Chakib, Abdelkrim; Khalil, Ibrahim; Ouaissa, Hamid; Sadik, Azeddine On a numerical approach for solving some geometrical shape optimization problems in fluid mechanics. (English) Zbl 07784297 Commun. Nonlinear Sci. Numer. Simul. 128, Article ID 107651, 24 p. (2024). MSC: 76-XX PDFBibTeX XMLCite \textit{A. Chakib} et al., Commun. Nonlinear Sci. Numer. Simul. 128, Article ID 107651, 24 p. (2024; Zbl 07784297) Full Text: DOI
Rabago, Julius Fergy Tiongson; Notsu, Hirofumi Numerical solution to a free boundary problem for the Stokes equation using the coupled complex boundary method in shape optimization setting. (English) Zbl 1528.35241 Appl. Math. Optim. 89, No. 1, Paper No. 2, 56 p. (2024). MSC: 35R35 35Q30 49Q10 76D07 PDFBibTeX XMLCite \textit{J. F. T. Rabago} and \textit{H. Notsu}, Appl. Math. Optim. 89, No. 1, Paper No. 2, 56 p. (2024; Zbl 1528.35241) Full Text: DOI arXiv
Geshkovski, Borjan; Zuazua, Enrique Turnpike in optimal control of PDEs, ResNets, and beyond. (English) Zbl 07674581 Acta Numerica 31, 135-263 (2022). MSC: 65Mxx 76-XX PDFBibTeX XMLCite \textit{B. Geshkovski} and \textit{E. Zuazua}, Acta Numerica 31, 135--263 (2022; Zbl 07674581) Full Text: DOI arXiv
Li, Jiajie; Zhu, Shengfeng Shape optimization of Navier-Stokes flows by a two-grid method. (English) Zbl 1507.49038 Comput. Methods Appl. Mech. Eng. 400, Article ID 115531, 28 p. (2022). MSC: 49Q10 49Q12 76D55 76M10 PDFBibTeX XMLCite \textit{J. Li} and \textit{S. Zhu}, Comput. Methods Appl. Mech. Eng. 400, Article ID 115531, 28 p. (2022; Zbl 1507.49038) Full Text: DOI
Duan, Xianbao; Li, Yichen; Tan, Hongxia; Li, Yangyang Adaptive level set method applied to drag minimization problems constrained by Stokes equations. (English) Zbl 07533168 Int. J. Nonlinear Sci. Numer. Simul. 23, No. 2, 257-271 (2022). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{X. Duan} et al., Int. J. Nonlinear Sci. Numer. Simul. 23, No. 2, 257--271 (2022; Zbl 07533168) Full Text: DOI
Li, Jiajie; Zhu, Shengfeng On distributed \(H^1\) shape gradient flows in optimal shape design of Stokes flows: convergence analysis and numerical applications. (English) Zbl 1499.49099 J. Comput. Math. 40, No. 2, 231-257 (2022). MSC: 49Q10 49Q12 76D55 76M10 65K10 PDFBibTeX XMLCite \textit{J. Li} and \textit{S. Zhu}, J. Comput. Math. 40, No. 2, 231--257 (2022; Zbl 1499.49099) Full Text: DOI
Simon, J. S. H.; Notsu, Hirofumi A shape design problem for the Navier-Stokes flow with a convective boundary condition. (English) Zbl 1499.76039 Comput. Appl. Math. 41, No. 4, Paper No. 167, 44 p. (2022). MSC: 76D05 35Q30 49M41 49Q10 PDFBibTeX XMLCite \textit{J. S. H. Simon} and \textit{H. Notsu}, Comput. Appl. Math. 41, No. 4, Paper No. 167, 44 p. (2022; Zbl 1499.76039) Full Text: DOI arXiv
Albuquerque, Yuri F.; Laurain, Antoine; Yousept, Irwin Level set-based shape optimization approach for sharp-interface reconstructions in time-domain full waveform inversion. (English) Zbl 1468.35223 SIAM J. Appl. Math. 81, No. 3, 939-964 (2021). MSC: 35Q93 35R30 35R05 76Q05 49Q10 86A15 PDFBibTeX XMLCite \textit{Y. F. Albuquerque} et al., SIAM J. Appl. Math. 81, No. 3, 939--964 (2021; Zbl 1468.35223) Full Text: DOI
Blauth, Sebastian; Leithäuser, Christian; Pinnau, René Shape sensitivity analysis for a microchannel cooling system. (English) Zbl 1457.76143 J. Math. Anal. Appl. 492, No. 2, Article ID 124476, 27 p. (2020). Reviewer: W. Sridhar (Vaddeswaram) MSC: 76R10 76D07 76R50 80A19 PDFBibTeX XMLCite \textit{S. Blauth} et al., J. Math. Anal. Appl. 492, No. 2, Article ID 124476, 27 p. (2020; Zbl 1457.76143) Full Text: DOI arXiv
Chaves-Silva, Felipe W.; Souza, Diego A.; Zhang, Can Observability inequalities on measurable sets for the Stokes system and applications. (English) Zbl 1446.49029 SIAM J. Control Optim. 58, No. 4, 2188-2205 (2020). MSC: 49Q10 76D55 93B07 49R05 28A05 28A75 PDFBibTeX XMLCite \textit{F. W. Chaves-Silva} et al., SIAM J. Control Optim. 58, No. 4, 2188--2205 (2020; Zbl 1446.49029) Full Text: DOI arXiv
Feppon, F.; Allaire, G.; Dapogny, C.; Jolivet, P. Topology optimization of thermal fluid-structure systems using body-fitted meshes and parallel computing. (English) Zbl 1437.74021 J. Comput. Phys. 417, Article ID 109574, 29 p. (2020). MSC: 74P15 74F10 74F05 76D05 PDFBibTeX XMLCite \textit{F. Feppon} et al., J. Comput. Phys. 417, Article ID 109574, 29 p. (2020; Zbl 1437.74021) Full Text: DOI
Bonnivard, Matthieu; Omnès, Florian; Privat, Yannick Modeling and optimization of hourglass-shaped aquaporins. (English) Zbl 1401.92074 Math. Models Methods Appl. Sci. 28, No. 8, 1529-1564 (2018). MSC: 92C40 92C37 49Q10 76D05 92C35 76Z05 PDFBibTeX XMLCite \textit{M. Bonnivard} et al., Math. Models Methods Appl. Sci. 28, No. 8, 1529--1564 (2018; Zbl 1401.92074) Full Text: DOI
Ta, Thi Thanh Mai; Le, Van Chien; Pham, Ha Thanh Corrigendum to: “Shape optimization for Stokes flows using sensitivity analysis and finite element method”. (English) Zbl 1466.65204 Appl. Numer. Math. 129, 192 (2018). MSC: 65N30 76D07 49Q10 49Q12 76M10 PDFBibTeX XMLCite \textit{T. T. M. Ta} et al., Appl. Numer. Math. 129, 192 (2018; Zbl 1466.65204) Full Text: DOI
Apte, Amit; Auroux, Didier; Ramaswamy, Mythily Observers for compressible Navier-Stokes equation. (English) Zbl 1383.93017 SIAM J. Control Optim. 56, No. 2, 1081-1104 (2018). MSC: 93B07 93C20 93C95 93B40 35Q30 76D05 PDFBibTeX XMLCite \textit{A. Apte} et al., SIAM J. Control Optim. 56, No. 2, 1081--1104 (2018; Zbl 1383.93017) Full Text: DOI
Duan, Xianbao; Qin, Xinqiang Optimality criteria coupled adaptive mesh method for optimal shape design of Stokes flow. (English) Zbl 1344.49067 Math. Methods Appl. Sci. 39, No. 13, 3910-3920 (2016). MSC: 49Q10 49M25 49M05 49Q12 65K10 76D07 76D55 PDFBibTeX XMLCite \textit{X. Duan} and \textit{X. Qin}, Math. Methods Appl. Sci. 39, No. 13, 3910--3920 (2016; Zbl 1344.49067) Full Text: DOI
Marck, Gilles; Nemer, Maroun; Harion, Jean-Luc Topology optimization of convective laminar heat transfer. (English. French summary) Zbl 1373.80003 ESAIM, Proc. Surv. 45, 369-378 (2014). MSC: 80A20 80M50 80M12 76D05 PDFBibTeX XMLCite \textit{G. Marck} et al., ESAIM, Proc. Surv. 45, 369--378 (2014; Zbl 1373.80003) Full Text: DOI
Ballarin, Francesco; Manzoni, Andrea; Rozza, Gianluigi; Salsa, Sandro Shape optimization by free-form deformation: existence results and numerical solution for Stokes flows. (English) Zbl 1303.49017 J. Sci. Comput. 60, No. 3, 537-563 (2014). MSC: 49Q10 49J20 65K10 65N30 76D55 PDFBibTeX XMLCite \textit{F. Ballarin} et al., J. Sci. Comput. 60, No. 3, 537--563 (2014; Zbl 1303.49017) Full Text: DOI
Schulz, Andreas The optimal shape of a pipe. (English) Zbl 1271.76083 Z. Angew. Math. Phys. 64, No. 4, 1177-1185 (2013). MSC: 76D55 PDFBibTeX XMLCite \textit{A. Schulz}, Z. Angew. Math. Phys. 64, No. 4, 1177--1185 (2013; Zbl 1271.76083) Full Text: DOI
Kasumba, H.; Kunisch, K. Vortex control of instationary channel flows using translation invariant cost functionals. (English) Zbl 1272.49092 Comput. Optim. Appl. 55, No. 1, 227-263 (2013). MSC: 49Q10 35Q30 76D05 PDFBibTeX XMLCite \textit{H. Kasumba} and \textit{K. Kunisch}, Comput. Optim. Appl. 55, No. 1, 227--263 (2013; Zbl 1272.49092) Full Text: DOI
Kasumba, H.; Kunisch, K. Vortex control in channel flows using translational invariant cost functionals. (English) Zbl 1258.49070 Comput. Optim. Appl. 52, No. 3, 691-717 (2012). MSC: 49Q10 35Q30 76D05 PDFBibTeX XMLCite \textit{H. Kasumba} and \textit{K. Kunisch}, Comput. Optim. Appl. 52, No. 3, 691--717 (2012; Zbl 1258.49070) Full Text: DOI Link
Henrot, Antoine; Privat, Yannick What is the optimal shape of a pipe? (English) Zbl 1304.76022 Arch. Ration. Mech. Anal. 196, No. 1, 281-302 (2010). MSC: 76D55 76D05 76M30 49J20 PDFBibTeX XMLCite \textit{A. Henrot} and \textit{Y. Privat}, Arch. Ration. Mech. Anal. 196, No. 1, 281--302 (2010; Zbl 1304.76022) Full Text: DOI arXiv
Henrot, Antoine; Privat, Yannick A cylindrical pipe is not optimal to minimize the energy dissipated by a fluid. (Une conduite cylindrique n’est pas optimale pour minimiser l’énergie dissipée par un fluide.) (French. Abridged English version) Zbl 1156.35444 C. R., Math., Acad. Sci. Paris 346, No. 19-20, 1057-1061 (2008). MSC: 35Q30 49K20 76D55 PDFBibTeX XMLCite \textit{A. Henrot} and \textit{Y. Privat}, C. R., Math., Acad. Sci. Paris 346, No. 19--20, 1057--1061 (2008; Zbl 1156.35444) Full Text: DOI