  Sensitivity analysis methods are important tools for research and design with
simulations. Many important simulations exhibit chaotic dynamics, including
scale-resolving turbulent fluid flow simulations. Unfortunately, conventional
sensitivity analysis methods are unable to compute useful gradient information
for long-time-averaged quantities in chaotic dynamical systems. Sensitivity
analysis with least squares shadowing (LSS) can compute useful gradient
information for a number of chaotic systems, including simulations of chaotic
vortex shedding and homogeneous isotropic turbulence. However, this gradient
information comes at a very high computational cost. This paper presents
multiple shooting shadowing (MSS), a more computationally efficient shadowing
approach than the original LSS approach. Through an analysis of the convergence
rate of MSS, it is shown that MSS can have lower memory usage and run time than
LSS.
