The sensitivity equation method for optimal design

In this work, we introduce the Sensitivity Equation Method (SEM) as a method for approximately solving infinite dimensional optimal design problems. The SEM couples a trust-region/quasi-Newton optimization algorithm with gradient information provided by apprOXimately solving the sensitivity equation for (design) sensitivities. The sensitivity equation is (in the problems considered here) a partial differential equation (POE) which describes the influence of a design parameter on the state of the system. It is shown that obtaining design sensitivities from the sensitivity equation has advantages over finite difference and semi-analytical methods in that there is no need to remesh or compute mesh sensitivities (even if the domain is parameter dependent), the sensitivity equation is a linear POE for the sensitivities and can be approximated in an efficient manner using the same approximation scheme used to approximate the states. The applicability of the SEM to shape optimization problems, where the state is described by the Euler equations, is studied in detail. In particular, we prove convergence of the method for a one dimensional test problem. These results are used to speculate on the applicability of the method for more complex problems. Finally. we solve a two dimensional forebody simulator design problem (for use in wind tunnel experiments) using the SEM, which is shown to be a very efficient method for this problem.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1994

Author dc:creator

• Borggaard, Jeffrey T.

Chair dc:contributor.committeechair

• Burns, John A.

Committee members dc:contributor.committeemember

• Cliff, Eugene M.
• Gunzburger, Max D.
• Hannsgen, Kenneth B.
• Herdman, Terry L.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-06072006-124214

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/38563