{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:40Z","timestamp":1787337280215,"version":"build-2736575974"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>This paper presents a numerical method for constrained aerodynamic shape optimization problems. It is based on simultaneous pseudo-timestepping in which stationary states are obtained by solving the pseudo-stationary system of equations representing the state, costate, and design equations. The main advantages of this method are that it blends in nicely with a previously existing pseudo-timestepping method for the states only, and that a preconditioner can be used for convergence acceleration which stems from the reduced SQP methods. Design examples for drag reduction with constant lift and drag reduction with constant pitching moment for an RAE2822 airfoil are included. The overall cost of computation is 4--8 times that of the forward simulation runs depending on the grid size and the number of design parameters.<\/jats:p>","DOI":"10.1137\/05062442x","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:30:19Z","timestamp":1156433419000},"page":"1078-1099","source":"Crossref","is-referenced-by-count":27,"title":["Simultaneous Pseudo-Timestepping for Aerodynamic Shape Optimization Problems with State Constraints"],"prefix":"10.1137","volume":"28","author":[{"given":"S. B.","family":"Hazra","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V.","family":"Schulz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,4]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7930(98)00041-3"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"A. Battermann, M. Heinkenschloss, Preconditioners for Karush\u2010Kuhn\u2010Tucker matrices arising in the optimal control of distributed systems, Internat. Ser. Numer. Math., Vol. 126, Birkh\u00e4user, Basel, 1998, 15\u20133299e:49042","DOI":"10.1007\/978-3-0348-8849-3_2"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"Astrid Battermann, Ekkehard Sachs, Block preconditioners for KKT systems in PDE\u2010governed optimal control problems, Internat. Ser. Numer. Math., Vol. 138, Birkh\u00e4user, Basel, 2001, 1\u2013182003k:49069","DOI":"10.1007\/978-3-0348-8233-0_1"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S106482750241565X"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"J. Brezillon,\n                      Application of the adjoint technique with the optimization framework Synaps Pointer Pro\n                      , in MEGAFLOW\u2014Numerical Flow Simulation for Aircraft Design, Notes Numer. Fluid Mech. Multidiscip. Des. 89, N. Kroll and J. Fassbender, eds., Springer\u2010Verlag, Berlin, 2002, pp. 195\u2013209.","DOI":"10.1007\/3-540-32382-1_14"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2004.07.006"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S106482750241044X"},{"key":"R8","volume-title":"Practical methods of optimization","author":"Fletcher R.","year":"1987"},{"key":"R9","unstructured":"O. Fromman,\n                      SynapsPointerPro v2.50\n                      , Synaps Ingenieure Gesellschaft mbH, Bremen, Germany, 2002."},{"key":"R10","volume-title":"Discrete modelling and discrete algorithms in continuum mechanics","author":"Sonar Th.","year":"2001"},{"key":"R11","unstructured":"N. R. Gauger,\n                      Das Adjungiertenverfahren in der aerodynamischen Formoptimierung\n                      , DLR\u2010Report DLR\u2010FB\u20102003\u201005, DLR, Braunschweig, Germany, 2003."},{"key":"R12","first-page":"247","volume":"54","author":"Gauger N. R.","year":"2002","journal-title":"J. Aero. Soc. of India","ISSN":"https:\/\/id.crossref.org\/issn\/0001-9267","issn-type":"print"},{"key":"R13","volume-title":"Practical optimization","author":"Gill Philip","year":"1981"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"S. B. Hazra,\n                      An efficient method for aerodynamic shape optimization\n                      , in Proceedings of the 10th AIAA\/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY, 2004, AIAA Paper 2004\u20104628.","DOI":"10.2514\/6.2004-4628"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1023\/B:BITN.0000046815.96929.b8"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2004.10.007"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.2514\/3.58379"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"Antony Jameson, Aerodynamic design via control theory, Lecture Notes in Engrg., Vol. 43, Springer, Berlin, 1989, 377\u201340191d:49046","DOI":"10.1007\/978-3-642-83733-3_14"},{"key":"R19","unstructured":"A. Jameson,\n                      Automatic design of transonic airfoils to reduce the shock induced pressure drag\n                      , in Proceedings of the 31st Israel Annual Conference on Aviation and Aeronautics, 1990, pp. 5\u201317."},{"key":"R20","doi-asserted-by":"crossref","unstructured":"A. Jameson,\n                      Optimum aerodynamic design using CFD and control theory\n                      , in Proceedings of the 12th AIAA Computational Fluid Dynamics Conference, San Diego, 1995, AIAA Paper 95\u20101729.","DOI":"10.2514\/6.1995-1729"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"A. Jameson and J. Reuther,\n                      Control theory based airfoil design using the Euler equations\n                      , in Proceedings of the AIAA\/USAF\/NASA\/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City Beach, FL, 1994, AIAA Paper 94\u20104272.","DOI":"10.2514\/6.1994-4272"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"A. Jameson, W. Schmidt, and E. Turkel,\n                      Numerical solution of the Euler equations by finite volume methods using Runge\u2010Kutta time\u2010stepping schemes\n                      , in Proceedings of the 14th AIAA Fluid and Plasma Dynamic Conference, Palo Alto, CA, 1981, AIAA Paper 81\u20101259.","DOI":"10.2514\/6.1981-1259"},{"key":"R23","unstructured":"N. Kroll and R. K. Jain,\n                      Solution of Two\u2010Dimensional Euler Equations\u2014Experience with a Finite Volume Code\n                      , Technical report DFVLR\u2010IB\u2010129\u201084\/19, DLR, Braunschweig, Germany, 1984."},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996304796"},{"key":"R25","unstructured":"N. Kroll, C. C. Rossow, K. Becker, and F. Thiele,\n                      The MEGAFLOW\u2014A Numerical Flow Simulation System\n                      , presented at the 21st ICAS Symposium, Melbourne, Australia, 1998, Paper 98\u20102.7.4."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1016\/S1270-9638(00)00131-0"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021882126367"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112074002023"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1017\/S002211207300145X"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-87722-3"},{"key":"R31","unstructured":"A. Iollo, G. Kuruvila, and S. Ta\u2019asan,\n                      Pseudo\u2010Time Method for Optimal Shape Design Using the Euler Equations\n                      , Technical report 95\u201059, ICASE, NASA Langley Research Center, Hampton, VA, 1995."},{"key":"R32","doi-asserted-by":"crossref","unstructured":"J. Reuther and A. Jameson,\n                      Aerodynamic shape optimization of wing and wing\u2010body configurations using control theory\n                      , in Proceedings of the 33rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 1995, AIAA Paper 95\u20100123.","DOI":"10.2514\/6.1995-123"},{"key":"R33","doi-asserted-by":"crossref","unstructured":"J. Reuther, A. Jameson, J. Farmer, L. Martinelli, and D. Saunders,\n                      Aerodynamic shape optimization of complex aircraft configurations via an adjoint formulation\n                      , in Proceedings of the 34rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 1996, AIAA Paper 96\u20100094.","DOI":"10.2514\/6.1996-94"},{"key":"R34","unstructured":"V. H. Schulz,\n                      Reduced SQP Methods for Large\u2010Scale Optimal Control Problems in DAE with Application to Path Planning Problems for Satellite Mounted Robots\n                      , Ph.D. thesis, Universit\u00e4t Heidelberg, Heidelberg, Germany, 1996."},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1007\/s007910050008"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594261917"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/05062442X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:53:59Z","timestamp":1787334839000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/05062442X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/05062442X"],"URL":"https:\/\/doi.org\/10.1137\/05062442x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}