An efficient Uniform Integrated Advection algorithm for Finite Time Lyapunov Exponent field computation on GPU and MIC

Abstract

Finite Time Lyapunov Exponent (FTLE) is widely used in Lagrangian Coherent Structure extraction and research on unsteady flow field. FTLE is computationally expensive due to the flow map calculation on dense samples in the field. In order to improve the computation efficiency, we investigate the most time-consuming flow map and propose UIA, a Uniform Integrated Advection algorithm based on piecewise linear hypothesis. FTLE coverts multiple spatiotemporal interpolations and multi-step time advection into single matrix multiplication so as to dramatically reduce computation and be applied to any type of grids. We also design an UIA based FTLE algorithm on GUP and MIC to further reduce computation time, and present corresponding performance optimization strategies. The correctness and accuracy of algorithm are also experimentally verified by applying the algorithm to an analytical 3-dimensional field. The speedup ratio of the proposed algorithm ranges from 6 to 143 compared with FTLE execution time based on traditional RK4 flow map, which demonstrates that UIA has significantly improve the efficiency of FTLE computation and visualization.