Hybrid Methods for Sensitivity Computations in Optimal Design

8:30 AM-9:15 AM

*Room: Capitol North/Center*

*Chair: Ekkehard W. Sachs, Universität Trier, Germany*

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. In particular, the goal is to show that by introducing approximations at the proper time in algorithm development can lead to optimal design tools that are both fast and accurate.

The speaker will describe a simple nonlinear inverse problem that involves the construction of a spatial domain to minimize the difference between a given field of data and the solution of a boundary value problem defined on this domain. He will use this model problem 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 illustrate how these methods are already being included in new commercial software products.

**John A. Burns**

*Center for Optimal Design and Control*

*Interdisciplinary Center for Applied Mathematics*

*Virginia Polytechnic Institute & State University*

*MMD, 1/4/99*