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Title: Application of the generalized multiscale finite element method in parameter-dependent PDE simulations with a variable-separation technique

Authors:
; ;
Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1358862
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 300; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-10-03 22:02:17; Journal ID: ISSN 0377-0427
Publisher:
Elsevier
Country of Publication:
Belgium
Language:
English

Citation Formats

Gao, Longfei, Tan, Xiaosi, and Chung, Eric T. Application of the generalized multiscale finite element method in parameter-dependent PDE simulations with a variable-separation technique. Belgium: N. p., 2016. Web. doi:10.1016/j.cam.2015.12.031.
Gao, Longfei, Tan, Xiaosi, & Chung, Eric T. Application of the generalized multiscale finite element method in parameter-dependent PDE simulations with a variable-separation technique. Belgium. doi:10.1016/j.cam.2015.12.031.
Gao, Longfei, Tan, Xiaosi, and Chung, Eric T. 2016. "Application of the generalized multiscale finite element method in parameter-dependent PDE simulations with a variable-separation technique". Belgium. doi:10.1016/j.cam.2015.12.031.
@article{osti_1358862,
title = {Application of the generalized multiscale finite element method in parameter-dependent PDE simulations with a variable-separation technique},
author = {Gao, Longfei and Tan, Xiaosi and Chung, Eric T.},
abstractNote = {},
doi = {10.1016/j.cam.2015.12.031},
journal = {Journal of Computational and Applied Mathematics},
number = C,
volume = 300,
place = {Belgium},
year = 2016,
month = 7
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.cam.2015.12.031

Citation Metrics:
Cited by: 2works
Citation information provided by
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  • It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less
  • Cited by 6
  • In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.