Volume 27, Issue 3
Constraint Energy Minimizing Generalized Multiscale Finite Element Method for High-Contrast Linear Elasticity Problem

Shubin Fu & Eric T. Chung

Commun. Comput. Phys., 27 (2020), pp. 809-827.

Published online: 2020-02

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  • Abstract

In this paper,weconsider the offline and online Constraint EnergyMinimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for high-contrast linear elasticity problem. Offline basis construction starts with an auxiliary multiscale space by solving local spectral problems. We select eigenfunctions that correspond to a few small eigenvalues to form the auxiliary space. Using the auxiliary space, we solve a constraint energy minimization problem to construct offline multiscale spaces. The minimization problem is defined in the oversampling domain, which is larger than the target coarse block. To get a good approximation space, the oversampling domain should be large enough. We also propose a relaxed minimization problem to construct multiscale basis functions, which will yield more accurate and robust solution. To take into account the influence of input parameters, such as source terms, we propose the construction of online multiscale basis and an adaptiveenrichment algorithm. We pro-vide extensive numerical experiments on 2D and 3D models to show the performance of the proposed method.

  • Keywords

Multiscale, elasticity, finite elements.

  • AMS Subject Headings

65M99, 74B05, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

shubinfu89@gmail. com (Shubin Fu)

eric .t. chung@gmail. com ( Eric T. Chung)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-809, author = {Fu , Shubin and Chung , Eric T. }, title = {Constraint Energy Minimizing Generalized Multiscale Finite Element Method for High-Contrast Linear Elasticity Problem}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {3}, pages = {809--827}, abstract = {

In this paper,weconsider the offline and online Constraint EnergyMinimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for high-contrast linear elasticity problem. Offline basis construction starts with an auxiliary multiscale space by solving local spectral problems. We select eigenfunctions that correspond to a few small eigenvalues to form the auxiliary space. Using the auxiliary space, we solve a constraint energy minimization problem to construct offline multiscale spaces. The minimization problem is defined in the oversampling domain, which is larger than the target coarse block. To get a good approximation space, the oversampling domain should be large enough. We also propose a relaxed minimization problem to construct multiscale basis functions, which will yield more accurate and robust solution. To take into account the influence of input parameters, such as source terms, we propose the construction of online multiscale basis and an adaptiveenrichment algorithm. We pro-vide extensive numerical experiments on 2D and 3D models to show the performance of the proposed method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0234}, url = {http://global-sci.org/intro/article_detail/cicp/13924.html} }
TY - JOUR T1 - Constraint Energy Minimizing Generalized Multiscale Finite Element Method for High-Contrast Linear Elasticity Problem AU - Fu , Shubin AU - Chung , Eric T. JO - Communications in Computational Physics VL - 3 SP - 809 EP - 827 PY - 2020 DA - 2020/02 SN - 27 DO - http://dor.org/10.4208/cicp.OA-2018-0234 UR - https://global-sci.org/intro/cicp/13924.html KW - Multiscale, elasticity, finite elements. AB -

In this paper,weconsider the offline and online Constraint EnergyMinimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for high-contrast linear elasticity problem. Offline basis construction starts with an auxiliary multiscale space by solving local spectral problems. We select eigenfunctions that correspond to a few small eigenvalues to form the auxiliary space. Using the auxiliary space, we solve a constraint energy minimization problem to construct offline multiscale spaces. The minimization problem is defined in the oversampling domain, which is larger than the target coarse block. To get a good approximation space, the oversampling domain should be large enough. We also propose a relaxed minimization problem to construct multiscale basis functions, which will yield more accurate and robust solution. To take into account the influence of input parameters, such as source terms, we propose the construction of online multiscale basis and an adaptiveenrichment algorithm. We pro-vide extensive numerical experiments on 2D and 3D models to show the performance of the proposed method.

Shubin Fu & Eric T. Chung. (2020). Constraint Energy Minimizing Generalized Multiscale Finite Element Method for High-Contrast Linear Elasticity Problem. Communications in Computational Physics. 27 (3). 809-827. doi:10.4208/cicp.OA-2018-0234
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