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International Journal for Multiscale Computational Engineering

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ISSN Druckformat: 1543-1649

ISSN Online: 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

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SPACE-TIME NONLINEAR UPSCALING FRAMEWORK USING NONLOCAL MULTICONTINUUM APPROACH

Volumen 17, Ausgabe 5, 2019, pp. 529-550
DOI: 10.1615/IntJMultCompEng.2019031829
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ABSTRAKT

In this paper, we develop a space-time upscaling framework that can be used for many challenging porous media applications without scale separation and high contrast. Our main focus is on nonlinear differential equations with multiscale coefficients. The framework is built on a nonlinear nonlocal multicontinuum upscaling concept and significantly extends the results of earlier work. Our approach starts with a coarse space-time partition and identifies test functions for each partition, which play the role of multicontinua. The test functions are defined via optimization and play a crucial role in nonlinear upscaling. In the second stage, we solve nonlinear local problems in oversampled regions with some constraints defined via test functions. These local solutions define a nonlinear map from macroscopic variables determined with the help of test functions to the fine-grid fields. This map can be thought as a downscaled map from macroscopic variables to the fine-grid solution. In the final stage, we seek macroscopic variables in the entire domain such that the downscaled field solves the global problem in a weak sense defined using the test functions. We present an analysis of our approach for an example nonlinear problem. Our unified framework plays an important role in designing various upscaled methods. Because local problems are directly related to the fine-grid problems, it simplifies the process of finding local solutions with appropriate constraints. Using machine learning (ML), we identify the complex map from macroscopic variablesto fine-grid solution. We present numerical results for several porous media applications, including two-phase flow and transport.

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REFERENZIERT VON
  1. Fu Shubin, Chung Eric, Mai Tina, Constraint energy minimizing generalized multiscale finite element method for nonlinear poroelasticity and elasticity, Journal of Computational Physics, 417, 2020. Crossref

  2. Park Jun Sur Richard, Cheung Siu Wun, Mai Tina, Multiscale simulations for multi-continuum Richards equations, Journal of Computational and Applied Mathematics, 397, 2021. Crossref

  3. Efendiev Yalchin, Leung Wing Tat, Multicontinuum homogenization and its relation to nonlocal multicontinuum theories, Journal of Computational Physics, 474, 2023. Crossref

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