Error-Controlled Hybrid Adaptive Fast Solver for Regularized Vortex Methods

TL;DR

This paper introduces an error-controlled hybrid adaptive fast solver that optimizes vortex method computations by balancing speed and accuracy through adaptive tree division, suitable for various hardware architectures.

Contribution

It presents a novel hybrid adaptive solver combining O(N) and O(N log N) schemes with error control for vortex methods, improving computational efficiency.

Findings

Enhanced computational speed for vortex calculations

Maintained desired accuracy levels

Effective balancing of near-field and far-field computations

Abstract

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.