{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:16:42Z","timestamp":1787329002360,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1319054"],"award-info":[{"award-number":["DMS-1319054"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We present a new multiorder Monte Carlo algorithm for computing the statistics of stochastic quantities of interest described by linear hyperbolic problems with stochastic parameters. The method is a nonintrusive technique based on a recently proposed high-order energy-based discontinuous Galerkin method for the second-order acoustic and elastic wave equations. The algorithm is built upon a hierarchy of degrees of polynomial basis functions rather than a mesh hierarchy used in multilevel Monte Carlo. Through complexity theorems and numerical experiments, we show that the proposed multiorder method is a valid alternative to the current multilevel Monte Carlo method for hyperbolic problems. Moreover, in addition to the convenience of working with a fixed mesh, which is desirable in many real applications with complex geometries, the multiorder method is particularly beneficial in reducing errors due to numerical dispersion in long-distance propagation of waves. The numerical examples verify that the multiorder approach is faster than the mesh-based multilevel approach for waves that traverse long distances.<\/jats:p>","DOI":"10.1137\/16m1086388","type":"journal-article","created":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T12:07:02Z","timestamp":1517486822000},"page":"448-468","source":"Crossref","is-referenced-by-count":9,"title":["A MultiOrder Discontinuous Galerkin Monte Carlo Method for Hyperbolic Problems with Stochastic Parameters"],"prefix":"10.1137","volume":"56","author":[{"given":"Mohammad","family":"Motamed","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Appel\u00f6","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,2,1]]},"reference":[{"key":"atypb1","volume-title":"dg-DATH: Discontinuous Galerkin Solver by Daniel Appelo & Thomas Hagstrom for the Elastic Wave Equation, https:\/\/bitbucket.org\/appelo\/dg_dath_elastic_v1.0","author":"Appel\u00f6 D.","year":"2015"},{"key":"atypb2","volume-title":"Comput. 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