Iterative multiscale finite-volume method

Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids

“…In this paper, we investigate the accuracy, efficiency and robustness of different multiscale control volume approximations when applied to heterogeneous problems on irregular grids. Our study shows that the reduced boundary condition, commonly applied with the MSFV methods [10,16,20], is not robust with respect to perturbations on the fine-scale grid. Even for regular Cartesian fine grids and isotropic permeability tensor, the spatial variability in the fine-scale permeability may produce anisotropies on the coarse scale.…”

“…for changing global boundary conditions. A third approach is to improve the accuracy by means of local iterations on the domain interfaces [16,28]. We will consider the latter approach.…”

Additive Schwarz preconditioner for the finite volume element discretization of symmetric elliptic problems

“…For problems with inclusions and channels both inside and across subdomains, it may be enough to replace the coarse space with the so called multiscale coarse space, cf. [18,19,27], or in extreme cases to enrich it with eigenfunctions corresponding to bad eigen modes of some local eigenvalue problems, cf. [14,21,31].…”

“…using oscillatory boundary conditions instead of the linear boundary conditions for the basis functions, cf. [18,19,27], or by enriching the coarse space with eigenfunctions from local eigenvalue problems, cf. [10,14,21,31], it will be possible to extend the methods to effectively deal with highly heterogeneous coefficients.…”

The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB)

“…As such, one can achieve systematic strategies for reducing the error through iterative procedures that combine the multiscale solver with a finescale smoother [23][24][25][26]. Iterative multiscale methods are scalable and deliver massconservative solutions after any MSFV stage.…”