Sparse subsampling of flow measurements for finite-time Lyapunov exponent in domains with obstacles

We propose an efficient approach to estimate the finite-time Lyapunov exponent (FTLE). Instead of incorporating all available velocity measurements, we develop a sparse subsampling approach to detect relevant flow measurements for velocity reconstruction. This work has two main contributions. We first extend our previous algorithm in Ng and Leung (2019) to reconstruct a flow field with an impermeable condition. To solve the corresponding under-determined system for reconstructing the global velocity field, we propose a L1 optimization framework that can lead to a sparse reconstruction algorithm. Therefore, the overall algorithm can automatically identify and extract a sparse subset of velocity measurements for the FTLE computations. We will provide synthetic and real-life numerical examples to demonstrate the effectiveness of the proposed algorithm.(c) 2023 Elsevier B.V. All rights reserved.