Impulse response approximations of discrete shape hessians with application in CFD

SIAM Journal on Control and Optimization

Volumn 48, Issue 4, 2009, Pages 2562-2580

  Schmidt, Stephan ^a   Schulz, Volker ^a  

^a UNIVERSITY OF TRIER   (Germany)

Author keywords

Approximative Newton method; Fourier mode; Navier Stokes; Operator symbol; Preconditioning; Shape Hessian; Shape optimization; Stokes

Indexed keywords

FOURIER MODES; NAVIER STOKES; OPERATOR SYMBOLS; PRECONDITIONING; SHAPE HESSIAN; STOKES;

SHAPE OPTIMIZATION;

EID: 79952324437     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/080719844     Document Type: Article

References (20)

1. E. ARIAN, Analysis of the Hessian for aeroelastic optimization, Technical report 95-84, ICASE, NASA Langley Research Center, Hampton, VA, 1995.
2. E. ARIAN and S. TA'ASAN, Analysis of the Hessian for aerodynamic optimization: Inviscid flow, Technical report 96-28, ICASE, NASA Langley Research Center, Hampton, VA, 1996.
3. E. ARIAN and V. N. VATSA, A preconditioning method for shape optimization governed by the Euler equations, Int. J. Comput. Fluid Dyn., 12 (1999), pp. 17-27.
4. C. CASTRO, C. LOZANO, F. PALACIOS, and E. ZUAZUA, Systematic continuous adjoint approach to viscous aerodynamic design on unstructured grids, AIAA J., 45 (2007), pp. 2125-2139.
5. F. COURTY and A. DERVIEUX, Multilevel functional preconditioning for shape optimisation, Int. J. Comput. Fluid Dyn., 20 (2006), pp. 481-490.
6. M. DELFOUR and J.-P. ZOLÉSIO, Shapes and Geometries, SIAM, Philadelphia, 2001.
7. K. EPPLER and H. HARBRECHT, A regularized Newton method in electrical impedance tomography using shape Hessian information, Control Cybernet., 34 (2005), pp. 203-225.
8. K. EPPLER, S. SCHMIDT, V. SCHULZ, and C. ILIC, Preconditioning the pressure tracking in fluid dynamics by shape Hessian information, J. Optim. Theory Appl., 141 (2009), pp. 513-531.
9. I. GHERMAN and V. SCHULZ, Preconditioning of one-shot pseudo-timestepping methods for shape optimization, PAMM, 5 (2005), pp. 741-742.
10. A. JAMESON, Aerodynamic design via control theory, J. Sci. Comput., 3 (1988), p. 260.
11. A. JAMESON, Future research avenues in computational engineering and design, in Proceedings of the Fourth International Congress on Industrial and Applied Mathematics, J. M. Ball, J. C. R. Hunt, eds., Oxford University Press, New York, 2000.
12. S. KIM, K. HOSSEINI, K. LEOVIRIYAKIT, and A. JAMESON, Enhancement of adjoint design methods via optimization of adjoint parameters, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 10-13, 2005.
13. A. LAURAIN, Structure of shape derivatives in nonsmooth domains and applications, Adv. Math. Sci. Appl., 1 (2005), pp. 199-226.
14. B. MOHAMMADI and O. PIRONNEAU, Applied Shape Optimization for Fluids, Oxford University Press, Oxford, 2001.
15. O. PIRONNEAU, On optimum profiles in Stokes flow, J. Fluid Mech., 59 (1973), pp. 117-128.
16. O. PIRONNEAU, On optimum design in fluid mechanics, J. Fluid Mech., 64 (1974), pp. 97-110.
17. P. I. PLOTNIKOV, E. V. RUBAN, and J. SOKOLOWSKI, Inhomogeneous boundary value problems for compressible Navier-Stokes equations: Well-posedness and sensitivity analysis, SIAM J. Math. Anal., 40 (2008), pp. 1152-1200.
18. P. I. PLOTNIKOV and J. SOKOLOWSKI, Stationary boundary value problems for compressible Navier-Stokes equations, in Handbook of Differential Equations 6, Elsevier, New York, 2008, pp. 313-410.
19. P. I. PLOTNIKOV and J. SOKOLOWSKI, On compactness, domain dependence and existence of steady state solutions to compressible isothermal Navier-Stokes equations, J. Math. Fluid Mech., 7 (2005), pp. 529-573.
20. J. SOKOLOWSKI and J.-P. ZOLÉSIO, Introduction to Shape Optimization, Springer, Berlin, 1992.