In this paper, we propose a general approach called Generalized Multiscale Finite Element
Method (GMsFEM) for performing multiscale simulations for problems without scale …

The aim of this monograph is to describe the main concepts and recent-vances in
multiscale? nite element methods. This monograph is intended for …

Numerical homogenization, ie, the finite-dimensional approximation of solution spaces of
PDEs with arbitrary rough coefficients, requires the identification of accurate basis elements …

In this paper, we discuss a general multiscale model reduction framework based on
multiscale finite element methods. We give a brief overview of related multiscale methods …

Although numerical approximation and statistical inference are traditionally covered as
entirely separate subjects, they are intimately connected through the common purpose of …

We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/
multiresolution method for PDEs with rough (L^∞) coefficients with rigorous a priori …

In this paper we study multiscale finite element methods (MsFEMs) using spectral multiscale
basis functions that are designed for high-contrast problems. Multiscale basis functions are …

The multiscale finite-volume (MSFV) method for the solution of elliptic problems is extended
to an efficient iterative algorithm that converges to the fine-scale numerical solution. The …

In this paper, we study domain decomposition preconditioners for multiscale flows in high-
contrast media. We consider flow equations governed by elliptic equations in …

The paper addresses a numerical method for solving second order elliptic partial differential
equations that describe fields inside heterogeneous media. The scope is general and treats …