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

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

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 p...

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Veröffentlicht in:Journal of computational physics 1989-07, Vol.83 (1), p.126-147
Hauptverfasser: van Dommelen, Leon, Rundensteiner, Elke A.
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Sprache:eng
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Exact sciences and technology
Fluid Mechanics And Heat Transfer
Mathematical methods in physics
Numerical approximation and analysis
Physics
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container_title Journal of computational physics
container_volume 83
creator van Dommelen, Leon
Rundensteiner, Elke A.
description 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.
doi_str_mv 10.1016/0021-9991(89)90225-8
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subjects Exact sciences and technology
Fluid Mechanics And Heat Transfer
Mathematical methods in physics
Numerical approximation and analysis
Physics
title Fast, adaptive summation of point forces in the two-dimensional Poisson equation
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