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国际多尺度计算工程期刊

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ISSN 打印: 1543-1649

ISSN 在线: 1940-4352

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.4 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.3 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 2.2 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.00034 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.46 SJR: 0.333 SNIP: 0.606 CiteScore™:: 3.1 H-Index: 31

Indexed in

BAYESIAN MULTISCALE FINITE ELEMENT METHODS. MODELING MISSING SUBGRID INFORMATION PROBABILISTICALLY

卷 15, 册 2, 2017, pp. 175-197
DOI: 10.1615/IntJMultCompEng.2017019851
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摘要

In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models cannot resolve all scales. Various subgrid models are proposed to represent unresolved scales. Here, we consider a probabilistic approach for modeling unresolved scales using the multiscale finite element method [cf., Chkrebtii et al., Bayesian Anal., vol. 11, no. 4, pp. 1239-1267, 2016; Mallick et al., Bayesian Anal., vol. 11, no. 4, p. 1279, 2016]. By representing dominant modes using the generalized multiscale finite element, we propose a Bayesian framework, which provides multiple inexpensive (computable) solutions for a deterministic problem. These approximate probabilistic solutions may not be very close to the exact solutions and, thus, many realizations are needed. In this way, we obtain a rigorous probabilistic description of approximate solutions. In the paper, we consider parabolic and wave equations in heterogeneous media. In each time interval, the domain is divided into subregions. Using residual information, we design appropriate prior and posterior distributions. The likelihood consists of the residual minimization. To sample from the resulting posterior distribution, we consider several sampling strategies. The sampling involves identifying important regions and important degrees of freedom beyond permanent basis functions, which are used in residual computation. Numerical results are presented. We consider two sampling algorithms. The first algorithm uses sequential sampling and is inexpensive. In the second algorithm, we perform full sampling using the Gibbs sampling algorithm, which is more accurate compared to the sequential sampling. The main novel ingredients of our approach consist of: defining appropriate permanent basis functions and the corresponding residual; setting up a proper posterior distribution; and sampling the posteriors.

对本文的引用
  1. Cheung Siu Wun, Guha Nilabja, Dynamic data-driven Bayesian GMsFEM, Journal of Computational and Applied Mathematics, 353, 2019. Crossref

  2. Wang Min, Cheung Siu Wun, Chung Eric T., Efendiev Yalchin, Leung Wing Tat, Wang Yating, Prediction of Discretization of GMsFEM Using Deep Learning, Mathematics, 7, 5, 2019. Crossref

  3. Cheung Siu Wun, Chung Eric T., Leung Wing Tat, Constraint energy minimizing generalized multiscale discontinuous Galerkin method, Journal of Computational and Applied Mathematics, 380, 2020. Crossref

  4. Cheung Siu Wun, Chung Eric T., Efendiev Yalchin, Leung Wing Tat, Explicit and Energy-Conserving Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method for Wave Propagation in Heterogeneous Media, Multiscale Modeling & Simulation, 19, 4, 2021. Crossref

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