Shi-Dong, Doug; Nadarajah, Siva Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework. (English) Zbl 1390.74161 Comput. Fluids 168, 265-284 (2018). MSC: 74P15 65K10 49Q10 76G25 PDF BibTeX XML Cite \textit{D. Shi-Dong} and \textit{S. Nadarajah}, Comput. Fluids 168, 265--284 (2018; Zbl 1390.74161) Full Text: DOI
Yan, Wenjing; Gao, Zhiming The application of adjoint method for shape optimization in Stokes-Oseen flow. (English) Zbl 1362.49023 Math. Methods Appl. Sci. 40, No. 4, 1114-1125 (2017). MSC: 49Q10 49K40 49J35 76D55 49M30 PDF BibTeX XML Cite \textit{W. Yan} and \textit{Z. Gao}, Math. Methods Appl. Sci. 40, No. 4, 1114--1125 (2017; Zbl 1362.49023) Full Text: DOI
Yan, Wenjing; Hou, Jiangyong; Gao, Zhiming Shape identification for convection-diffusion problem based on the continuous adjoint method. (English) Zbl 1353.65103 Appl. Math. Lett. 64, 74-80 (2017). MSC: 65M32 35K20 35R30 PDF BibTeX XML Cite \textit{W. Yan} et al., Appl. Math. Lett. 64, 74--80 (2017; Zbl 1353.65103) Full Text: DOI
Papadimitriou, Dimitrios I.; Papadimitriou, Costas Bayesian uncertainty quantification of turbulence models based on high-order adjoint. (English) Zbl 1390.76113 Comput. Fluids 120, 82-97 (2015). MSC: 76F55 62F15 PDF BibTeX XML Cite \textit{D. I. Papadimitriou} and \textit{C. Papadimitriou}, Comput. Fluids 120, 82--97 (2015; Zbl 1390.76113) Full Text: DOI
Mittal, Sanjay; Bhatt, Varun; Srinath, D. N. Aerodynamic shape optimization using stabilized finite element method. (English) Zbl 1330.76076 Math. Models Methods Appl. Sci. 25, No. 12, 2319-2348 (2015). MSC: 76M10 74P20 49M05 35Q30 49M15 65M60 74S05 PDF BibTeX XML Cite \textit{S. Mittal} et al., Math. Models Methods Appl. Sci. 25, No. 12, 2319--2348 (2015; Zbl 1330.76076) Full Text: DOI
Vergnault, E.; Sagaut, P. An adjoint-based lattice Boltzmann method for noise control problems. (English) Zbl 1349.76744 J. Comput. Phys. 276, 39-61 (2014). MSC: 76M28 76Q05 PDF BibTeX XML Cite \textit{E. Vergnault} and \textit{P. Sagaut}, J. Comput. Phys. 276, 39--61 (2014; Zbl 1349.76744) Full Text: DOI
Papadimitriou, D. I.; Giannakoglou, K. C. Aerodynamic design using the truncated Newton algorithm and the continuous adjoint approach. (English) Zbl 1452.76209 Int. J. Numer. Methods Fluids 68, No. 6, 724-739 (2012). MSC: 76N25 76M99 65K10 PDF BibTeX XML Cite \textit{D. I. Papadimitriou} and \textit{K. C. Giannakoglou}, Int. J. Numer. Methods Fluids 68, No. 6, 724--739 (2012; Zbl 1452.76209) Full Text: DOI
Rumpfkeil, Markus P.; Yamazaki, Wataru; Mavriplis, Dimitri J. Uncertainty analysis utilizing gradient and Hessian information. (English) Zbl 1346.76166 Kuzmin, Alexander (ed.), Computational fluid dynamics 2010. Proceedings of the 6th international conference on computational fluid dynamics, ICCFD6, St. Petersburg, Russia, July 12–16, 2010. Berlin: Springer (ISBN 978-3-642-17883-2/hbk; 978-3-642-17884-9/ebook). 261-268 (2011). MSC: 76M35 PDF BibTeX XML Cite \textit{M. P. Rumpfkeil} et al., in: Computational fluid dynamics 2010. Proceedings of the 6th international conference on computational fluid dynamics, ICCFD6, St. Petersburg, Russia, July 12--16, 2010. Berlin: Springer. 261--268 (2011; Zbl 1346.76166) Full Text: DOI
Telib, H.; Arian, E.; Iollo, A. The effect of shocks on second order sensitivities for the quasi-one-dimensional Euler equations. (English) Zbl 1367.76032 J. Comput. Phys. 230, No. 23, 8603-8618 (2011). MSC: 76L05 76M12 76N15 PDF BibTeX XML Cite \textit{H. Telib} et al., J. Comput. Phys. 230, No. 23, 8603--8618 (2011; Zbl 1367.76032) Full Text: DOI
Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A. The independent set perturbation adjoint method: a new method of differentiating mesh-based fluids models. (English) Zbl 1285.76015 Int. J. Numer. Methods Fluids 66, No. 8, 976-999 (2011). MSC: 76M10 65M99 PDF BibTeX XML Cite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 66, No. 8, 976--999 (2011; Zbl 1285.76015) Full Text: DOI
Martinelli, M.; Duvigneau, R. On the use of second-order derivatives and metamodel-based Monte Carlo method for uncertainty estimation in aerodynamics. (English) Zbl 1242.76288 Comput. Fluids 39, No. 6, 953-964 (2010). MSC: 76M35 PDF BibTeX XML Cite \textit{M. Martinelli} and \textit{R. Duvigneau}, Comput. Fluids 39, No. 6, 953--964 (2010; Zbl 1242.76288) Full Text: DOI
Peter, Jacques E. V.; Dwight, Richard P. Numerical sensitivity analysis for aerodynamic optimization: a survey of approaches. (English) Zbl 1242.76301 Comput. Fluids 39, No. 3, 373-391 (2010). MSC: 76N25 76D55 76M99 76-02 PDF BibTeX XML Cite \textit{J. E. V. Peter} and \textit{R. P. Dwight}, Comput. Fluids 39, No. 3, 373--391 (2010; Zbl 1242.76301) Full Text: DOI
Zervogiannis, T.; Papadimitriou, D. I.; Giannakoglou, K. C. Total pressure losses minimization in turbomachinery cascades using the exact Hessian. (English) Zbl 1231.76247 Comput. Methods Appl. Mech. Eng. 199, No. 41-44, 2697-2708 (2010). MSC: 76N25 76M12 PDF BibTeX XML Cite \textit{T. Zervogiannis} et al., Comput. Methods Appl. Mech. Eng. 199, No. 41--44, 2697--2708 (2010; Zbl 1231.76247) Full Text: DOI
Srinath, D. N.; Mittal, Sanjay Optimal aerodynamic design of airfoils in unsteady viscous flows. (English) Zbl 1231.76094 Comput. Methods Appl. Mech. Eng. 199, No. 29-32, 1976-1991 (2010). MSC: 76D55 76D05 PDF BibTeX XML Cite \textit{D. N. Srinath} and \textit{S. Mittal}, Comput. Methods Appl. Mech. Eng. 199, No. 29--32, 1976--1991 (2010; Zbl 1231.76094) Full Text: DOI
Srinath, D. N.; Mittal, Sanjay An adjoint method for shape optimization in unsteady viscous flows. (English) Zbl 1303.76091 J. Comput. Phys. 229, No. 6, 1994-2008 (2010). MSC: 76M10 76B10 65M60 65K10 PDF BibTeX XML Cite \textit{D. N. Srinath} and \textit{S. Mittal}, J. Comput. Phys. 229, No. 6, 1994--2008 (2010; Zbl 1303.76091) Full Text: DOI
Papadimitriou, D. I.; Giannakoglou, K. C. The continuous direct-adjoint approach for second-order sensitivities in viscous aerodynamic inverse design problems. (English) Zbl 1242.76300 Comput. Fluids 38, No. 8, 1539-1548 (2009). MSC: 76N25 PDF BibTeX XML Cite \textit{D. I. Papadimitriou} and \textit{K. C. Giannakoglou}, Comput. Fluids 38, No. 8, 1539--1548 (2009; Zbl 1242.76300) Full Text: DOI
Arian, Eyal; Iollo, Angelo Analytic Hessian derivation for the quasi-one-dimensional Euler equations. (English) Zbl 1162.76049 J. Comput. Phys. 228, No. 2, 476-490 (2009). MSC: 76N15 76N25 PDF BibTeX XML Cite \textit{E. Arian} and \textit{A. Iollo}, J. Comput. Phys. 228, No. 2, 476--490 (2009; Zbl 1162.76049) Full Text: DOI
Papadimitriou, D. I.; Giannakoglou, K. C. Computation of the Hessian matrix in aerodynamic inverse design using continuous adjoint formulations. (English) Zbl 1237.76162 Comput. Fluids 37, No. 8, 1029-1039 (2008). MSC: 76N25 PDF BibTeX XML Cite \textit{D. I. Papadimitriou} and \textit{K. C. Giannakoglou}, Comput. Fluids 37, No. 8, 1029--1039 (2008; Zbl 1237.76162) Full Text: DOI
Papadimitriou, Dimitrios I.; Giannakoglou, Kyriakos C. Aerodynamic shape optimization using first and second order adjoint and direct approaches. (English) Zbl 1170.76348 Arch. Comput. Methods Eng. 15, No. 4, 447-488 (2008). MSC: 76N25 76M25 76-02 PDF BibTeX XML Cite \textit{D. I. Papadimitriou} and \textit{K. C. Giannakoglou}, Arch. Comput. Methods Eng. 15, No. 4, 447--488 (2008; Zbl 1170.76348) Full Text: DOI
Ilinca, F.; Pelletier, D.; Hay, A. First- and second-order sensitivity equation methods for value and shape parameters. (English) Zbl 1338.76055 Int. J. Numer. Methods Fluids 57, No. 9, 1349-1370 (2008). MSC: 76M10 76G25 PDF BibTeX XML Cite \textit{F. Ilinca} et al., Int. J. Numer. Methods Fluids 57, No. 9, 1349--1370 (2008; Zbl 1338.76055) Full Text: DOI
Marta, A. C.; Mader, C. A.; Martins, J. R. R. A.; Van Der Weide, E.; Alonso, J. J. A methodology for the development of discrete adjoint solvers using automatic differentiation tools. (English) Zbl 1184.76832 Int. J. Comput. Fluid Dyn. 21, No. 9-10, 307-327 (2007). MSC: 76N25 76W05 76M99 PDF BibTeX XML Cite \textit{A. C. Marta} et al., Int. J. Comput. Fluid Dyn. 21, No. 9--10, 307--327 (2007; Zbl 1184.76832) Full Text: DOI
Ilinca, F.; Pelletier, D. A continuous shape sensitivity equation method for unsteady laminar flows. (English) Zbl 1184.76657 Int. J. Comput. Fluid Dyn. 21, No. 7-8, 255-266 (2007). MSC: 76D55 76M10 PDF BibTeX XML Cite \textit{F. Ilinca} and \textit{D. Pelletier}, Int. J. Comput. Fluid Dyn. 21, No. 7--8, 255--266 (2007; Zbl 1184.76657) Full Text: DOI
Cao, Yanzhao; Hussaini, M. Y.; Zang, T.; Zatezalo, A. A variance reduction method based on sensitivity derivatives. (English) Zbl 1098.65003 Appl. Numer. Math. 56, No. 6, 800-813 (2006). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 65C05 60H15 60H35 35Q53 PDF BibTeX XML Cite \textit{Y. Cao} et al., Appl. Numer. Math. 56, No. 6, 800--813 (2006; Zbl 1098.65003) Full Text: DOI
van Keulen, F.; Haftka, R. T.; Kim, N. H. Review of options for structural design sensitivity analysis. I: Linear systems. (English) Zbl 1091.74040 Comput. Methods Appl. Mech. Eng. 194, No. 30-33, 3213-3243 (2005). MSC: 74P99 74-02 PDF BibTeX XML Cite \textit{F. van Keulen} et al., Comput. Methods Appl. Mech. Eng. 194, No. 30--33, 3213--3243 (2005; Zbl 1091.74040) Full Text: DOI
Mahieu, J.-N.; Étienne, S.; Pelletier, D.; Borggaard, J. A second-order sensitivity equation method for laminar flow. (English) Zbl 1286.76113 Int. J. Comput. Fluid Dyn. 19, No. 2, 143-157 (2005). MSC: 76M25 76D05 76B10 PDF BibTeX XML Cite \textit{J. N. Mahieu} et al., Int. J. Comput. Fluid Dyn. 19, No. 2, 143--157 (2005; Zbl 1286.76113) Full Text: DOI