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Original Articles

New Regularization Method for Calibrated POD Reduced-Order Models

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Pages 47-62 | Received 18 Nov 2014, Published online: 26 Jan 2016

References

  • A.K. Alekseev and I.M. Navon. The analysis of an ill-posed problem using multi-scale resolution and second-order adjoint techniques. Computer Methods in Applied Mechanics and Engineering, 190(15-17):1937–1953, 2001. http://dx.doi.org/10.1016/S0045-7825(00)00299-1.
  • M. Bergmann and L. Cordier. Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models. Journal of Computational Physics, 227(16):7813–7840, 2008. http://dx.doi.org/10.1016/j.jcp.2008.04.034.
  • M. Bergmann, L. Cordier and J.-P. Brancher. Optimal rotary control of the cylinder wake using POD reduced-order model. Physics of Fluids, 17(9), 2005. http://dx.doi.org/10.1063/1.2033624.
  • C. C. Homescu, I.M. Navon and Z. Li. Suppression of vortex shedding for flow around a circular cylinder using optimal control. Int. J. Numer. Meth. Fluids, 38(1):43–69, 2002. http://dx.doi.org/10.1002/fld.203.
  • D. Calvetti, S. Morigi, L. Reichel and F. Sgallari. Tikhonov regularization and the L-curve for large discrete ill-posed problems. Journal of Computational and Applied Mathematics, 123(1-2):423–446, 2000. http://dx.doi.org/10.1016/S0377-0427(00)00414-3. Numerical Analysis 2000. Vol. III: Linear Algebra
  • L. Cordier and M. Bergmann. Proper orthogonal decomposition: an overview. In VKI(Ed.), Lecture series 2002-04, 2003-03 and 2008-01 on post-processing of experimental and numerical data. Von Karman Institute for Fluid Dynamics, 2008.
  • L. Cordier and M. Bergmann. Two typical applications of POD: coherent structures eduction and reduced order modelling. In Lecture series 2002-04, 2003-03 and 2008-01 on post-processing of experimental and numerical data. Von Karman Institute for Fluid Dynamics, 2008.
  • L. Cordier, B. Abou El Majd and J. Favier. Calibration of POD reduced-order models using Tikhonov regularization. International Journal for Numerical Methods in Fluids, 63(2):269–296, 2010. http://dx.doi.org/10.1002/fld.2074.
  • L. Cordier, B.R. Noack, G. Tissot, G. Lehnasch, J. Delville, M. Balajewicz, G. Daviller and R.K. Niven. Identification strategies for model-based control. Experiments in Fluids, 54(8):1580, 2013. http://dx.doi.org/10.1007/s00348-013-1580-9.
  • M. Couplet, C. Basdevant and P. Sagaut. Calibrated reduced-order POD-Galerkin system for fluid flow modelling. Journal of Computational Physics, 207(1):192–220, 2005. http://dx.doi.org/10.1016/j.jcp.2005.01.008.
  • J.-A. Dèsidèri, R. Duvigneau and B. Abou El Majd. Algorithms for efficient shape optimization in aerodynamics and coupled disciplines. 42nd AAAF Congress on Applied Aerodynamics, (Sophia-Antipolis, France), 2007.
  • R. Duvigneau, B. Abou El Majd and J.-A. Dèsidèri. Towards a self-adaptive parameterization for aerodynamic shape optimization. In ESAIM: Proc., volume 22, pp. 169–174, 2008. http://dx.doi.org/10.1051/proc:072221.
  • J. Favier. Contrôle d'ècoulements : approche expèrimentale et modèlisation de dimension rèduite. Institut National Polytechnique de Toulouse, France, 2007.
  • B. Galletti, C.H. Bruneau, L. Zannetti and A. Iollo. Low-order modelling of laminar flow regimes past a confined square cylinder. Journal of Fluid Mechanics, 503:161–170, 2004. http://dx.doi.org/10.1017/S0022112004007906.
  • G.H. Golub and Ch. F. Van Loan. Matrix Computations. The Johns Hopkins University Press; 3rd edition, Baltimore and London, 1996.
  • P. Hansen, J. Nagy and D. O'Leary. Deblurring images: matrices, spectra, and filtering. SIAM, 2006. http://dx.doi.org/10.1137/1.9780898718874.
  • P. C. Hansen. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review, 34(4):561–672, 1992. http://dx.doi.org/10.1137/1034115.
  • P. Holmes, J. Lumley and G. Berkooz. Turbulence, coherent structures, dynamical systems and symmetry. Cambridge University Press, Cambridge, MA, 1998.
  • B. Abou El Majd. Parameterization adaption for 3D shape optimization in aerodynamics. International Journal of Science and Engineering, 6(1):61–69, 2014. http://dx.doi.org/10.12777/ijse.6.1.61-69.
  • B. Abou El Majd. Optimisation de forme paramètrique: Stratègies hièrarchiques, adaptatives, et concourantes. Editions Universitaires Europeennes, 2015.
  • B. Abou El Majd, J.-A. Dèsidèri and R. Duvigneau. Multilevel strategies for parametric shape optimization in aerodynamics. European Journal of Computational Mechanics, 17(1-2):149–168, 2008.
  • B. Abou El Majd, J.-A. Dèsidèri and A. Habbal. Aerodynamic and structural optimization of a business-jet wingshape by a Nash game and an adapted split of variables. Mècanique & Industries, 11(3–4):209–214, 2010. http://dx.doi.org/10.1051/meca/2010041.
  • L. Sirovich. Turbulence and the dynamics of coherent structures. Quart. of Appl. Math., 45(3):561–590, 1987.
  • J. Zhao, J.-A. Dèsidèri and B. Abou El Majd. Two level correction algorithms for model problems. INRIA, 2007.
  • J. Zhao, B.Abou El Majd and J.A. Desideri. Two level correction algorithm for parametric shape inverse optimization. International Journal of Engineering and Mathematical Modelling, 2(1):17–30, 2015.

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