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 construction of local reduced-order models via multiscale basis functions has been an
area of active research. In this paper, we propose online multiscale basis functions which …

Complex processes in perforated domains occur in many real-world applications. These
problems are typically characterized by physical processes in domains with multiple scales …

Inherently coupled flow and geomechanics processes in fractured shale media have
implications for shale gas production. The system involves highly complex geo-textures …

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

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 …

In this work, we present a novel nonlocal nonlinear coarse grid approximation using a
machine learning algorithm. We consider unsaturated and two-phase flow problems in …

In this contribution we present a survey of concepts in localized model order reduction
methods for parameterized partial differential equations. The key concept of localized model …

In this paper, we present two adaptive methods for the basis enrichment of the mixed
Generalized Multiscale Finite Element Method (GMsFEM) for solving the flow problem in …