An extension of Draghicescu's fast tree-code algorithm to the vortex method on a sphere

  • Authors:

  • Takashi Sakajo

  • Affiliations:

  • Department of Mathematics, Hokkaido University, Japan and PRESTO, Japan Science and Technology Agency, Japan

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

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Abstract

A fast and accurate algorithm to compute interactions between N point vortices and between N vortex blobs on a sphere is proposed. It is an extension of the fast tree-code algorithm developed by Draghicescu for the vortex method in the plane. When we choose numerical parameters in the fast algorithm suitably, the computational cost of O(N^2) is reduced to O(N(logN)^4) and the approximation error decreases like O(1/N) when N-~, as demonstrated in the present article. We also apply the fast method to long-time evolution of two vortex sheets on the sphere to see the efficiency. A key point is to describe the equation of motion for the N points in the three-dimensional Cartesian coordinates.