{"title":"多尺度抛物线随机偏微分方程的局部正交分解","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":"{\"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}","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}
Localized Orthogonal Decomposition for a Multiscale Parabolic Stochastic Partial Differential Equation
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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