CEM-GMsFEM for Poisson equations in heterogeneous perforated domains
CoRR(2024)
摘要
In this paper, we propose a novel multiscale model reduction strategy
tailored to address the Poisson equation within heterogeneous perforated
domains. The numerical simulation of this intricate problem is impeded by its
multiscale characteristics, necessitating an exceptionally fine mesh to
adequately capture all relevant details. To overcome the challenges inherent in
the multiscale nature of the perforations, we introduce a coarse space
constructed using the Constraint Energy Minimizing Generalized Multiscale
Finite Element Method (CEM-GMsFEM). This involves constructing basis functions
through a sequence of local energy minimization problems over eigenspaces
containing localized information pertaining to the heterogeneities. Through our
analysis, we demonstrate that the oversampling layers depend on the local
eigenvalues, thereby implicating the local geometry as well. Additionally, we
provide numerical examples to illustrate the efficacy of the proposed scheme.
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