9700569 Kelley The principal investigator will continue his research program in the numerical solution of large systems of nonlinear equations and bound constrained optimization problems. In the area of nonlinear equations the PI will expand his recent work on nonlinear equations in two directions: (1) pseudo transient continuation, a popular method for computing steady-state solutions of certain problems in fluid mechanics and combustion, and (2) research into termination criteria for nonlinear iterations with applications to the method-of-lines solution of partial differential equations. The PI will also continue his work on multilevel methods for compact fixed point problems. In the area of bound constrained optimization in function spaces, the principal investigator will continue his work on methods for bound constrained parabolic control problems, begin a new project on preconditioners for bound constrained problems in infinite dimension, and redesign his implicit filtering code with a view toward applications in automotive engineering and environmental monitoring. New algorithmic features will be added to the code, the code will be ported to a parallel computer, and theoretical questions related to the new algorithms will be addressed. Such questions include detection of and escape from stagnation in Nelder-Mead and related algorithms and convergence of quasi-Newton methods in the presence of noise. Many processes and models in engineering and science are expressed as nonlinear equations. Numerical simulation of these processes requires the rapid and accurate solution of these equations and a clear understanding of the methods and their limitations. Simulation is then used in design and optimization for manufacturing. The optimization problems that arise in industrial design are often noisy because of measurement or simulation error. The principal investigator will continue his work on the computational solution of nonlinear equations and optimization p roblems. The work will consist of study of algorithms, needed to ensure robustness and reliability of simulations, implementation on distributed memory computers for rapid turn around, and testing in the context of engineering applications. Through the principal investigator's collaborations with scientists and engineers in industry, national laboratories, and academia, the work will be used in (a) environmental measurement and remediation, (b) simulation, optimal design, and control in the aerospace industry, and (c) optimal design in automotive engineering.
