This monograph is the first to provide a comprehensive, self-contained and rigorous
presentation of some of the most powerful preconditioning methods for solving finite element …

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

Since their popularization in the late 1970s and early 1980s, multigrid methods have been a
central tool in the numerical solution of the linear and nonlinear systems that arise from the …

We apply a recently proposed [5] robust overlapping Schwarz method with a certain spectral
construction of the coarse space in the setting of element agglomeration algebraic multigrid …

In this paper, we present a high-order expansion for elliptic equations in high-contrast
media. The background conductivity is taken to be one and we assume the medium contains …

This paper proposes new finite element spaces that can be constructed for agglomerates of
standard elements that have certain regular structure. The main requirement is that the …

In this paper, we give an overview of our results [36, 39, 46, 47] from the point of view of
coarse-grid multiscale model reduction by highlighting some common issues in coarse …

A two–level smoothed aggregation (or SA) scheme with tentative coarse space constructed
by spectral element agglomeration method is shown to provide weak–approximation …

We propose two multilevel spectral techniques for constructing coarse discretization spaces
for saddle-point problems corresponding to PDEs involving a divergence constraint, with a …

We give an overview of a number of algebraic multigrid methods targeting finite element
discretization problems. The focus is on the properties of the constructed hierarchy of coarse …