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

This paper constructs a local generalized finite element basis for elliptic problems with
heterogeneous and highly varying coefficients. The basis functions are solutions of local …

The objective of this book is to introduce the reader to the Localized Orthogonal
Decomposition (LOD) method for solving partial differential equations with multiscale data …

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

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 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 …

In this paper, robust preconditioners for multiscale flow problems are investigated. We
consider elliptic equations with highly varying coefficients. We design and analyze two-level …

Numerical homogenization aims to efficiently and accurately approximate the solution space
of an elliptic partial differential operator with arbitrarily rough coefficients in a $ d …

In this paper, we propose oversampling strategies in the generalized multiscale finite
element method (GMsFEM) framework. The GMsFEM, which has been recently introduced …