This paper presents the basic concepts and the module structure of the Distributed and
Unified Numerics Environment and reflects on recent developments and general changes …

Numerical homogenization is a methodology for the computational solution of multiscale
partial differential equations. It aims at reducing complex large-scale problems to simplified …

An posteriori error analysis for the virtual element method (VEM) applied to general elliptic
problems is presented. The resulting error estimator is of residual-type and applies on very …

We present a general kernel-based framework for learning operators between Banach
spaces along with a priori error analysis and comprehensive numerical comparisons with …

In this paper, we propose Constraint Energy Minimizing Generalized Multiscale Finite
Element Method (CEM-GMsFEM). The main goal of this paper is to design multiscale basis …

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

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 …

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

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

We propose to compute a sparse approximate inverse Cholesky factor L of a dense
covariance matrix Θ by minimizing the Kullback--Leibler divergence between the Gaussian …