On the efficiency of fast algorithms in 2D vortex element method - Kuzmina, Kseniia S.; Marchevsky, Ilia K. (Proceedings of the Conference Algoritmy, 2016)
The analogue of the Barnes --- Hut algorithm is considered as one of the most efficient ways to acceleration of the velocities computation in vortex element method. When calculating the convective velocities this algorithm makes it possible to take into account the influence of vortex elements, which are located far enough from each other, approximately. The tree-based algorithm is developed for the calculation of diffusive velocities. The estimations of computational complexity are obtained for the algorithms for convective and diffusive velocities calculation. Also estimations for the errors of the vortex elements velocities computation are constructed, which depend on the algorithm parameters. These estimates allow in practice to choice the optimal parameters of the whole algorithm and achieve the maximum possible acceleration of the computations for the given maximum error level.