{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T11:33:24Z","timestamp":1774870404096,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"crossref","award":["14-11-00083"],"award-info":[{"award-number":["14-11-00083"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A generalization of a polynomial chaos-based algorithm for solving PDEs with random input data\nis suggested. The input random field is assumed to be defined by its mean and correlation function.\nThe method uses the Karhunen\u2013Lo\u00e8ve expansion, in its analytical form, for the input random field.\nPotentially, however, if desired, the\nKarhunen\u2013Lo\u00e8ve expansion can be also constructed by a randomized singular value decomposition of the correlation function recently\nsuggested in our paper [Math. Comput. Simulation 82 (2011), 295\u2013317].\nThe polynomial chaos expansion is then constructed by\nresolving a probabilistic collocation-based system of linear equations. The method is compared against a direct Monte Carlo\nmethod which solves repeatedly many times the PDE for a set of samples of the input random field.\nAlong with the commonly used statistical characteristics like the mean and variance of the solution,\nwe were able to calculate more sophisticated functionals like the instant velocity samples and the mean\nfor Eulerian and Lagrangian velocity fields.<\/jats:p>","DOI":"10.1515\/mcma-2014-0006","type":"journal-article","created":{"date-parts":[[2014,10,29]],"date-time":"2014-10-29T13:59:06Z","timestamp":1414591146000},"page":"279-289","source":"Crossref","is-referenced-by-count":4,"title":["Stochastic polynomial chaos based algorithm for solving PDEs with random coefficients"],"prefix":"10.1515","volume":"20","author":[{"given":"Irina A.","family":"Shalimova","sequence":"first","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics, Russian Acad.Sci, 630090, Novosibirsk, Lavrentieve Str. 6, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karl K.","family":"Sabelfeld","sequence":"additional","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics, Russian Acad.Sci, 630090, Novosibirsk, Lavrentieve Str. 6, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2014,10,29]]},"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2014-0006\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2014-0006\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T22:35:52Z","timestamp":1680388552000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2014-0006\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,29]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,9,13]]},"published-print":{"date-parts":[[2014,12,1]]}},"alternative-id":["10.1515\/mcma-2014-0006"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2014-0006","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,29]]}}}