florida State University, Tallahassee, Florida 32306, USA
Venue:
Journal of Computational Physics
Year:
1989

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Abstract

Direct summation of the velocity field introduced by point vortices tends to be time consuming since the velocity of each vortex is found as a sum over all other vortices. The resulting number of numerical operations is proportional to the square of the number of vortices. Here a relatively simple procedure is outlined which significantly reduces the number of operations by replacing selected partial sums by asymptotic series. The resulting number of operations appears to vary roughly in proportion to the number of unknowns, corresponding to a ''fast'' solver.