{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T21:26:22Z","timestamp":1740173182187,"version":"3.37.3"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,11,25]],"date-time":"2015-11-25T00:00:00Z","timestamp":1448409600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Spanish Ministry of Science and Competitiveness","award":["CICYT- DPI2014-51844-C2-2-R"],"award-info":[{"award-number":["CICYT- DPI2014-51844-C2-2-R"]}]},{"DOI":"10.13039\/501100002809","name":"Generalitat de Catalunya","doi-asserted-by":"publisher","award":["2014-SGR-1471"],"award-info":[{"award-number":["2014-SGR-1471"]}],"id":[{"id":"10.13039\/501100002809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Spanish Ministry of Science and Competitiveness","award":["DPI2014-51844-C2-1-R"],"award-info":[{"award-number":["DPI2014-51844-C2-1-R"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv. Model. and Simul. in Eng. Sci."],"published-print":{"date-parts":[[2015,12]]},"DOI":"10.1186\/s40323-015-0052-6","type":"journal-article","created":{"date-parts":[[2015,11,25]],"date-time":"2015-11-25T03:13:19Z","timestamp":1448421199000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Effect of the separated approximation of input data in the accuracy of the resulting PGD solution"],"prefix":"10.1186","volume":"2","author":[{"given":"Sergio","family":"Zlotnik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro","family":"D\u00edez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Gonzalez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"El\u00edas","family":"Cueto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Huerta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,11,25]]},"reference":[{"key":"52_CR1","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.jnnfm.2006.07.007","volume":"139","author":"A Ammar","year":"2006","unstructured":"Ammar A, Mokdad B, Chinesta F, Keunings R. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. J Non Newton Fluid Mech. 2006;139:153\u201376.","journal-title":"J Non Newton Fluid Mech"},{"key":"52_CR2","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.jnnfm.2007.03.009","volume":"144","author":"A Ammar","year":"2007","unstructured":"Ammar A, Mokdad B, Chinesta F, Keunings R. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Part II: transient simulation using space-time separated representations. J Non Newton Fluid Mech. 2007;144:98\u2013121.","journal-title":"J Non Newton Fluid Mech"},{"key":"52_CR3","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.cma.2013.09.003","volume":"268","author":"A Ammar","year":"2014","unstructured":"Ammar A, Huerta A, Chinesta F, Cueto E. Parametric solutions involving geometry: a step towards efficient shape optimization. Comput Methods Appl Mech Eng. 2014;268:178\u201393.","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"10","key":"52_CR4","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1002\/nme.4909","volume":"103","author":"S Zlotnik","year":"2015","unstructured":"Zlotnik S, D\u00edez P, Modesto D, Huerta A. Proper generalized decomposition of a geometrically parametrized heat problem with geophysical applications. Int J Numer Meth Eng. 2015;103(10):737\u201358. doi: 10.1002\/nme.4909 .","journal-title":"Int J Numer Meth Eng"},{"issue":"9","key":"52_CR5","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1002\/nme.4691","volume":"99","author":"D Gonz\u00e1lez","year":"2014","unstructured":"Gonz\u00e1lez D, Cueto E, Chinesta F. Real-time direct integration of reduced solid dynamics equations. Int J Numer Meth Eng. 2014;99(9):633\u201353.","journal-title":"Int J Numer Meth Eng"},{"key":"52_CR6","doi-asserted-by":"crossref","first-page":"1872","DOI":"10.1016\/j.cma.2010.02.012","volume":"199","author":"A Ammar","year":"2010","unstructured":"Ammar A, Chinesta F, D\u00edez P, Huerta A. An error estimator for separated representations of highly multidimensional models. Comput Methods Appl Mech Eng. 2010;199:1872\u201380.","journal-title":"Comput Methods Appl Mech Eng"},{"key":"52_CR7","doi-asserted-by":"crossref","unstructured":"Bouclier R, Louf F, Chamoin L. Real-time validation of mechanical models coupling PGD and constitutive relation error. Comput Mech. 2013;52(4):861\u201383.","DOI":"10.1007\/s00466-013-0850-y"},{"issue":"2","key":"52_CR8","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s00466-014-1097-y","volume":"55","author":"E Nadal","year":"2015","unstructured":"Nadal E, Leygue A, Chinesta F, Beringhier M, R\u00f3denas JJ, Fuenmayor FJ. A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework. Comput Mech. 2015;55(2):251\u201366.","journal-title":"Comput Mech"},{"issue":"2","key":"52_CR9","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1137\/S0036142999360044","volume":"38","author":"P Morin","year":"2000","unstructured":"Morin P, Nochetto RH, Siebert KG. Data oscillation and convergence of adaptive FEM. SIAM J Numer Anal. 2000;38(2):466\u201388.","journal-title":"SIAM J Numer Anal"},{"key":"52_CR10","doi-asserted-by":"crossref","unstructured":"Abdulle A. On a priori error analysis of fully discrete heterogeneous multiscale FEM. Multiscale Modeling and Simulation. SIAM Interdiscip J. 2005;4(2):447\u201359.","DOI":"10.1137\/040607137"},{"key":"52_CR11","doi-asserted-by":"crossref","unstructured":"Ming P, Zhang P. Analysis of the heterogeneous multiscale method for elliptic homogenization problems. J Am Math Soc. 2005;18(1):121\u201356.","DOI":"10.1090\/S0894-0347-04-00469-2"},{"issue":"3","key":"52_CR12","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda TG, Bader BW. Tensor decompositions and applications. SIAM Rev. 2009;51(3):455\u2013500.","journal-title":"SIAM Rev"},{"issue":"4","key":"52_CR13","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1137\/S0895479896305696","volume":"21","author":"L Lathauwer De","year":"2000","unstructured":"De Lathauwer L, De Moor B, Vandewalle J. A multilinear singular value decomposition. SIAM J Matrix Anal Appl. 2000;21(4):1253\u201378.","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"3","key":"52_CR14","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/BF02310791","volume":"35","author":"JD Carroll","year":"1970","unstructured":"Carroll JD, Chang J-J. Analysis of individual differences in multidimensional scaling via an n-way generalization of \u201cEckart-Young\u201d decomposition. Psychometrika. 1970;35(3):283\u2013319.","journal-title":"Psychometrika"},{"key":"52_CR15","unstructured":"Harshman RA. Foundations of the PARAFAC procedure: models and conditions for an \u201cexplanatory\u201d multimodal factor analysis. UCLA Work Pap phon. 1970;16:1\u201384."},{"key":"52_CR16","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02289464","volume":"31","author":"LR Tucker","year":"1966","unstructured":"Tucker LR. Some mathematical notes on three-mode factor analysis. Psychometrika. 1966;31:279\u2013311.","journal-title":"Psychometrika"},{"key":"52_CR17","doi-asserted-by":"crossref","unstructured":"Modesto D, Zlotnik S, Huerta A. Proper generalized decomposition for parameterized helmholtz problems in heterogeneous and unbounded domains: application to harbor agitation. Comput Methods Appl Mech Eng. 2015. doi: 10.1016\/j.cma.2015.03.026 .","DOI":"10.1016\/j.cma.2015.03.026"}],"container-title":["Advanced Modeling and Simulation in Engineering Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s40323-015-0052-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/s40323-015-0052-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s40323-015-0052-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,1]],"date-time":"2019-09-01T18:10:48Z","timestamp":1567361448000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.amses-journal.com\/content\/2\/1\/28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,25]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,12]]}},"alternative-id":["52"],"URL":"https:\/\/doi.org\/10.1186\/s40323-015-0052-6","relation":{},"ISSN":["2213-7467"],"issn-type":[{"type":"electronic","value":"2213-7467"}],"subject":[],"published":{"date-parts":[[2015,11,25]]},"article-number":"28"}}