Generalized Multiscale Finite Element Method for scattering problem in heterogeneous media

Kalachikova, Uygulaana; Vasilyeva, Maria; Harris, Isaac; Chung, Eric T.

doi:10.1016/j.cam.2022.114977

Cited by 5 publications

(2 citation statements)

References 28 publications

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“…The construction of snapshot space involves solving the local problems from a set of parameter-dependent inputs. Being different from the standard multiscale finite element method solving the local problem (7), an eigenvalue computation is utilized in this generalized multiscale finite element method.…”

Section: Offline Stagementioning

confidence: 99%

“…In the research history, the multiscale finite element method (MsFEM) was first proposed by Hou and Chen in [1,2]. Then it evolved to a generalized multiscale version and had many applications in scientific fields, see [3][4][5][6][7]. For example, in [3] the generalized multiscale finite element (GMsFEM) approximated the solution space locally by employing the enriched multiscale basis functions.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Multiscale Finite Element Method and Balanced Truncation for Parameter-Dependent Parabolic Problems

Jiang,

Cheng,

Cheng

et al. 2023

Mathematics

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We propose a generalized multiscale finite element method combined with a balanced truncation to solve a parameter-dependent parabolic problem. As an updated version of the standard multiscale method, the generalized multiscale method contains the necessary eigenvalue computation, in which the enriched multiscale basis functions are picked up from a snapshot space on users’ demand. Based upon the generalized multiscale simulation on the coarse scale, the balanced truncation is applied to solve its Lyapunov equations on the reduced scale for further savings while ensuring high accuracy. A θ-implicit scheme is utilized for the fully discretization process. Finally, numerical results validate the uniform stability and robustness of our proposed method.

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Section: Offline Stagementioning

confidence: 99%