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A Projection Method for Accurate Computation of Design Sensitivities

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Optimal Control

Part of the book series: Applied Optimization ((APOP,volume 15))

Abstract

In this paper we discuss the problem of constructing accurate numerical schemes for calculating state sensitivities for application to design. We concentrate on a model problem and use this model to develop the fundamental ideas and to illustrate the mathematical difficulties. Numerical results are given for the model problem and a 2-D fluid flow example. The goal of this paper is to introduce the basic idea and to illustrate its application to a practical flow problem.

This research was supported in part by the Air Force Office of Scientific Research under grants F49620-93-1-0280 and F49620-96-1-0329 and the National Science Foundation under grant DMS-9508773.

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References

  1. Ainsworth, M., Zhu, J.Z., Craig, A.W. and Zienkiewicz, O.C. (1989),“Analysis of the Zienkiewicz-Zhu a-posteriori error estimator in the finite element method,” International Journal for Numerical Methods in Engineering, Vol. 28, 2161–2174.

    Article  MathSciNet  MATH  Google Scholar 

  2. Borggaard, J.T. (1994), The Sensitivity Equation Method for Optimal Design, Ph.D. dissertation, Virginia Tech, Blacksburg, VA.

    Google Scholar 

  3. Borggaard, J., Burkardt, J., Cliff, E., Gunzburger, M., Kim, H., Lee, J., Peterson, J., Shenoy, A. and Wu, X. (1995), “Algorithms for flow control and optimization,” in Optimal Design and Control, J. Borggaard, J. Burkardt, M. Gunzburger and J. Peterson, eds., Birkhäuser Verlag, Basel, 97–116.

    Chapter  Google Scholar 

  4. Borggaard, J.T. and Burns, J.A., “A PDE sensitivity equation method for optimal aerodynamic design,” Journal of Computational Physics,to appear.

    Google Scholar 

  5. Borggaard, J.T. and Burns, J.A.(1994)“A sensitivity equation approach to optimal design of nozzles,” 5th AIAA /USAF/NASA/ISSMO Sysposium on Multidisciplinary Analysis and Design,AIAA Paper 944274, 232–241.

    Google Scholar 

  6. Borggard, J.T. and Burns, J.A. (1995), “A sensitivity equation approach to shape optimization in fluid flows,” in Flow Control, Proceedings of the IMA, Vol. 68, M. Gunzburger, ed., Springer-Verlag, Berlin.

    Google Scholar 

  7. Borggard, J.T. and Pelletier, D. (1996), `Computing design sensitivities using an adaptive finite element method,“ 27th AIAA Fluid Dynamics Conference, AIAA Paper 96–1938.

    Google Scholar 

  8. Burns, J.A. and Spies, R. (1994), “A numerical study of parameter sensitivities in Landau-Ginzburg models of phase transitions in shape memory alloys,” Journal of Intelligent Material Systems and Structures, Vol. 5, 321–332.

    Article  Google Scholar 

  9. Burns, J.A. and Spies, R. (1992), “Sensitivity analysis for a dynamic model of phase transition in materials with memory,” in Recent Advances in Adaptive and Sensory Materials and their Applications, C. A. Rogers, and R. C. Rogers, eds., Technomic Publishing Co., Basel, 82–93.

    Google Scholar 

  10. Hétu, J.F. and Pelletier, D (1992), “Adaptive remeshing for viscous incompressible flows,” AIAA Journal, Vol. 30, No. 8, 1986–1992.

    Google Scholar 

  11. Zienkiewicz, O.C. and Zhu, J.Z. (1987), “A simple error estimator and adaptive procedure for practical engineering analysis,” International Journal for Numerical Methods in Engineering, Vol. 24, 337–357.

    Article  MathSciNet  MATH  Google Scholar 

  12. Zienkiewicz, O.C. and Zhu, J.Z. (1992), “A super convergent patch recovery and a posteriori error estimators. Part I: The Recovery Technique,” International Journal for Numerical Methods in Engineering, Vol. 33, 1331–1364.

    Article  MathSciNet  MATH  Google Scholar 

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© 1998 Springer Science+Business Media Dordrecht

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Burns, J.A., Stanley, L.G., Stewart, D.L. (1998). A Projection Method for Accurate Computation of Design Sensitivities. In: Optimal Control. Applied Optimization, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6095-8_3

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  • DOI: https://doi.org/10.1007/978-1-4757-6095-8_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4796-3

  • Online ISBN: 978-1-4757-6095-8

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