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

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 …

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 …

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 …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …

We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of
the Helmholtz equation with large wave number $\kappa $ in bounded domains in $\mathbb …

In this paper we revisit a two-level discretization based on localized orthogonal
decomposition (LOD). It was originally proposed in [P. Henning, A. Målqvist, and D …

In this paper we propose a local orthogonal decomposition method (LOD) for elliptic partial
differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. For …

While deep learning algorithms demonstrate a great potential in scientific computing, its
application to multi-scale problems remains to be a big challenge. This is manifested by the …

This paper reviews the variational multiscale stabilization of standard finite element methods
for linear partial differential equations that exhibit multiscale features. The stabilization is of …