{"title":"Localized Orthogonal Decomposition for a Multiscale Parabolic Stochastic Partial Differential Equation","authors":"Annika Lang, Per Ljung, Axel Målqvist","doi":"10.1137/23m1569216","DOIUrl":null,"url":null,"abstract":"Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 204-229, March 2024. <br/> Abstract. A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localized orthogonal decomposition (LOD) method and computes a coarse-scale representation of the elliptic operator, enriched by fine-scale information on the diffusion. Optimal order strong convergence is derived. The LOD technique is combined with a (multilevel) Monte Carlo estimator and the weak error is analyzed. Numerical examples that confirm the theoretical findings are provided, and the computational efficiency of the method is highlighted.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"20 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Multiscale Modeling and Simulation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/23m1569216","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 204-229, March 2024. Abstract. A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localized orthogonal decomposition (LOD) method and computes a coarse-scale representation of the elliptic operator, enriched by fine-scale information on the diffusion. Optimal order strong convergence is derived. The LOD technique is combined with a (multilevel) Monte Carlo estimator and the weak error is analyzed. Numerical examples that confirm the theoretical findings are provided, and the computational efficiency of the method is highlighted.
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