{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:41:58Z","timestamp":1787330518872,"version":"build-2736575974"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-AC52-07NA27344"],"award-info":[{"award-number":["DE-AC52-07NA27344"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Lo\u00e8ve (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving a mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.<\/jats:p>","DOI":"10.1137\/16m1082688","type":"journal-article","created":{"date-parts":[[2017,10,26]],"date-time":"2017-10-26T16:24:40Z","timestamp":1509035080000},"page":"S543-S562","source":"Crossref","is-referenced-by-count":22,"title":["A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields"],"prefix":"10.1137","volume":"39","author":[{"given":"Sarah","family":"Osborn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Panayot S.","family":"Vassilevski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Umberto","family":"Villa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,10,26]]},"reference":[{"key":"atypb5","volume-title":"Norsk","author":"Abrahamsen P.","year":"1997"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492906210018"},{"key":"atypb7","first-page":"281","volume":"47","author":"Arnold D. N.","year":"2010","journal-title":"S.)"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.75.066701"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36519-5"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOAS383"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/12089586X"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/100800531"},{"key":"atypb13","volume-title":"Modern Spatiotemporal Geostatistics","author":"Christakos G.","year":"2012"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-011-0160-x"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1002\/9781119115151"},{"key":"atypb17","volume-title":"Mixed and Hybrid Finite Element Methods","author":"Fortin M.","year":"1991"},{"key":"atypb18","volume-title":"Stochastic Subsurface Hyrdology","author":"Gelhar L. W.","year":"1993"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1070.0496"},{"key":"atypb20","volume-title":"Scheduling Massively Parallel Multigrid for Multilevel Monte Carlo Methods, preprint, arXiv:1607.03252","author":"Gmeiner B.","year":"2016"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-5851-3"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595287997"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8655(83)90025-9"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1137\/110859361"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1515\/cmam-2014-0004"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1819"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v063.i19"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2011.00777.x"},{"key":"atypb29","first-page":"0","volume":"46","author":"Lo\u00e9ve M.","year":"1978","journal-title":"Grad. Texts Math."},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1002\/nla.716"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-7892-5"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599355153"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1137\/070698178"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00720-X"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2026"},{"key":"atypb36","volume-title":"Comput. Sci. Eng. 12","author":"Smith R. C.","year":"2013"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492910000061"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/41.3-4.434"},{"key":"atypb39","first-page":"974","volume":"40","author":"Whittle P.","year":"1963","journal-title":"Bull. Int. Stat. Inst."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1082688","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:10:23Z","timestamp":1787328623000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1082688"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":34,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1082688"],"URL":"https:\/\/doi.org\/10.1137\/16m1082688","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}