Computation of the Hessian matrix in aerodynamic inverse design using continuous adjoint formulations

Papadimitriou, DI; Giannakoglou, KC

dc.contributor.author	Papadimitriou, DI	en
dc.contributor.author	Giannakoglou, KC	en
dc.date.accessioned	2014-03-01T01:28:04Z
dc.date.available	2014-03-01T01:28:04Z
dc.date.issued	2008	en
dc.identifier.issn	0045-7930	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18691
dc.subject	Degree of Freedom	en
dc.subject	Newton Method	en
dc.subject	Objective Function	en
dc.subject	Optimization Problem	en
dc.subject	Pressure Distribution	en
dc.subject	Problem Solving	en
dc.subject	Direct Differentiation Method	en
dc.subject	Second Order	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	SENSITIVITY-ANALYSIS	en
dc.subject.other	SHAPE OPTIMIZATION	en
dc.subject.other	DERIVATIVES	en
dc.title	Computation of the Hessian matrix in aerodynamic inverse design using continuous adjoint formulations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.compfluid.2007.11.001	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.compfluid.2007.11.001	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	Continuous adjoint formulations for the computation of (first and) second order derivatives of the objective function governing inverse design problems in 2D inviscid flows are presented. These are prerequisites for the use of the very efficient exact Newton method. Four new formulations based on all possible combinations of the direct differentiation method and the continuous adjoint approach to compute the sensitivity derivatives of objective functions, constrained by the flow equations, are presented. They are compared in terms of the expected CPU cost to compute the Hessian of the objective function used in single-objective optimization problems with N degrees of freedom. The less costly among them was selected for further study and tested in inverse design problems solved by means of the Newton method. The selected approach, which will be referred to as the direct-adjoint one, since it performs direct differentiation for the gradient and, then, uses the adjoint approach to compute the Hessian, requires as many as N + 2 equivalent flow solutions for each Newton step. The major part of the CPU cost (N equivalent flow solutions) is for the computation of the gradient but, fortunately, this task is directly amenable to parallelization. The method is used to reconstruct ducts or cascade airfoils for a known pressure distribution along their solid boundaries, at inviscid flow conditions. The examined cases aim at demonstrating the accuracy of the proposed method in computing the exact Hessian matrix as well as the efficiency of the exact Newton method as an optimization tool in aerodynamic design. (C) 2007 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	COMPUTERS & FLUIDS	en
dc.identifier.doi	10.1016/j.compfluid.2007.11.001	en
dc.identifier.isi	ISI:000258022200008	en
dc.identifier.volume	37	en
dc.identifier.issue	8	en
dc.identifier.spage	1029	en
dc.identifier.epage	1039	en