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

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 …

In this contribution we provide benchmark problems in the field of computational solid
mechanics. In detail, we address classical fields as elasticity, incompressibility, material …

In this contribution, a variational diffuse modeling framework for cracks in heterogeneous
media is presented. A static order parameter smoothly bridges the discontinuity at material …

In this thesis, we consider the numerical approximation of solutions of partial differential
equations that exhibit some kind of multiscale features. Such equations describe, for …

In this paper, we propose an offline-online strategy based on the Localized Orthogonal
Decomposition (LOD) method for elliptic multiscale problems with randomly perturbed …

In this paper, we construct and analyze a multiscale (finite element) method for parabolic
problems with heterogeneous dynamic boundary conditions. As the origin, we consider a …

Abstract (DE) Die Vorhersage des Bruchverhaltens ist für die Entwicklung moderner,
speziell zugeschnittener technischer Werkstoffe von größter Bedeutung. Diese Materialien …

The development of innovative products demands multi-material lightweight designs with
complex heterogeneous local material structures. Their computer-aided engineering relies …

Abstract (EN) In this thesis, a robust, reliable and efficient isogeometric analysis framework
is presented that allows for an adaptive spatial discretization of non-linear and time …