{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T13:28:32Z","timestamp":1748352512234,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,4,29]],"date-time":"2021-04-29T00:00:00Z","timestamp":1619654400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,29]],"date-time":"2021-04-29T00:00:00Z","timestamp":1619654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100018618","name":"National Numerical Wind Tunnel Project","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100018618","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U1730118","91530325"],"award-info":[{"award-number":["U1730118","91530325"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s10915-021-01499-8","type":"journal-article","created":{"date-parts":[[2021,4,29]],"date-time":"2021-04-29T10:03:22Z","timestamp":1619690602000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Local-Maximum-and-Minimum-Preserving Solution Remapping Technique to Accelerate Flow Convergence for Discontinuous Galerkin Methods in Shape Optimization Design"],"prefix":"10.1007","volume":"87","author":[{"given":"Jufang","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tiegang","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,4,29]]},"reference":[{"key":"1499_CR1","doi-asserted-by":"publisher","unstructured":"Bhabra, M., Nadarajah, S.: Aerodynamic shape optimization for the NURBS-enhanced discontinuous Galerkin method. In: AIAA Aviation 2019 Forum (2019). https:\/\/doi.org\/10.2514\/6.2019-3197","DOI":"10.2514\/6.2019-3197"},{"key":"1499_CR2","doi-asserted-by":"publisher","unstructured":"Blazek, J.: Computational Fluid Dynamics: Principles and Applications. Elsevier (2005). https:\/\/doi.org\/10.1016\/B978-0-08-044506-9.X5000-0","DOI":"10.1016\/B978-0-08-044506-9.X5000-0"},{"issue":"11\u201314","key":"1499_CR3","doi-asserted-by":"publisher","first-page":"784","DOI":"10.1016\/j.compstruc.2007.01.013","volume":"85","author":"A de Boer","year":"2007","unstructured":"de Boer, A., van der Schoot, M.S., Bijl, H.: Mesh deformation based on radial basis function interpolation. Comput. Struct. 85(11\u201314), 784\u2013795 (2007). https:\/\/doi.org\/10.1016\/j.compstruc.2007.01.013","journal-title":"Comput. Struct."},{"key":"1499_CR4","doi-asserted-by":"publisher","unstructured":"Chan, C., Bai, H., He, D.: Blade shape optimization of the Savonius wind turbine using a genetic algorithm. Appl. Energy 213, 148\u2013157 (2018) https:\/\/doi.org\/10.1016\/j.apenergy.2018.01.029. http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0306261918300291","DOI":"10.1016\/j.apenergy.2018.01.029"},{"key":"1499_CR5","doi-asserted-by":"publisher","unstructured":"Chen, G., Fidkowski, K.J.: Discretization error control for constrained aerodynamic shape optimization. J. Comput. Phys. 387, 163\u2013185 (2019) https:\/\/doi.org\/10.1016\/j.jcp.2019.02.038. http:\/\/www.sciencedirect.com\/science\/article\/pii\/S002199911930155X","DOI":"10.1016\/j.jcp.2019.02.038"},{"issue":"190","key":"1499_CR6","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1090\/S0025-5718-1990-1010597-0","volume":"54","author":"B Cockburn","year":"1990","unstructured":"Cockburn, B., Hou, S., Shu, C.W.: The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case. Math. Comput. 54(190), 545\u2013581 (1990). https:\/\/doi.org\/10.1090\/S0025-5718-1990-1010597-0","journal-title":"Math. Comput."},{"issue":"1","key":"1499_CR7","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/0021-9991(89)90183-6","volume":"84","author":"B Cockburn","year":"1989","unstructured":"Cockburn, B., Lin, S.Y., Shu, C.W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems. J. Comput. Phys. 84(1), 90\u2013113 (1989). https:\/\/doi.org\/10.1016\/0021-9991(89)90183-6","journal-title":"J. Comput. Phys."},{"issue":"186","key":"1499_CR8","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1090\/S0025-5718-1989-0983311-4","volume":"52","author":"B Cockburn","year":"1989","unstructured":"Cockburn, B., Shu, C.W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Math. Comput. 52(186), 411\u2013435 (1989). https:\/\/doi.org\/10.1090\/S0025-5718-1989-0983311-4","journal-title":"Math. Comput."},{"key":"1499_CR9","doi-asserted-by":"publisher","unstructured":"Cockburn, B., Shu, C.W.: The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141(2), 199\u2013224 (1998) https:\/\/doi.org\/10.1006\/jcph.1998.5892. http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0021999198958922","DOI":"10.1006\/jcph.1998.5892"},{"key":"1499_CR10","doi-asserted-by":"publisher","unstructured":"Hartmann, R., Houston, P.: Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. J. Comput. Phys. 183(2), 508\u2013532 (2002) https:\/\/doi.org\/10.1006\/jcph.2002.7206. http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0021999102972062","DOI":"10.1006\/jcph.2002.7206"},{"issue":"3","key":"1499_CR11","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1137\/S1064827501389084","volume":"24","author":"R Hartmann","year":"2003","unstructured":"Hartmann, R., Houston, P.: Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservation laws. SIAM J. Sci. Comput. 24(3), 979\u20131004 (2003). https:\/\/doi.org\/10.1137\/S1064827501389084","journal-title":"SIAM J. Sci. Comput."},{"issue":"7","key":"1499_CR12","doi-asserted-by":"publisher","first-page":"407","DOI":"10.2514\/3.58379","volume":"15","author":"RM Hicks","year":"1978","unstructured":"Hicks, R.M., Henne, P.A.: Wing design by numerical optimization. J. Aircr. 15(7), 407\u2013412 (1978). https:\/\/doi.org\/10.2514\/3.58379","journal-title":"J. Aircr."},{"key":"1499_CR13","unstructured":"Holland, J.: Adaptation in Natural and Artificial Systems. University of Michigan Press (1975)"},{"key":"1499_CR14","doi-asserted-by":"publisher","unstructured":"Jameson, A., Schmidt, W., Turkel, E.: Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. In: AIAA 14th Fluid and Plasma Dynamics Conference, p. 1259 (1981). https:\/\/doi.org\/10.2514\/6.1981-1259","DOI":"10.2514\/6.1981-1259"},{"key":"1499_CR15","doi-asserted-by":"publisher","unstructured":"Kaland, L., Sonntag, M., Gauger, N.R.: Adaptive aerodynamic design optimization for Navier-Stokes using shape derivatives with discontinuous Galerkin methods. In: D. Greiner, B. Galv\u00e1n, J. P\u00e9riaux, N. Gauger, K. Giannakoglou, G. Winter (eds.) Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences, pp. 143\u2013158. Springer International Publishing, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-11541-2_9","DOI":"10.1007\/978-3-319-11541-2_9"},{"key":"1499_CR16","doi-asserted-by":"crossref","unstructured":"LeVeque, R.J.: Finite volume methods for hyperbolic problems. Cambridge University Press, Cambridge (2002)","DOI":"10.1017\/CBO9780511791253"},{"issue":"1","key":"1499_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/fld.3971","volume":"77","author":"D Li","year":"2015","unstructured":"Li, D., Hartmann, R.: Adjoint-based airfoil optimization with discretization error control. Int. J. Numeri. Methods Fluids 77(1), 1\u201317 (2015). https:\/\/doi.org\/10.1002\/fld.3971","journal-title":"Int. J. Numeri. Methods Fluids"},{"key":"1499_CR18","unstructured":"Lu, J.: An a Posteriori Error Control Framework for Adaptive Precision Optimization Using Discontinuous Galerkin Finite Element Method. Ph.D. thesis, Massachusetts Institute of Technology (2005)"},{"issue":"4","key":"1499_CR19","doi-asserted-by":"publisher","first-page":"968","DOI":"10.2514\/1.J053318","volume":"53","author":"Z Lyu","year":"2015","unstructured":"Lyu, Z., Kenway, G.K.W., Martins, J.R.R.A.: Aerodynamic shape optimization investigations of the common research model wing benchmark. AIAA J. 53(4), 968\u2013985 (2015). https:\/\/doi.org\/10.2514\/1.J053318","journal-title":"AIAA J."},{"key":"1499_CR20","doi-asserted-by":"publisher","unstructured":"Naumann, D., Evans, B., Walton, S., Hassan, O.: A novel implementation of computational aerodynamic shape optimisation using Modified Cuckoo Search. Appl. Math. Modell. 40(7), 4543\u20134559 (2016) https:\/\/doi.org\/10.1016\/j.apm.2015.11.023. http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0307904X15007374","DOI":"10.1016\/j.apm.2015.11.023"},{"issue":"6","key":"1499_CR21","doi-asserted-by":"publisher","first-page":"2709","DOI":"10.1137\/070692108","volume":"30","author":"PO Persson","year":"2008","unstructured":"Persson, P.O., Peraire, J.: Newton-GMRES preconditioning for discontinuous Galerkin discretizations of the Navier-Stokes equations. SIAM J. Sci. Comput. 30(6), 2709\u20132733 (2008). https:\/\/doi.org\/10.1137\/070692108","journal-title":"SIAM J. Sci. Comput."},{"issue":"4\u20135","key":"1499_CR22","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1080\/10618562.2018.1514115","volume":"32","author":"F Salmoiraghi","year":"2018","unstructured":"Salmoiraghi, F., Scardigli, A., Telib, H., Rozza, G.: Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation. Int. J. Comput. Fluid Dyn. 32(4\u20135), 233\u2013247 (2018). https:\/\/doi.org\/10.1080\/10618562.2018.1514115","journal-title":"Int. J. Comput. Fluid Dyn."},{"key":"1499_CR23","unstructured":"Slotnick, J., Khodadoust, A., Alonso, J., Darmofal, D., Gropp, W., Lurie, E., Mavriplis, D.: CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences. NASA\/CR-2014-218178, NF1676L-18332 (2014)"},{"issue":"4","key":"1499_CR24","first-page":"482","volume":"19","author":"JC Spall","year":"1998","unstructured":"Spall, J.C.: An overview of the simultaneous perturbation method for efficient optimization. Johns Hopkins APL Tech. Digest 19(4), 482\u2013492 (1998)","journal-title":"Johns Hopkins APL Tech. Digest"},{"key":"1499_CR25","unstructured":"Spall, J.C.: Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control. John Wiley & Sons, New Jersey (2005)"},{"key":"1499_CR26","doi-asserted-by":"publisher","unstructured":"Toman, U.T., Hassan, A.K.S., Owis, F.M., Mohamed, A.S.: Blade shape optimization of an aircraft propeller using space mapping surrogates. Adv. Mech. Eng. 11(7) (2019). https:\/\/doi.org\/10.1177\/1687814019865071","DOI":"10.1177\/1687814019865071"},{"key":"1499_CR27","doi-asserted-by":"publisher","unstructured":"Wang, J., Wang, Z., Liu, T.: Solution remapping technique to accelerate flow convergence for finite volume methods applied to shape optimization design. Numeri. Math. Theory Methods Appl. 13(4), 863\u2013880 (2020) https:\/\/doi.org\/10.4208\/nmtma.OA-2019-0164. http:\/\/global-sci.org\/intro\/article_detail\/nmtma\/16957.html","DOI":"10.4208\/nmtma.OA-2019-0164"},{"key":"1499_CR28","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1016\/j.cma.2018.10.033","volume":"344","author":"K Wang","year":"2019","unstructured":"Wang, K., Yu, S., Wang, Z., Feng, R., Liu, T.: Adjoint-based airfoil optimization with adaptive isogeometric discontinuous Galerkin method. Comput. Methods Appl. Mech. Eng. 344, 602\u2013625 (2019). https:\/\/doi.org\/10.1016\/j.cma.2018.10.033","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"1499_CR29","doi-asserted-by":"publisher","first-page":"614701","DOI":"10.1007\/s11433-015-5706-3","volume":"59","author":"Z Wang","year":"2016","unstructured":"Wang, Z.: A perspective on high-order methods in computational fluid dynamics. Sci. China Phys. Mech. Astron. 59(1), 614701 (2016). https:\/\/doi.org\/10.1007\/s11433-015-5706-3","journal-title":"Sci. China Phys. Mech. Astron."},{"issue":"2022","key":"1499_CR30","doi-asserted-by":"publisher","first-page":"20130318","DOI":"10.1098\/rsta.2013.0318","volume":"372","author":"ZJ Wang","year":"2014","unstructured":"Wang, Z.J.: High-order computational fluid dynamics tools for aircraft design. Philos. Trans. Roy. Soc. A Math. Phys. Eng. Sci. 372(2022), 20130318 (2014). https:\/\/doi.org\/10.1098\/rsta.2013.0318","journal-title":"Philos. Trans. Roy. Soc. A Math. Phys. Eng. Sci."},{"issue":"8","key":"1499_CR31","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1002\/fld.3767","volume":"72","author":"ZJ Wang","year":"2013","unstructured":"Wang, Z.J., Fidkowski, K., Abgrall, R., Bassi, F., Caraeni, D., Cary, A., Deconinck, H., Hartmann, R., Hillewaert, K., Huynh, H.T., Kroll, N., May, G., Persson, P.O., van Leer, B., Visbal, M.: High-order CFD methods: current status and perspective. Int. J. Numer. Methods Fluids 72(8), 811\u2013845 (2013). https:\/\/doi.org\/10.1002\/fld.3767","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"2","key":"1499_CR32","doi-asserted-by":"publisher","first-page":"284","DOI":"10.2514\/1.9484","volume":"43","author":"XQ Xing","year":"2005","unstructured":"Xing, X.Q., Damodaran, M.: Application of simultaneous perturbation stochastic approximation method for aerodynamic shape design optimization. AIAA J. 43(2), 284\u2013294 (2005). https:\/\/doi.org\/10.2514\/1.9484","journal-title":"AIAA J."},{"key":"1499_CR33","doi-asserted-by":"publisher","unstructured":"Zahr, M.J., Persson, P.O.: High-order, time-dependent aerodynamic optimization using a discontinuous Galerkin discretization of the Navier-Stokes equations. In: 54th AIAA Aerospace Sciences Meeting (2016). https:\/\/doi.org\/10.2514\/6.2016-0064","DOI":"10.2514\/6.2016-0064"},{"key":"1499_CR34","doi-asserted-by":"publisher","unstructured":"Zahr, M.J., Persson, P.O.: Energetically optimal flapping wing motions via adjoint-based optimization and high-order discretizations. In: H. Antil, D.P. Kouri, M.D. Lacasse, D. Ridzal (eds.) Frontiers in PDE-Constrained Optimization, pp. 259\u2013289. Springer, New York, NY (2018). https:\/\/doi.org\/10.1007\/978-1-4939-8636-1_7","DOI":"10.1007\/978-1-4939-8636-1_7"},{"key":"1499_CR35","doi-asserted-by":"publisher","unstructured":"Zhang, X., Shu, C.W.: On maximum-principle-satisfying high order schemes for scalar conservation laws. J. Comput. Phys. 229(9), 3091\u20133120 (2010) https:\/\/doi.org\/10.1016\/j.jcp.2009.12.030. http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0021999109007165","DOI":"10.1016\/j.jcp.2009.12.030"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01499-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-021-01499-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01499-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T18:29:15Z","timestamp":1621880955000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-021-01499-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,29]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1499"],"URL":"https:\/\/doi.org\/10.1007\/s10915-021-01499-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2021,4,29]]},"assertion":[{"value":"30 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 April 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 April 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}],"article-number":"79"}}