Upscaling method for problems in perforated domains with non-homogeneous boundary conditions on perforations using Non-Local Multi-Continuum method (NLMC)

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:357

Article

Vasilyeva, Maria^1,2  Chung, Eric T.³  Leung, Wing Tat⁴  Wang, Yating⁵  Spiridonov, Denis⁶ 

[1] Texas A&M Univ, Inst Sci Computat, College Stn, TX 77843 USA

[2] North Eastern Fed Univ, Dept Computat Technol, Yakutsk 677980, Republic Of Sak, Russia

[3] CUHK, Dept Math, Hong Kong, Peoples R China

[4] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA

[5] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[6] North Eastern Fed Univ, Yakutsk 677980, Republic Of Sak, Russia

关键词: Upscaling;    Non-local multicontinuum method;    Constrained energy minimization;    Perforated domain;    Non-homogeneous boundary condition;   

DOI  :  10.1016/j.cam.2019.02.030

来源: Elsevier

【 摘 要 】

In this paper, we present an upscaling method for problems in perforated domains with non-homogeneous boundary conditions on perforations. Our methodology is based on the recently developed Non-local multicontinuum method (NLMC). The main ingredient of the method is the construction of suitable local basis functions with the capability of capturing multiscale features and non-local effects. We will construct multiscale basis functions for the coarse regions and additional multiscale basis functions for perforations, with the aim of handling non-homogeneous boundary conditions on perforations. We start with describing our method for the Laplace equation, and then extending the framework for the elasticity problem and parabolic equations. The resulting upscaled model has minimal size and the solution has physical meaning on the coarse grid. We will present numerical results (1) for steady and unsteady problems, (2) for Laplace and Elastic operators, and (3) for Neumann and Robin non-homogeneous boundary conditions on perforations. Numerical results show that the proposed method can provide good accuracy and provide significant reduction on the degrees of freedoms. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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