  In this paper, an error-controlled hybrid adaptive fast solver that combine
both O(N) and O(N log N) scheme is proposed. For a given accuracy, the adaptive
solver is used in the context of regularized vortex methods to optimize the
speed of the velocity and vortex stretching calculation. This is accomplished
by introducing three critical numbers in order to limit the depth of the tree
division and to balance the near-field and far-field calculations for any
hardware architecture. The adaptive solver is analyzed in term of speed and
accuracy.
