{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:39:34Z","timestamp":1740123574310,"version":"3.37.3"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,10,22]],"date-time":"2019-10-22T00:00:00Z","timestamp":1571702400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,10,22]],"date-time":"2019-10-22T00:00:00Z","timestamp":1571702400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1007\/s10915-019-01069-z","type":"journal-article","created":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T12:45:04Z","timestamp":1571834704000},"page":"1987-2009","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Polynomial Chaos Level Points Method for One-Dimensional Uncertain Steep Problems"],"prefix":"10.1007","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8223-9335","authenticated-orcid":false,"given":"Pierre","family":"Sochala","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3811-7787","authenticated-orcid":false,"given":"Olivier","family":"Le Ma\u00eetre","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,10,22]]},"reference":[{"issue":"2","key":"1069_CR1","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1007\/s10915-011-9486-2","volume":"50","author":"A Alexanderian","year":"2012","unstructured":"Alexanderian, A., Le Ma\u00eetre, O., Najm, H., Iskandarani, M., Knio, O.: Multiscale stochastic preconditioners in non-intrusive spectral projection. SIAM J. Sci. Comput. 50(2), 306\u2013340 (2012). \nhttps:\/\/doi.org\/10.1007\/s10915-011-9486-2","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"1069_CR2","doi-asserted-by":"publisher","first-page":"592","DOI":"10.1007\/s10915-013-9745-5","volume":"58","author":"A Alexanderian","year":"2014","unstructured":"Alexanderian, A., Rizzi, F., Rathinam, M., Le Ma\u00eetre, O., Knio, O.: Preconditioned Bayesian regression for stochastic chemical kinetics. J. Sci. Comput. 58(3), 592\u2013626 (2014). \nhttps:\/\/doi.org\/10.1007\/s10915-013-9745-5","journal-title":"J. Sci. Comput."},{"key":"1069_CR3","unstructured":"Brooks, R.H., Corey, A.T.: Hydraulic properties of porous media. Colorado State University Hydrology Papers. Colorado State University (1964)"},{"issue":"19","key":"1069_CR4","doi-asserted-by":"publisher","first-page":"7159","DOI":"10.1016\/j.jcp.2009.06.024","volume":"228","author":"T Chantrasmi","year":"2009","unstructured":"Chantrasmi, T., Doostan, A., Iaccarino, G.: Pad\u00e9\u2013Legendre approximants for uncertainty analysis with discontinuous response surfaces. J. Comput. Phys. 228(19), 7159\u20137180 (2009). \nhttps:\/\/doi.org\/10.1016\/j.jcp.2009.06.024","journal-title":"J. Comput. Phys."},{"issue":"6","key":"1069_CR5","doi-asserted-by":"publisher","first-page":"A2643","DOI":"10.1137\/120890715","volume":"35","author":"PR Conrad","year":"2013","unstructured":"Conrad, P.R., Marzouk, Y.M.: Adaptive Smolyak pseudospectral approximations. SIAM J. Sci. Comput. 35(6), A2643\u2013A2670 (2013). \nhttps:\/\/doi.org\/10.1137\/120890715","journal-title":"SIAM J. Sci. Comput."},{"key":"1069_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cma.2012.03.019","volume":"229","author":"PG Constantine","year":"2012","unstructured":"Constantine, P.G., Eldred, M.S., Phipps, E.T.: Sparse pseudospectral approximation method. Comput. Methods Appl. Mech. Eng. 229, 1\u201312 (2012)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1069_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3094-6","volume-title":"Stochastic Finite Elements: A Spectral Approach","author":"RG Ghanem","year":"1991","unstructured":"Ghanem, R.G., Spanos, S.D.: Stochastic Finite Elements: A Spectral Approach. Springer, Berlin (1991)"},{"key":"1069_CR8","unstructured":"Karhunen, K.: \u00dcber lineare Methoden in der Wahrscheinlichkeitsrechnung. Annales Academiae scientiarum Fennicae: Mathematica - Physica. Universitat Helsinki (1947). \nhttps:\/\/books.google.com\/books?id=bGUUAQAAIAAJ\n\n. Accessed 18 Oct 2019"},{"key":"1069_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-90-481-3520-2","volume-title":"Spectral Methods for Uncertainty Quantification. Scientific Computation","author":"O Le Ma\u00eetre","year":"2010","unstructured":"Le Ma\u00eetre, O., Knio, O.M.: Spectral Methods for Uncertainty Quantification. Scientific Computation. Springer, Berlin (2010)"},{"issue":"1","key":"1069_CR10","doi-asserted-by":"publisher","first-page":"199","DOI":"10.3934\/dcds.2010.28.199","volume":"28","author":"O Le Ma\u00eetre","year":"2010","unstructured":"Le Ma\u00eetre, O., Mathelin, L., Knio, O.M., Hussaini, M.Y.: Asynchronous time integration for polynomial chaos expansion of uncertain periodic dynamics. Discrete Contin. Dyn. Syst. 28(1), 199\u2013226 (2010). \nhttps:\/\/doi.org\/10.3934\/dcds.2010.28.199","journal-title":"Discrete Contin. Dyn. Syst."},{"issue":"2","key":"1069_CR11","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1016\/j.jcp.2003.12.020","volume":"197","author":"O Le Ma\u00eetre","year":"2004","unstructured":"Le Ma\u00eetre, O., Najm, H., Ghanem, R., Knio, O.: Multi-resolution analysis of Wiener-type uncertainty propagation schemes. J. Comput. Phys. 197(2), 502\u2013531 (2004). 10.1016\/j.jcp.2003.12.020","journal-title":"J. Comput. Phys."},{"issue":"1","key":"1069_CR12","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1006\/jcph.2002.7104","volume":"181","author":"O Le Ma\u00eetre","year":"2002","unstructured":"Le Ma\u00eetre, O., Reagan, M.T., Najm, H.N., Ghanem, R.G., Knio, O.M.: A stochastic projection method for fluid flow: II. Random process. J. Comput. Phys 181(1), 9\u201344 (2002). \nhttps:\/\/doi.org\/10.1006\/jcph.2002.7104","journal-title":"J. Comput. Phys"},{"issue":"9","key":"1069_CR13","doi-asserted-by":"publisher","first-page":"3587","DOI":"10.1016\/j.jcp.2011.12.038","volume":"231","author":"G Po\u00ebtte","year":"2012","unstructured":"Po\u00ebtte, G., Lucor, D.: Non intrusive iterative stochastic spectral representation with application to compressible gas dynamics. J. Comput. Phys. 231(9), 3587\u20133609 (2012). \nhttps:\/\/doi.org\/10.1016\/j.jcp.2011.12.038","journal-title":"J. Comput. Phys."},{"key":"1069_CR14","volume-title":"Numerical Mathematics. Texts in Applied Mathematics","author":"AM Quarteroni","year":"2006","unstructured":"Quarteroni, A.M., Sacco, R., Saleri, F.: Numerical Mathematics. Texts in Applied Mathematics. Springer, New York (2006)"},{"issue":"3","key":"1069_CR15","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1016\/S0010-2180(02)00503-5","volume":"132","author":"MT Reagan","year":"2003","unstructured":"Reagan, M.T., Najm, H.M., Ghanem, R.G., Knio, O.M.: Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection. Combust. Flame 132(3), 545\u2013555 (2003). \nhttps:\/\/doi.org\/10.1016\/S0010-2180(02)00503-5","journal-title":"Combust. Flame"},{"key":"1069_CR16","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1063\/1.1745010","volume":"1","author":"L Richards","year":"1931","unstructured":"Richards, L.: Capillary conduction of liquids through porous mediums. Physics 1, 318\u2013333 (1931)","journal-title":"Physics"},{"issue":"240\u2013243","key":"1069_CR17","first-page":"123","volume":"4","author":"S Smolyak","year":"1963","unstructured":"Smolyak, S.: Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Akad. Nauk SSSR 4(240\u2013243), 123 (1963)","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"1069_CR18","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/j.advwatres.2013.10.003","volume":"62","author":"P Sochala","year":"2013","unstructured":"Sochala, P., Le Ma\u00eetre, O.: Polynomial chaos expansion for subsurface flows with uncertain soil parameters. Adv. Water. Resour. 62, 139\u2013154 (2013). \nhttps:\/\/doi.org\/10.1016\/j.advwatres.2013.10.003","journal-title":"Adv. Water. Resour."},{"issue":"5","key":"1069_CR19","doi-asserted-by":"publisher","first-page":"A2459","DOI":"10.1137\/120863927","volume":"34","author":"J Tryoen","year":"2012","unstructured":"Tryoen, J., Le Ma\u00eetre, O., Ern, A.: Adaptive anisotropic spectral stochastic methods for uncertain scalar conservation laws. SIAM J. Sci. Comput. 34(5), A2459\u2013A2481 (2012). \nhttps:\/\/doi.org\/10.1137\/120863927","journal-title":"SIAM J. Sci. Comput."},{"issue":"18","key":"1069_CR20","doi-asserted-by":"publisher","first-page":"6485","DOI":"10.1016\/j.jcp.2010.05.007","volume":"229","author":"J Tryoen","year":"2010","unstructured":"Tryoen, J., Le Ma\u00eetre, O., Ndjinga, M., Ern, A.: Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems. J. Comput. Phys. 229(18), 6485\u20136511 (2010). \nhttps:\/\/doi.org\/10.1016\/j.jcp.2010.05.007","journal-title":"J. Comput. Phys."},{"issue":"3","key":"1069_CR21","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1137\/050627630","volume":"28","author":"X Wan","year":"2006","unstructured":"Wan, X., Karniadakis, G.: Multi-element generalized polynomial chaos for arbitrary probability measures. SIAM J. Sci. Comput. 28(3), 901\u2013928 (2006)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"1069_CR22","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1007\/s10915-015-0153-x","volume":"68","author":"J Winokur","year":"2016","unstructured":"Winokur, J., Kim, D., Bisetti, F., Le Ma\u00eetre, O., Knio, O.M.: Sparse pseudo spectral projection methods with directional adaptation for uncertainty quantification. J. Sci. Comput. 68(2), 596\u2013623 (2016). \nhttps:\/\/doi.org\/10.1007\/s10915-015-0153-x","journal-title":"J. Sci. Comput."},{"issue":"12","key":"1069_CR23","doi-asserted-by":"publisher","first-page":"2114","DOI":"10.1002\/nme.1152","volume":"61","author":"D Xiu","year":"2004","unstructured":"Xiu, D., Karniadakis, G.: Supersensitivity due to uncertain boundary conditions. Int. J. Numer. Methods Eng. 61(12), 2114\u20132138 (2004)","journal-title":"Int. J. Numer. Methods Eng."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-019-01069-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-019-01069-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-019-01069-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,20]],"date-time":"2020-10-20T23:08:24Z","timestamp":1603235304000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-019-01069-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,22]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["1069"],"URL":"https:\/\/doi.org\/10.1007\/s10915-019-01069-z","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2019,10,22]]},"assertion":[{"value":"27 September 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}