A Comparison of Local and Global Projections in Design Sensitivity Computations
In this paper we discuss the problem of constructing accurate numerical schemes for calculating state sensitivities for application to design. In computing sensitivities, spatial derivatives of finite element state approximations are required. We introduce two projection techniques, motivated by a-posteriori error estimators used in adaptive finite element schemes, for computing improved derivative approximations. We briefly describe the techniques and their implementation for calculating sensitivities for a 1-D model problem. Numerical results illustrating the improved accuracy of the sensitivities are presented for the 1-D model problem as well as for two dimensional flow around a cylinder.
KeywordsModel Problem Projection Technique Local Projection Projection Scheme Sensitivity Equation
Unable to display preview. Download preview PDF.
- J.T. Borggaard. The Sensitivity Equation Method for Optimal Design. Ph.D. Thesis, Virginia Tech, Blacksburg, VA, 1994.Google Scholar
- J.T. Borggaard and J.A. Burns. A PDE Sensitivity Equation Method for Optimal Aerodynamic Design, Journal of Computational Physics. Google Scholar
- J.T. Borggaard and J.A. Burns. A Sensitivity Equation Approach to Optimal Design of Nozzles, 5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Design, AIAA Paper 94–4274, 232–241, 1994.Google Scholar
- J.T. Borggaard and J.A. Burns. A Sensitivity Equation Approach to Shape Optimization in Fluid Flows, Flow Control, Proceedings of the IMA, Vol. 68, M. Gunzburger, Ed., Springer-Verlag, 1995.Google Scholar
- J.T. Borggaard and D. Pelletier. Computing Design Sensitivities using an Adaptive Finite Element Method, 27th AIAA Fluid Dynamics Conference, AIAA Paper 96–1938, 1996.Google Scholar
- J.A. Burns and R. Spies. Sensitivity Analysis for a Dynamic Model of Phase Transition in Materials with Memory, Recent Advances in Adaptive and Sensory Materials and their Applications, C.A. Rogers and R.C. Rogers, Eds., Technomic Publishing Co., Basel, 82–93, 1992.Google Scholar