Aerodynamic design using the truncated Newton algorithm and the continuous adjoint approach

Papadimitriou, DI; Giannakoglou, KC

dc.contributor.author	Papadimitriou, DI	en
dc.contributor.author	Giannakoglou, KC	en
dc.date.accessioned	2014-03-01T02:07:36Z
dc.date.available	2014-03-01T02:07:36Z
dc.date.issued	2012	en
dc.identifier.issn	02712091	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29588
dc.subject	Aerodynamic shape optimization	en
dc.subject	Continuous adjoint	en
dc.subject	Direct differentiation	en
dc.subject	Hessian matrix	en
dc.subject	Second-order sensitivity derivatives	en
dc.subject	Truncated Newton method	en
dc.subject.other	Aerodynamic shape optimization	en
dc.subject.other	Continuous adjoint	en
dc.subject.other	Direct differentiation	en
dc.subject.other	Hessian matrices	en
dc.subject.other	Second-order sensitivity	en
dc.subject.other	Truncated Newton method	en
dc.subject.other	Aerodynamics	en
dc.subject.other	Airfoils	en
dc.subject.other	Algorithms	en
dc.subject.other	Conjugate gradient method	en
dc.subject.other	Design	en
dc.subject.other	Euler equations	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Newton-Raphson method	en
dc.subject.other	Shape optimization	en
dc.title	Aerodynamic design using the truncated Newton algorithm and the continuous adjoint approach	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/fld.2530	en
heal.identifier.secondary	http://dx.doi.org/10.1002/fld.2530	en
heal.publicationDate	2012	en
heal.abstract	In this paper, the so-called 'continuous adjoint-direct approach' is used within the truncated Newton algorithm for the optimization of aerodynamic shapes, using the Euler equations. It is known that the direct differentiation (DD) of the flow equations with respect to the design variables, followed by the adjoint approach, is the best way to compute the exact matrix, for use along with the Newton optimization method. In contrast to this, in this paper, the adjoint approach followed by the DD of both the flow and adjoint equations (i.e. the other way round) is proved to be the most efficient way to compute the product of the Hessian matrix with any vector required by the truncated Newton algorithm, in which the Newton equations are solved iteratively by means of the conjugate gradient (CG) method. Using numerical experiments, it is demonstrated that just a few CG steps per Newton iteration are enough. Considering that the cost of solving either the adjoint or the DD equations is approximately equal to that of solving the flow equations, the cost per Newton iteration scales linearly with the (small) number of CG steps, rather than the (much higher, in large-scale problems) number of design variables. By doing so, the curse of dimensionality is alleviated, as shown in a number of applications related to the inverse design of ducts or cascade airfoils for inviscid flows. © 2011 John Wiley & Sons, Ltd.	en
heal.journalName	International Journal for Numerical Methods in Fluids	en
dc.identifier.doi	10.1002/fld.2530	en
dc.identifier.volume	68	en
dc.identifier.issue	6	en
dc.identifier.spage	724	en
dc.identifier.epage	739	en