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dc.contributor.authorAllahverdi, N.
dc.contributor.authorPozo, A.
dc.contributor.authorZuazua, E.
dc.date.accessioned2016-11-01T20:47:55Z
dc.date.available2016-11-01T20:47:55Z
dc.date.issued2015-10-13
dc.identifier.issn0764-583X
dc.identifier.urihttp://hdl.handle.net/20.500.11824/321
dc.description.abstractIn this paper, we discuss the efficiency of various numerical methods for the inverse design of the Burgers equation, both in the viscous and in the inviscid case, in long time-horizons. Roughly, the problem consists in, given a final desired target, to identify the initial datum that leads to it along the Burgers dynamics. This constitutes an ill-posed backward problem. We highlight the importance of employing a proper discretization scheme in the numerical approximation of the equation under consideration to obtain an accurate approximation of the optimal control problem. Convergence in the classical sense of numerical analysis does not suffice since numerical schemes can alter the dynamics of the underlying continuous system in long time intervals. As we shall see, this may end up affecting the efficiency on the numerical approximation of the inverse design, that could be polluted by spurious high frequency numerical oscillations. To illustrate this, two well-known numerical schemes are employed: the modified Lax−Friedrichs scheme (MLF) and the Engquist−Osher (EO) one. It is by now well-known that the MLF scheme, as time tends to infinity, leads to asymptotic profiles with an excess of viscosity, while EO captures the correct asymptotic dynamics. We solve the inverse design problem by means of a gradient descent method and show that EO performs robustly, reaching efficiently a good approximation of the minimizer, while MLF shows a very strong sensitivity to the selection of cell and time-step sizes, due to excess of numerical viscosity. The achieved numerical results are confirmed by numerical experiments run with the open source nonlinear optimization package (IPOPT).en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectBurgers equationen_US
dc.subjectinverse designen_US
dc.subjectoptimizationen_US
dc.subjectnumericsen_US
dc.subjectdescent methoden_US
dc.titleNumerical aspects of large-time optimal control of Burgers equationen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1051/m2an/2015076
dc.relation.publisherversionhttp://www.esaim-m2an.org/articles/m2an/abs/2016/05/m2an150015/m2an150015.htmlen_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.title​ESAIM: Mathematical Modelling and Numerical Analysis​en_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España