Parallel multigrid for large-scale least squares sensitivity

Abstract

This thesis presents two approaches for efficiently computing the "climate" (long- time average) sensitivities for dynamical systems. Computing these sensitivities is essential to performing engineering analysis and design. The first technique is a novel approach to solving the "climate" sensitivity problem for periodic systems. A small change to the traditional adjoint sensitivity equations results in a method which can accurately compute both instantaneous and long-time averaged sensitivities. The second approach deals with the recently developed Least Squares Sensitivity (LSS) method. A multigrid algorithm is developed that can, in parallel, solve the discrete LSS system. This generic algorithm can be applied to ordinary differential equations such as the Lorenz System. Additionally, this parallel method enables the estimation of climate sensitivities for a homogeneous isotropic turbulence model, the largest scale LSS computation performed to date.