Large scale PDE-constrained optimization applied to CFD applications

This thesis describes a tailored strategy for nonlinear programming (NLP) with partial differential equation (PDE) models. This approach is based on a reduced space Successive Quadratic Programming (rSQP) algorithm, and it allows the reuse of existing PDE-based modeling codes. This approach leads to an efficient simultaneous strategy, where the NLP and the PDE model are solved at the same time. A number of refinements were made to the NLP algorithm to enhance its performance and reliability for large, nonlinear models. This study considers PDE-based optimization problems to demonstrate the effectiveness of this approach.; In particular, we apply this approach to MPSalsa, a finite element PDE Solver developed at Sandia National Laboratories, and consider Chemical Vapor Deposition (CVD) and Catalytic Partial Oxidation (CPO) reactor models as the optimization application. Here our goals are to produce uniform gallium nitride microelectronic film and maximize the selectivity to syngas (CO and H₂). To minimize nonuniformity of the film, a novel NLP formulation is described and evaluated based on constraint aggregation. In addition to the design optimization strategy, we incorporate a stability analysis of the optimal design using the LOCA (Library of Continuation Algorithms) suite developed at Sandia National Laboratories.; An algorithm is explored to remove the bottleneck of calculating direct sensitivities by lumping the resulting inequality constraints of the QP into one constraint using a penalty parameter known as a KS approximation. An algorithm has been developed and tested on small test problems in which the end goal is to apply the technique to large scale PDE-constrained optimization problems.; A sensitivity algorithm has been developed to recalculate optimal values for small changes in the parameter values without resolving the optimization problem. The results of using this approach on the catalytic partial oxidation reactor are shown. An extensive literature review is given describing the recent progress in the solution of large scale PDE-constrained optimization problems. A conclusions section is given which summarizes the results and describes the advancement of the work.