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Tuesday, May 11

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IP4

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*