# Mathematics Colloquia and Seminars

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### Sensitivity Computations for Optimal Design and Control of Systems Governed by Partial Differential Equations

**Mathematical Physics & Probability**

Speaker: | John A. Burns, Center for Optimal Design and Control, Virginia Tech |

Location: | 693 Kerr |

Start time: | Mon, Jan 10 2000, 2:10PM |

Many modern aerospace design problems can be viewed as distributed parameter variational and optimal control problems. In 1686, Newton proposed the famous problem of determining the body of revolution that produces a minimum drag nose shape in a hypersonic flow. Modern versions of such design challenges lead to complex shape optimization problems. In this presentation, the speaker will discuss an optimal control approach to design and illustrate how this approach can provide theoretical and computational insight into algorithm development. The goal is to show that introducing approximations at the proper time in algorithm development can lead to optimal design tools that are fast, accurate and often easy to implement by modifying existing simulation tools.

The speaker will use a application involving the control and optimization of thin film growth to motivate the basic problem. A simple nonlinear inverse problem will be used to describe various numerical algorithms based on sensitivity equation methods. These algorithms are then used to demonstrate the central ideas. Finally, he will close with an application to a scramjet design problem and present other examples to illustrate how these methods are already being included in new commercial software products.

This research project is part of the AFOSR PRET Center activities funded under grant F49620-96-1-0329.