Direct, adjoint and mixed approaches for the computation of Hessian in airfoil design problems
In this paper, four approaches to compute the Hessian matrix of an objective function used often in aerodynamic inverse design problems are presented. The computationally less expensive among them is selected and applied to the reconstruction of cascade airfoils that reproduce a prescribed pressure...
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| Veröffentlicht in: | International journal for numerical methods in fluids 2008-04, Vol.56 (10), p.1929-1943 |
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| container_end_page | 1943 |
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| container_issue | 10 |
| container_start_page | 1929 |
| container_title | International journal for numerical methods in fluids |
| container_volume | 56 |
| creator | Papadimitriou, D. I. Giannakoglou, K. C. |
| description | In this paper, four approaches to compute the Hessian matrix of an objective function used often in aerodynamic inverse design problems are presented. The computationally less expensive among them is selected and applied to the reconstruction of cascade airfoils that reproduce a prescribed pressure distribution over their walls, under inviscid and viscous flow considerations. The selected approach is based on the direct sensitivity analysis method for the computation of first derivatives, followed by the discrete adjoint method for the computation of the Hessian matrix. The applications presented in this paper show that the Newton method, based on exact Hessian matrices, outperforms other gradient‐based algorithms such as steepest descent or BFGS algorithm. Copyright © 2007 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/fld.1584 |
| format | Article |
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I.</creatorcontrib><creatorcontrib>Giannakoglou, K. C.</creatorcontrib><title>Direct, adjoint and mixed approaches for the computation of Hessian in airfoil design problems</title><title>International journal for numerical methods in fluids</title><addtitle>Int. J. Numer. Meth. Fluids</addtitle><description>In this paper, four approaches to compute the Hessian matrix of an objective function used often in aerodynamic inverse design problems are presented. The computationally less expensive among them is selected and applied to the reconstruction of cascade airfoils that reproduce a prescribed pressure distribution over their walls, under inviscid and viscous flow considerations. The selected approach is based on the direct sensitivity analysis method for the computation of first derivatives, followed by the discrete adjoint method for the computation of the Hessian matrix. The applications presented in this paper show that the Newton method, based on exact Hessian matrices, outperforms other gradient‐based algorithms such as steepest descent or BFGS algorithm. 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The selected approach is based on the direct sensitivity analysis method for the computation of first derivatives, followed by the discrete adjoint method for the computation of the Hessian matrix. The applications presented in this paper show that the Newton method, based on exact Hessian matrices, outperforms other gradient‐based algorithms such as steepest descent or BFGS algorithm. Copyright © 2007 John Wiley & Sons, Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley & Sons, Ltd</pub><doi>10.1002/fld.1584</doi><tpages>15</tpages></addata></record> |
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| identifier | ISSN: 0271-2091 |
| ispartof | International journal for numerical methods in fluids, 2008-04, Vol.56 (10), p.1929-1943 |
| issn | 0271-2091 1097-0363 |
| language | eng |
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| source | Wiley-Blackwell Journals |
| subjects | adjoint method aerodynamic shape optimization Applied fluid mechanics Computational methods in fluid dynamics Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Hessian matrix Hydraulic and pneumatic machinery Physics |
| title | Direct, adjoint and mixed approaches for the computation of Hessian in airfoil design problems |
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