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dc.contributor.authorFulmański, Piotr
dc.contributor.authorNowakowski, Andrzej
dc.contributor.authorPustelnik, Jan
dc.date.accessioned2015-04-08T08:04:39Z
dc.date.available2015-04-08T08:04:39Z
dc.date.issued2014
dc.identifier.issn2300−6919
dc.identifier.urihttp://hdl.handle.net/11089/7782
dc.description.abstractIn this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed.pl_PL
dc.language.isoenpl_PL
dc.publisherAGH University of Science and Technology Presspl_PL
dc.relation.ispartofseriesOpuscula Mathematica;34, no. 4
dc.rightsUznanie autorstwa 3.0 Polska*
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/pl/*
dc.titleDynamic programming approach to structural optimization problem – numerical algorithmpl_PL
dc.typeArticlepl_PL
dc.page.number699-724pl_PL
dc.contributor.authorAffiliationUniversity of Łódź Faculty of Mathematics and Computer Science Computer Sciencepl_PL
dc.referencesM. Burger, B. Hackl, W. Ring, Incorporating topological derivatives into level set methods, Journal of Computational Physics 194 (2004) 1, 344–362.pl_PL
dc.referencesD. Bucur, G. Buttazzo, Variational Methods in Shape Optimization Problems, Birkhäuser, 2005.pl_PL
dc.referencesC. Castaing, M. Valadier, Convex analysis and measurable multifunctions, Springer- -Verlag, 1977pl_PL
dc.referencesM. Dambrine, On variations of the shape Hessian and sufficient conditions for the stability of critical shapes, Rev. R. Acad. Cien. Serie A. Mat. RACSAM 96 (2002) 1, 95–121.pl_PL
dc.referencesM.C. Delfour, J.P. Zolésio, Shapes and Geometries: Analysis, Differential Calculus and Optimization, Adv. Des. Control, SIAM, Philadelphia, 2001.pl_PL
dc.referencesK. Eppler, Second derivatives and sufficient optimality conditions for shape functionals, Control Cybernet. 29 (2000), 485–512.pl_PL
dc.referencesK. Eppler, H. Harbrecht, Numerical solution of elliptic shape optimization problems using wavelet-based BEM, Optim. Methods Softw. 18 (2003), 105–123.pl_PL
dc.referencesK. Eppler, H. Harbrecht, 2nd order shape optimization using wavelet BEM, Optim. Methods Softw. 21 (2006), 135–153.pl_PL
dc.referencesK. Eppler, H. Harbrecht, R. Schneider, On convergence in elliptic shape optimization, SIAM J. Control Optim. 46 (2007) 1, 61–83.pl_PL
dc.referencesW.H. Fleming, R.W. Rishel, Deterministic and Stochastic Optimal Control, New York, Springer-Verlag, 1975.pl_PL
dc.referencesP. Fulmański, A. Laurin, J.F. Scheid, J. Sokolowski, A level set method in shape and topology optimization for variational inequalities, Int. J. Appl. Math. Comput. Sci. 17 (2007), 413–430.pl_PL
dc.referencesP. Fulmański, A. Nowakowski, Dual dynamic approach to shape optimization, Control Cybernet. 35 (2006) 2, 205–218.pl_PL
dc.referencesS. Garreau, P. Guillaume, M. Masmoudi, The topological asymptotic for PDE systems: the elasticity case, SIAM J. Control Optim. 39 (2001), 1756–1778.pl_PL
dc.referencesJ. Haslinger, R. Mäkinen, Introduction to Shape Optimization. Theory, Approximation and Computation, SIAM Publications, Philadelphia, 2003.pl_PL
dc.referencesI. Hlavaček, J. Haslinger, J. Nečas, J. Lovišek, Solving of variational Inequalities in Mechancs, Mir, Moscow, 1996 [in Russian].pl_PL
dc.referencesH. Maurer, J. Oberle, Second order sufficient conditions for optimal control problems with free final time: the Riccati approach, SIAM J. Control Optim. 41 (2002), 380–403.pl_PL
dc.referencesA. Nowakowski, Shape optimization of control problems described by wave equations, Control Cybernet. 37 (2008) 4, 1045–1055.pl_PL
dc.referencesJ. Pustelnik, Approximation of optimal value for Bolza problem, Ph.D. Thesis, 2009 [in Polish].pl_PL
dc.referencesJ. Sokołowski, J.P. Zolésio, Introduction to Shape Optimiation, Springer-Verlag, 1992.pl_PL
dc.referencesJ. Sokołowski, A. Żochowski, Optimality conditions for simultaneous topology and shape optimization, SIAM J. Control Optim. 42 (2003) 4, 1198–1221.pl_PL
dc.referencesJ. Sokołowski, A. Żochowski, On Topological Derivative in Shape Optimization, [in:] T. Lewiśki, O. Sigmund, J. Sokołowski, A. Żochowski, Optimal Shape Design and Modelling, Academic Printing House EXIT, Warsaw, Poland, 2004, 55–143.pl_PL
dc.referencesJ. Sokołowski, A. Żochowski, A Modeling of topological derivatives for contact problems, Numer. Math. 102 (2005) 1, 145–179.pl_PL
dc.referencesG. Stadler, Semismooth Newton and augmented Lagrangian methods for a simplified friction problem, SIAM J. Optim. 15 (2004) 1, 39–62.pl_PL
dc.contributor.authorEmailannowako@math.uni.lodz.plpl_PL


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