{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T02:50:22Z","timestamp":1718160622808},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,3,9]],"date-time":"2016-03-09T00:00:00Z","timestamp":1457481600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv. Model. and Simul. in Eng. Sci."],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1186\/s40323-016-0060-1","type":"journal-article","created":{"date-parts":[[2016,3,5]],"date-time":"2016-03-05T02:53:04Z","timestamp":1457146384000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Recursive POD expansion for reaction-diffusion equation"],"prefix":"10.1186","volume":"3","author":[{"given":"M.","family":"Aza\u00efez","sequence":"first","affiliation":[]},{"given":"F. Ben","family":"Belgacem","sequence":"additional","affiliation":[]},{"given":"T. Chac\u00f3n","family":"Rebollo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,3,9]]},"reference":[{"key":"60_CR1","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.cma.2015.02.019","volume":"290","author":"M Aza\u00efez","year":"2015","unstructured":"Aza\u00efez M, Belgacem Ben F. Karhunen-Lo\u00e8ve\u2019s truncation error for bivariate functions. Comput Methods Appl Mech Eng. 2015;290:57\u201372.","journal-title":"Comput Methods Appl Mech Eng"},{"key":"60_CR2","unstructured":"Azaiez M, Ben Belgacem F and Chac\u00f3n Rebollo T. Error bounds for POD expansions of parameterized transient temperatures. Submitted to Comp. Methods App. Mech. Eng."},{"key":"60_CR3","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1146\/annurev.fl.25.010193.002543","volume":"25","author":"G Berkoz","year":"1993","unstructured":"Berkoz G, Holmes P, Lumley JL. The proper orthogonal decomposition in the analysis of turbulent flows. Annu Rev Fluids Mech. 1993;25:539\u201375.","journal-title":"Annu Rev Fluids Mech"},{"key":"60_CR4","volume-title":"Approximations spectrales de probl\u00e8mes aux limites elliptiques, Math\u00e9matiques et applications","author":"C Bernardi","year":"1992","unstructured":"Bernardi C, Maday Y. Approximations spectrales de probl\u00e8mes aux limites elliptiques, Math\u00e9matiques et applications. Berlin: Springer; 1992."},{"key":"60_CR5","volume-title":"The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer","author":"F Chinesta","year":"2013","unstructured":"Chinesta F, Keunings R, Leygue A. The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer. New York: Springer Publishing Company, Incorporated; 2013."},{"key":"60_CR6","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s11831-011-9064-7","volume":"18","author":"F Chinesta","year":"2011","unstructured":"Chinesta F, Ladev\u00e8se P, Cueto E. A Short Review on Model Order Reduction Based on Proper Generalized Decomposition. Arch Comput Methods Eng. 2011;18:395\u2013404.","journal-title":"Arch Comput Methods Eng"},{"issue":"4","key":"60_CR7","first-page":"12531278","volume":"21","author":"L Lathauwer De","year":"2000","unstructured":"De Lathauwer L, De Moor B, Vandewalle J. A multilinear singular value decomposition. SIAM J Matr Anal Appl. 2000;21(4):12531278.","journal-title":"SIAM J Matr Anal Appl"},{"issue":"4","key":"60_CR8","first-page":"13241342","volume":"21","author":"L Lathauwer De","year":"2000","unstructured":"De Lathauwer L, De Moor B, Vandewalle J. On the Best Rank-One and Rank-R1; R2;.; RN Approximation of Higher Order Tensors. SIAM J Matr Anal Appl. 2000;21(4):13241342.","journal-title":"SIAM J Matr Anal Appl"},{"issue":"3","key":"60_CR9","doi-asserted-by":"crossref","first-page":"1084","DOI":"10.1137\/06066518X","volume":"20","author":"V Silva De","year":"2008","unstructured":"De Silva V, Lim LH. Tensor rank and the ill posedness of the best low-rank approximation problem. SIAM J Matrix Anal Appl. 2008;20(3):1084\u2013127.","journal-title":"SIAM J Matrix Anal Appl"},{"key":"60_CR10","doi-asserted-by":"crossref","unstructured":"Diestel J and Uhl. Vector measures. AMS J J; 1977.","DOI":"10.1090\/surv\/015"},{"key":"60_CR11","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1016\/S0020-7462(03)00090-8","volume":"39","author":"BI Epureanu","year":"2004","unstructured":"Epureanu BI, Tang LS, Paidoussis MP. Coherent structures and their influence on the dynamics of aeroelastic panels. Int J Non-Linear Mech. 2004;39:977\u201391.","journal-title":"Int J Non-Linear Mech"},{"key":"60_CR12","doi-asserted-by":"crossref","unstructured":"Ghanem R and Spanos P. Stochastic finite elements: a spectral approach. Springer-Verlag; 1991.","DOI":"10.1007\/978-1-4612-3094-6"},{"key":"60_CR13","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"Golub GH, Van Loan CF. Matrix Computations. 3rd ed. Baltimore: The Johns Hopkins University Press; 1996.","edition":"3"},{"key":"60_CR14","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.cma.2013.03.002","volume":"259","author":"C Heyberger","year":"2013","unstructured":"Heyberger C, Boucard PA, N\u00e9ron D. A rational strategy for the resolution of parametrized problems in the PGD framework. Comp Meth Appl Mech Eng. 2013;259:40\u20139.","journal-title":"Comp Meth Appl Mech Eng"},{"issue":"3","key":"60_CR15","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s00466-011-0646-x","volume":"49","author":"C Heyberger","year":"2012","unstructured":"Heyberger C, Boucard PA, N\u00e9ron D. Multiparametric Analysis within the Proper Generalized Decomposition Framework. Comput Mech. 2012;49(3):277\u201389.","journal-title":"Comput Mech"},{"key":"60_CR16","volume-title":"Coherent Structures, Synamical Systems and Symmetry, Cambridge Monographs on Mechanis","author":"P Holmes","year":"1996","unstructured":"Holmes P, Lumley JL, Berkooz G. Coherent Structures, Synamical Systems and Symmetry, Cambridge Monographs on Mechanis. Cambridge: Cambridge University Press; 1996."},{"key":"60_CR17","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1037\/h0071325","volume":"24","author":"H Hotelling","year":"1933","unstructured":"Hotelling H. Analysis of a complex of statistical variables into principal componentse. J Educ Psychol. 1933;24:417\u201341.","journal-title":"J Educ Psychol"},{"key":"60_CR18","doi-asserted-by":"crossref","unstructured":"Jolliffe IT. Principal Component Analysis. Springer; 1986.","DOI":"10.1007\/978-1-4757-1904-8"},{"key":"60_CR19","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1137\/0515009","volume":"15","author":"G Little","year":"1984","unstructured":"Little G, Reade JB. Eigenvalues of analytic kernels. SIAM J Math Anal. 1984;15:133\u20136.","journal-title":"SIAM J Math Anal"},{"key":"60_CR20","volume-title":"Probability Theory","author":"MM Lo\u00e8ve","year":"1988","unstructured":"Lo\u00e8ve MM. Probability Theory. Princeton: Van Nostrand; 1988."},{"issue":"5","key":"60_CR21","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.2514\/1.35258","volume":"45","author":"LS Lorente","year":"2008","unstructured":"Lorente LS, Vega JM, Velazquez A. Generation of Aerodynamic Databases Using High-Order Singular Value Decomposition. J Aircraft. 2008;45(5):1779\u201388.","journal-title":"J Aircraft"},{"key":"60_CR22","unstructured":"Muller M. On the POD Method. An Abstract Investigation with Applications to Reduced-Order Modeling and Suboptimal Control, Ph D Thesis. Georg-August Universit\u00e4t, G\u00f6ttingen; 2008."},{"key":"60_CR23","doi-asserted-by":"crossref","first-page":"4521","DOI":"10.1016\/j.cma.2007.05.016","volume":"196","author":"A Nouy","year":"2007","unstructured":"Nouy A. A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations. Comput Meth Appl Mech Eng. 2007;196:4521\u201337.","journal-title":"Comput Meth Appl Mech Eng"},{"key":"60_CR24","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1080\/14786440109462720","volume":"2","author":"K Pearson","year":"1901","unstructured":"Pearson K. On lines and planes of closest fit system of points in space. Philo Mag J Sci. 1901;2:559\u201372.","journal-title":"Philo Mag J Sci"},{"key":"60_CR25","volume-title":"Approximation theory and approximation practice. Software, Environments, and Tools","author":"LN Trefethen","year":"2013","unstructured":"Trefethen LN. Approximation theory and approximation practice. Software, Environments, and Tools. Philadel-phia: Society for Industrial and Applied Mathematics (SIAM); 2013."},{"key":"60_CR26","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.2514\/2.1570","volume":"40","author":"K Willcox","year":"2002","unstructured":"Willcox K, Peraire J. Balanced Model Reduction via the Proper Orthogonal Decomposition. AIAA. 2002;40:2323\u201330.","journal-title":"AIAA"},{"key":"60_CR27","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1137\/120903300","volume":"36","author":"M Yano","year":"2013","unstructured":"Yano M. A Space-Time Petrov-Galerkin Certified Reduced Basis Method: Application to the Boussinesq Equations. SIAM J Sci Comput. 2013;36:232\u201366.","journal-title":"SIAM J Sci Comput"}],"container-title":["Advanced Modeling and Simulation in Engineering Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s40323-016-0060-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/s40323-016-0060-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s40323-016-0060-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,5]],"date-time":"2019-09-05T07:34:01Z","timestamp":1567668841000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.amses-journal.com\/content\/3\/1\/3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,9]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["60"],"URL":"https:\/\/doi.org\/10.1186\/s40323-016-0060-1","relation":{},"ISSN":["2213-7467"],"issn-type":[{"value":"2213-7467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,9]]},"article-number":"3"}}