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

Authors
Journal
Journal of Computational Physics
0021-9991
Publisher
Elsevier
Publication Date
Volume
83
Issue
1
Identifiers
DOI: 10.1016/0021-9991(89)90225-8

Abstract

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.

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