In this paper, we develop a multiscale numerical method based on the discontinuous Galerkin generalized multiscale finite element method (DG-GMsFEM) for solving linear elasticity problems in heterogeneous perforated domains with multicontinuum structure. Such media arise in the modeling of fractured rocks, composite materials, and biological tissues, where multiple interacting continua coexist at different spatial scales and are further complicated by geometric perforations. The proposed method constructs localized multiscale basis functions for displacement fields, allowing accurate and efficient approximation on coarse grids. A local spectral decomposition is used to select dominant modes in each coarse neighborhood, capturing fine-scale heterogeneities and the interactions between continua. We apply the method to benchmark problems with dual-continuum behavior and complex perforation geometries. Numerical results demonstrate that the DG-GMsFEM achieves high accuracy while significantly reducing computational cost compared to fine-scale discretizations.
В.Н. Алексеев (2026) studied this question.