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We propose an efficient importance sampling scheme to compute the small failure probability in the high threshold limit. The change of measure in our scheme is parametrized by two density functions. The efficiency of the importance sampling scheme is validated by numerical examples.<\/jats:p>","DOI":"10.1137\/140965569","type":"journal-article","created":{"date-parts":[[2015,3,3]],"date-time":"2015-03-03T14:12:16Z","timestamp":1425391936000},"page":"A609-A624","source":"Crossref","is-referenced-by-count":8,"title":["Efficient Rare Event Simulation for Failure Problems in Random Media"],"prefix":"10.1137","volume":"37","author":[{"given":"Jingchen","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianfeng","family":"Lu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiang","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,3,3]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1214\/11-AAP792"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-69033-9"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/070709311"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0404096101"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1231340166"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2012.05.001"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s11134-007-9047-4"},{"key":"atypb8","volume-title":"Large Deviation Techniques in Decision, Simulation and Estimation","author":"Bucklew J.","year":"1990"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/100789373"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1080\/10451120410001733845"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.physchem.040808.090412"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOP571"},{"key":"atypb13","volume-title":"Quantitative results on the corrector equation in stochastic homogenization, preprint, arXiv:1409.0801","author":"Gloria A.","year":"2014"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2011.08.008"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOP639"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1214\/11-AOS960"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1214\/13-AAP960"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1370870124"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2013.v11.n2.a9"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1421763325"},{"key":"atypb21","first-page":"161","author":"Lucas C.","year":"2004","journal-title":"LA-PACK Working Note"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511613357"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/080722977"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-013-0517-9"},{"key":"atypb25","volume-title":"Reliability and Failure of Electronic Materials and Devices","author":"Ohring M.","year":"1998"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2013.08.016"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.04.011"},{"key":"atypb28","volume-title":"Probability of Failure in Hypersonic Engines Using Large Deviations, arXiv:1208.5029","author":"Papanicolaou G.","year":"2012"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4321-0"},{"key":"atypb30","volume-title":"Random Heterogeneous Materials: Microstructure and Macroscopic Properties","author":"Torquato S.","year":"2001"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1115\/1.4010337"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/140965569","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:34:00Z","timestamp":1787326440000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/140965569"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":31,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/140965569"],"URL":"https:\/\/doi.org\/10.1137\/140965569","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}