{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T02:45:09Z","timestamp":1719888309745},"reference-count":35,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T00:00:00Z","timestamp":1538352000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"content-version":"am","delay-in-days":256,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"funder":[{"DOI":"10.13039\/100006754","name":"Army Research Laboratory","doi-asserted-by":"publisher","award":["W911NF-12-2-0023","W911NF-12-2-0022"],"id":[{"id":"10.13039\/100006754","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Physics"],"published-print":{"date-parts":[[2018,10]]},"DOI":"10.1016\/j.jcp.2018.06.003","type":"journal-article","created":{"date-parts":[[2018,6,5]],"date-time":"2018-06-05T17:48:49Z","timestamp":1528220929000},"page":"732-750","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":25,"special_numbering":"C","title":["Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis"],"prefix":"10.1016","volume":"371","author":[{"given":"Anindya","family":"Bhaduri","sequence":"first","affiliation":[]},{"given":"Yanyan","family":"He","sequence":"additional","affiliation":[]},{"given":"Michael D.","family":"Shields","sequence":"additional","affiliation":[]},{"given":"Lori","family":"Graham-Brady","sequence":"additional","affiliation":[]},{"given":"Robert M.","family":"Kirby","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"4","key":"10.1016\/j.jcp.2018.06.003_br0010","doi-asserted-by":"crossref","first-page":"897","DOI":"10.2307\/2371268","article-title":"The homogeneous chaos","volume":"60","author":"Wiener","year":"1938","journal-title":"Am. J. Math."},{"key":"10.1016\/j.jcp.2018.06.003_br0020","series-title":"Stochastic Finite Elements: A Spectral Approach","author":"Ghanem","year":"2003"},{"issue":"2","key":"10.1016\/j.jcp.2018.06.003_br0030","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1137\/S1064827501387826","article-title":"The Wiener\u2013Askey polynomial chaos for stochastic differential equations","volume":"24","author":"Xiu","year":"2002","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"10.1016\/j.jcp.2018.06.003_br0040","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/S0021-9991(03)00092-5","article-title":"Modeling uncertainty in flow simulations via generalized polynomial chaos","volume":"187","author":"Xiu","year":"2003","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2018.06.003_br0050","article-title":"Some Basic Hypergeometric Polynomials that Generalize Jacobi Polynomials","volume":"vol. 319","author":"Askey","year":"1985"},{"key":"10.1016\/j.jcp.2018.06.003_br0060","series-title":"44th AIAA Aerospace Sciences Meeting and Exhibit","first-page":"896","article-title":"Modeling arbitrary uncertainties using Gram\u2013Schmidt polynomial chaos","author":"Witteveen","year":"2006"},{"issue":"1","key":"10.1016\/j.jcp.2018.06.003_br0070","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/s10915-005-9038-8","article-title":"Beyond Wiener\u2013Askey expansions: handling arbitrary PDFs","volume":"27","author":"Wan","year":"2006","journal-title":"J. Sci. Comput."},{"issue":"2","key":"10.1016\/j.jcp.2018.06.003_br0080","first-page":"293","article-title":"Efficient collocational approach for parametric uncertainty analysis","volume":"2","author":"Xiu","year":"2007","journal-title":"Commun. Comput. Phys."},{"issue":"3","key":"10.1016\/j.jcp.2018.06.003_br0090","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1137\/050645142","article-title":"A stochastic collocation method for elliptic partial differential equations with random input data","volume":"45","author":"Babu\u0161ka","year":"2007","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"10.1016\/j.jcp.2018.06.003_br0100","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0377-0427(02)00517-4","article-title":"Advances in multidimensional integration","volume":"149","author":"Cools","year":"2002","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.jcp.2018.06.003_br0110","first-page":"240","article-title":"Quadrature and interpolation formulas for tensor products of certain classes of functions","volume":"4","author":"Smolyak","year":"1963","journal-title":"Sov. Math. Dokl."},{"key":"10.1016\/j.jcp.2018.06.003_br0120","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1017\/S0962492904000182","article-title":"Sparse grids","volume":"13","author":"Bungartz","year":"2004","journal-title":"Acta Numer."},{"issue":"3","key":"10.1016\/j.jcp.2018.06.003_br0130","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1137\/040615201","article-title":"High-order collocation methods for differential equations with random inputs","volume":"27","author":"Xiu","year":"2005","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"10.1016\/j.jcp.2018.06.003_br0140","doi-asserted-by":"crossref","first-page":"2309","DOI":"10.1137\/060663660","article-title":"A sparse grid stochastic collocation method for partial differential equations with random input data","volume":"46","author":"Nobile","year":"2008","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"10.1016\/j.jcp.2018.06.003_br0150","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/j.jcp.2005.03.023","article-title":"An adaptive multi-element generalized polynomial chaos method for stochastic differential equations","volume":"209","author":"Wan","year":"2005","journal-title":"J. Comput. Phys."},{"issue":"22","key":"10.1016\/j.jcp.2018.06.003_br0160","doi-asserted-by":"crossref","first-page":"9572","DOI":"10.1016\/j.jcp.2008.07.009","article-title":"The multi-element probabilistic collocation method (ME-PCM): error analysis and applications","volume":"227","author":"Foo","year":"2008","journal-title":"J. Comput. Phys."},{"issue":"5","key":"10.1016\/j.jcp.2018.06.003_br0170","doi-asserted-by":"crossref","first-page":"1536","DOI":"10.1016\/j.jcp.2009.10.043","article-title":"Multi-element probabilistic collocation method in high dimensions","volume":"229","author":"Foo","year":"2010","journal-title":"J. Comput. Phys."},{"issue":"2","key":"10.1016\/j.jcp.2018.06.003_br0180","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/S0951-8320(02)00229-6","article-title":"Theorems and examples on high dimensional model representation","volume":"79","author":"Sobol","year":"2003","journal-title":"Reliab. Eng. Syst. Saf."},{"issue":"1\u20132","key":"10.1016\/j.jcp.2018.06.003_br0190","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/S0010-4655(98)00152-0","article-title":"Efficient input-output model representations","volume":"117","author":"Rabitz","year":"1999","journal-title":"Comput. Phys. Commun."},{"issue":"7","key":"10.1016\/j.jcp.2018.06.003_br0200","doi-asserted-by":"crossref","first-page":"2676","DOI":"10.1016\/j.jcp.2009.01.001","article-title":"Discontinuity detection in multivariate space for stochastic simulations","volume":"228","author":"Archibald","year":"2009","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2018.06.003_br0210","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1016\/j.jcp.2013.02.035","article-title":"Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions","volume":"242","author":"Jakeman","year":"2013","journal-title":"J. Comput. Phys."},{"issue":"6","key":"10.1016\/j.jcp.2018.06.003_br0220","doi-asserted-by":"crossref","first-page":"A2584","DOI":"10.1137\/140953137","article-title":"Efficient localization of discontinuities in complex computational simulations","volume":"36","author":"Gorodetsky","year":"2014","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"10.1016\/j.jcp.2018.06.003_br0230","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.jcp.2003.11.033","article-title":"Uncertainty propagation using Wiener\u2013Haar expansions","volume":"197","author":"Le Ma\u0131tre","year":"2004","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2018.06.003_br0240","unstructured":"L. Mathelin, M.Y. Hussaini, T.A. Zang, A stochastic collocation algorithm for uncertainty analysis."},{"issue":"4","key":"10.1016\/j.jcp.2018.06.003_br0250","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1145\/1114268.1114275","article-title":"Algorithm 847: spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB","volume":"31","author":"Klimke","year":"2005","journal-title":"ACM Trans. Math. Softw."},{"issue":"8","key":"10.1016\/j.jcp.2018.06.003_br0260","doi-asserted-by":"crossref","first-page":"3084","DOI":"10.1016\/j.jcp.2009.01.006","article-title":"An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations","volume":"228","author":"Ma","year":"2009","journal-title":"J. Comput. Phys."},{"issue":"10","key":"10.1016\/j.jcp.2018.06.003_br0270","doi-asserted-by":"crossref","first-page":"3884","DOI":"10.1016\/j.jcp.2010.01.033","article-title":"An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations","volume":"229","author":"Ma","year":"2010","journal-title":"J. Comput. Phys."},{"issue":"6","key":"10.1016\/j.jcp.2018.06.003_br0280","doi-asserted-by":"crossref","first-page":"A2488","DOI":"10.1137\/140997385","article-title":"An efficient method for uncertainty propagation using fuzzy sets","volume":"37","author":"Chen","year":"2015","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.jcp.2018.06.003_br0290","series-title":"Numerical Methods for Stochastic Computations: A Spectral Method Approach","author":"Xiu","year":"2010"},{"issue":"2\u20133","key":"10.1016\/j.jcp.2018.06.003_br0300","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1023\/A:1019188517934","article-title":"General foundations of high-dimensional model representations","volume":"25","author":"Rabitz","year":"1999","journal-title":"J. Math. Chem."},{"issue":"1","key":"10.1016\/j.jcp.2018.06.003_br0310","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1013172329778","article-title":"High dimensional model representations generated from low dimensional data samples, I: mp-Cut-HDMR","volume":"30","author":"Li","year":"2001","journal-title":"J. Math. Chem."},{"issue":"33","key":"10.1016\/j.jcp.2018.06.003_br0320","doi-asserted-by":"crossref","first-page":"7765","DOI":"10.1021\/jp010450t","article-title":"High dimensional model representations","volume":"105","author":"Li","year":"2001","journal-title":"J. Phys. Chem. A"},{"issue":"12","key":"10.1016\/j.jcp.2018.06.003_br0330","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.1002\/nme.1135","article-title":"A generalized dimension-reduction method for multidimensional integration in stochastic mechanics","volume":"61","author":"Xu","year":"2004","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"5","key":"10.1016\/j.jcp.2018.06.003_br0340","doi-asserted-by":"crossref","DOI":"10.1115\/1.4001597","article-title":"Metamodeling for high dimensional simulation-based design problems","volume":"132","author":"Shan","year":"2010","journal-title":"J. Mech. Des."},{"issue":"20","key":"10.1016\/j.jcp.2018.06.003_br0350","doi-asserted-by":"crossref","first-page":"7662","DOI":"10.1016\/j.jcp.2009.07.014","article-title":"A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties","volume":"228","author":"Agarwal","year":"2009","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Computational Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999118303814?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999118303814?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2021,4,11]],"date-time":"2021-04-11T01:53:54Z","timestamp":1618106034000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0021999118303814"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10]]},"references-count":35,"alternative-id":["S0021999118303814"],"URL":"https:\/\/doi.org\/10.1016\/j.jcp.2018.06.003","relation":{},"ISSN":["0021-9991"],"issn-type":[{"value":"0021-9991","type":"print"}],"subject":[],"published":{"date-parts":[[2018,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational Physics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jcp.2018.06.003","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2018 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}]}}