On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers

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A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials (2017, methodology): “multi-grid methods [50], quasi-continuum methods [45], wavelet-based methods, generalized finite element method [51].”
Homogenization and two‐scale simulations of granular materials for different microstructural constraints (2010, unknown): “Following conceptually the recent work Miehe and Bayreuther [34], we outline a unified implementation of the boundary constraints by penalty methods.”
Multi‐scale computational homogenization–localization for propagating discontinuities using X‐FEM (2015, background): “Among classical boundary conditions (Taylor, linear displacement BCs, periodic BCs, and traction BCs), periodic boundary conditions are frequently used in microstructural simulations as they generally yield sufficiently accurate results for smaller model sizes [49, 50].”
Extended multiscale finite element method for mechanical analysis of heterogeneous materials (2010, methodology): “These methods contain the asymptotic computational homogenization method [8–17], the multilevel finite element method (FE2) [18,19], the heterogeneous multiscale method (HMM) [20,21], the Voronoi cell method [22,23] and the RVE (representative volume element) method [24–27] et al.”