Upscaling method for problems in perforated domains with non-homogeneous boundary conditions on perforations using Non-Local Multi-Continuum method (NLMC)
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AbstractIn 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.
All Author(s) ListMaria Vasilyeva, Eric T. Chung, Wing Tat Leung, Yating Wang, Denis Spiridonov
Journal nameJournal of Computational and Applied Mathematics
Year2019
Month9
Volume Number357
Pages215 - 227
ISSN0377-0427
eISSN1879-1778
LanguagesEnglish-United States

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