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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

REITERATED MULTISCALE MODEL REDUCTION USING THE GENERALIZED MULTISCALE FINITE ELEMENT METHOD

卷 14, 册 6, 2016, pp. 535-554
DOI: 10.1615/IntJMultCompEng.2016017697
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摘要

Numerical homogenization and multiscale finite element methods construct effective properties on a coarse grid by solving local problems and extracting the average effective properties from these local solutions. In some cases, the solutions of local problems can be expensive to compute due to scale disparity. In this setting, one can basically apply a homogenization or multiscale method reiteratively to solve for the local problems. This process is known as reiterated homogenization and has many variations in the numerical context. Though the process seems to be a straightforward extension of two-level process, it requires some careful implementation and the concept development for problems without scale separation and high contrast. In this paper, we consider the generalized multiscale finite element method (GMsFEM) and apply it iteratively to construct its multiscale basis functions. The main idea of the GMsFEM is to construct snapshot functions and then extract multiscale basis functions (called offline space) using local spectral decompositions in the snapshot spaces. The extension of this construction to several levels uses snapshots and offline spaces interchangeably to achieve this goal. At each coarse-grid scale, we assume that the offline space is a good approximation of the solution and use all possible offline functions or randomization as boundary conditions and solve the local problems in the offline space at the previous (finer) level, to construct snapshot space. We present an adaptivity strategy and show numerical results for flows in heterogeneous media and in perforated domains.

对本文的引用
  1. Chung Eric, Efendiev Yalchin, Hou Thomas Y., Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods, Journal of Computational Physics, 320, 2016. Crossref

  2. Spiridonov Denis, Vasilyeva Maria, Leung Wing Tat, A Generalized Multiscale Finite Element Method (GMsFEM) for perforated domain flows with Robin boundary conditions, Journal of Computational and Applied Mathematics, 357, 2019. Crossref

  3. Yang Zhiqiang, Sun Yi, Cui Junzhi, Ma Qiang, A high-order three-scale reduced homogenization for nonlinear heterogeneous materials with multiple configurations, Journal of Computational Physics, 425, 2021. Crossref

  4. Chen Ke, Li Qin, Lu Jianfeng, Wright Stephen J., A Low-Rank Schwarz Method for Radiative Transfer Equation With Heterogeneous Scattering Coefficient, Multiscale Modeling & Simulation, 19, 2, 2021. Crossref

  5. Dong Hao, Yang Zihao, Guan Xiaofei, Cui Junzhi, Stochastic higher-order three-scale strength prediction model for composite structures with micromechanical analysis, Journal of Computational Physics, 465, 2022. Crossref

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