Implicit constraint handling for shape optimisation with POD-morphing

References

• Allaire , G. , DeGournay , F. , Jouve , F. and Toader , A.M. 2005 . Structural optimization using topological and shape sensitivity via a level set method . Control & Cybernetics , 34 : 59 – 80 .
   Google Scholar
• Berkooz , G. , Holmes , P. and Lumley , J.L. 1993 . The proper orthogonal decomposition in the analysis of turbulent flows . Annual Review of Fluid Mechanics , 25 ( 1 ) : 539 – 575 .
   Google Scholar
• Bregler , C. and Omohundro , S.M. 1995 . “ Nonlinear image interpolation using manifold learning ” . In Advances in Neural Information Processing Systems 7 , Edited by: Tesauro , G. , Touretzky , D.S. and Leen , T.K. 973 – 980 . Cambridge , MA : MIT Press .
   Google Scholar
• Breitkopf , P. 1998 . An algorithm for construction of iso-valued surfaces for finite elements . Engineering with Computers , 14 ( 2 ) : 146 – 149 .
   Google Scholar
• Breitkopf , P. , Naceur , H. , Rassineux , A. and Villon , P. 2005 . Moving least squares response surface approximation: Formulation and metal forming applications . Computers and Structures , 83 ( 17–18 ) : 1411 – 1428 .
   Google Scholar
• Bui-Thanh , T. , Willcox , K. , Ghattas , O. and van Bloemen , W.B. 2007 . Goal-oriented, model-constrained optimization for reduction of large-scale systems . Journal of Computational Physics , 224 ( 2 ) : 880 – 896 .
   Google Scholar
• Canny , J. 1986 . A computational approach to edge detection . IEEE Transactions on Pattern Analysis and Machine Intelligence , 8 ( 6 ) : 679 – 698 .
   Google Scholar
• Carlberg , K. and Farhat , C. 2010 . A low-cost, goal-oriented compact proper orthogonal decomposition basis for model reduction of static systems . International Journal for Numerical Methods in Engineering , 86 ( 3 ) : 381 – 402 .
   Google Scholar
• Carlberg K., & Farhat C. (2008). A compact proper orthogonal decomposition basis for optimization-oriented reduced-order models. 12th AIAA/ISSMO multidisciplinary analysis and optimization conference, Victoria, Canada, 10–12, 2008.
   Google Scholar
• Chappuis , C. , Rassineux , A. , Breitkopf , P. and Villon , P. 2004 . Improving surface remeshing by feature recognition . Engineering with Computers , 20 ( 3 ) : 202 – 209 .
   Google Scholar
• Chatterjee , A. 2005 . An introduction to the proper orthogonal decomposition . Current Science, Special Section: Computational Science , 78 ( 7 ) : 808 – 817 .
   Google Scholar
• Coelho , R.F. , Breitkopf , P. and Knopf-Lenoir , C. 2009 . Bi-level model reduction for coupled problems . Structural and Multidisciplinary Optimization , 39 ( 4 ) : 401 – 418 .
   Google Scholar
• Cordier , L. , El Majd , B.A. and Favier , J. 2010 . Calibration of POD reduced order models using Tikhonov regularization . International Journal for Numerical Methods in Fluids , 63 ( 2 ) : 269 – 296 .
   Google Scholar
• Couplet , M. , Basdevant , C. and Sagaut , P. 2005 . Calibrated reduced-order POD-Galerkin system for fluid flow modeling . Journal of Computational Physics , 207 ( 1 ) : 192 – 220 .
   Google Scholar
• Dulong , J.-L. , Druesne , F. and Villon , P. 2007 . A model reduction approach for real-time part deformation with nonlinear mechanical behavior . International Journal on Interactive Design and Manufacturing , 1 ( 4 ) : 229 – 238 .
   Google Scholar
• Kaufman , A. , Cohen , D. and Yagel , R. 1993 . Volume graphics . IEEE, Computer , 26 ( 7 ) : 51 – 64 .
   Google Scholar
• Larsson , F. , Diez , P. and Huerta , A. 2010 . A flux-free a posteriori error estimator for the incompressible Stokes problem using a mixed FE formulation . AIAA Journal , 199 ( 37–40 ) : 2383 – 2402 .
   Google Scholar
• Launder , B.E. and Spalding , D.B. 1974 . The numerical computation of turbulent flows . Computer Methods in Applied Mechanics and Engineering , 3 ( 2 ) : 269 – 289 .
   Google Scholar
• Nayroles , B. , Touzot , G. and Villon , P. 1992 . Generalizing the finite element method: Diffuse approximation and diffuse elements . Computational Mechanics , 10 ( 5 ) : 307 – 318 .
   Google Scholar
• Raghavan, B., & Breitkopf, P. (2012). Asynchronous evolutionary shape optimization based on high-quality surrogates: application to an air-conditioning duct. Engineering with Computers.
   Google Scholar
• Raghavan , B. , Breitkopf , P. and Villon , P. 2011 . POD-morphing: an a posteriori reparametrization approach for shape optimization . European Journal of Computational Mechanics , 19 ( 5–7 ) : 673 – 699 .
   Google Scholar
• Ravindran , S.S. 2000 . A reduced-order approach for optimal control of fluids using proper orthogonal decomposition . International Journal for Numerical Methods in Fluids , 34 ( 5 ) : 425 – 448 .
   Google Scholar
• Sofia , A.Y.N. , Meguid , S.A. and Tan , K.T. 2010 . Shape morphing of aircraft wing: Status and challenges . Materials & Design , 31 ( 3 ) : 1284 – 1292 .
   Google Scholar
• Willcox , K. and Peraire , J. 2002 . Balanced model reduction via the proper orthogonal decomposition . AIAA Journal , 40 ( 11 ) : 2323 – 2330 .
   Google Scholar