Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least   Square Shadowing (NILSS)
  This paper develops the non-intrusive formulation of the Least-squares shadowing (LSS) method, for computing the sensitivity of long-time averaged objectives in chaotic dynamical systems. This non-intrusive formulation constrains the computation to only the unstable subspace, greatly reducing the cost of LSS for many problems; moreover, it reparametrizes the LSS problem, requiring only minor modifications to existing tangent solvers. NILSS is demonstrated on a chaotic flow over a backward-facing step simulated with a mesh of 12e3 cells. 
Angxiu Ni, Qiqi Wang
physics.comp-ph cs.CE cs.NA math.NA nlin.CD