Hadamard incomplete sensitivity and shape optimization

• Autorzy: Mohammadi B.
• Języki publikacji: EN

Abstrakty

EN

The paper discusses incomplete sensitivity evaluations for shape optimization problems. It also shows how reduced order models can be introduced to extend the validity domain of the approach.

Słowa kluczowe

EN

Hadamard boundary condition; shape optimization; incomplete sensitivity; multi-criteria; unsteady; turbomachinery

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2010
• Tom: Vol. 39, no 3
• Strony: 615--626
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Mohammadi B.

• Universite Montpellier II, ISM, CC 51, 34095 Montpellier, France

Bibliografia

• ALLAIRE, G., JOUVE, F. and TOADER, AM. (2001) A level-set method for shape optimization. C. R. Acad. Sci. Paris, 334, 1-8.
• BARDOS, C. and PIRONNEAU, O. (1994) Petites perturbations et equations d’Euler pour l’aeroelasticite. Modelisation Mathematique et Analyse Numerique 28(4).
• BUNGARTZ, H.-J.and GRIEBEL, M. (1989) Sparse Grids. Ada Numerica 13, 147-269.
• CHILES, JP.and DELFINER, P. (1989) Geostatistics, Modeling Spatial Uncertainty. Wiley, London.
• FINKEL, R. and BENTLEY, J.L. (1974) Quad Trees: A Data Structure for Retrieval on Composite Keys. Acta Informatica, 4(1), 120-156.
• GARREAU, S., GUILLAUME, PH. and MASMOUDI, M. (2001) The Topological Asymptotic for PDE Systems: The Elasticity. SIAM J. Control Optim., 39(6), 35-59.
• GILES, M. and PIERCE, N. (1997) Adjoint equations in CFD: duality, boundary conditions and solution behaviour. AIAA, 97-1850.
• GORBAN, A., KEGL, B., WUNSCH, D.and ZINOVYEV, A.(2007) Principal Manifolds for Data Visualisation and Dimension Reduction. LNCSE 58, Springer, Berlin.
• HOEL, P.G. (1971) Introduction to Mathematical Statistics. Wiley, London.
• JAMESON, A. (1994) Optimum aerodynamic design via boundary control. AGARD Report 803, Von Karman Institute Courses.
• JEONG, S., CHIBA, E. and OBAYASHI, S. (2005) Data Mining for Aerodynamic Design Space. Journal of Aerospace Computing, Information, and Communication, 2, 12-56.
• JOLLIFFE, I.T. (2002) Principal Component Analysis. Springer Series in Statistics, 2nd ed., Springer, NY.
• KOHONEN, T. (1995) Self-Organizing Maps. Springer, NY.
• KRIGE, D.G.(1951) A statistical approach to some mine valuations and allied problems at the Witwatersrand. Master thesis of the University of Witwatersrand.
• KUMANO, T., JEONG, S., OBAYASHI, S., ITO, Y., HATANAKA, K. and MORINO, H. (2006) Multidisciplinary Design Optimization of Wing Shape for a Small Jet Aircraft Using Kriging Model. AIAA, 2006-932.
• LINDMAN, H.R. (1974) Analysis of Variance in Complex Experimental Designs. Freeman, NY.
• MANDIC, D.and CHAMBERS, J. (2001) Recurrent Neural Networks for Prediction: Architectures, Learning Algorithms and Stability. Wiley, London.
• MOHAMMADI, B. and PIRONNEAU, O. (1994) Analysis of the k-epsilon Turbulence Model. Wiley, London.
• MOHAMMADI, B. and PIRONNEAU, O. (2001) Applied Shape Optimization for Fluids. Oxford University Press, 2nd Ed. 2009.
• MOHAMMADI, B. (2007) Global optimization, level set dynamics, incomplete sensitivity and regularity control. Int. J. CFD, 21(2), 22-49.
• OSHER, S. and SETHIAN, J. (1998) Fronts propagating with curvature-depen-dent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79(1), 12-49.
• PESKIN, CH. (1998) The fluid dynamics of heart valves: experimental, theoretical and computational methods. Annu. Rev. Fluid Mech., 14, 235-259.
• PIRONNEAU, O. (1984) Optimal Shape Design for Elliptic Systems. Springer-Verlag, Berlin.
• PLOTNIKOV, P.I. and SOKOLOWSKI, J. (2010) Shape derivative of the drag functional. SIAM J. Control Optim., in press.
• SMOLYAK, SA. (1963) Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Akad. Nauk SSSR, 148, 1042-1043. Russian, Engl. Transl.: Soviet Math. Dokl. 4, 240-243.
• STANCIU, M., MOHAMMADI, B. and MOREAU, S.(2002) Low Complexity Models to Improve Incomplete Sensitivities for Shape Optimization. IJCFD 11(2), 22-48.
• SPOONER, J.T., MAGGIORE, M., ONEZ, R.O. and PASSING, K.M. (2001) Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator Techniques. Wiley, NY.
• VEROY, K. and PATERA A. (2005) Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: Rigorous reduced-basis a posteriori error bounds. Int. J. Numer. Meth. Fluids, 47(2), 272-299.