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In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin…
This paper presents a combined numerical-theoretical study of the macroscopic behavior and local field distributions in a special class of two-dimensional periodic composites with viscoplastic phases. The emphasis is on strongly nonlinear…
This work focuses on computing the homogenized elastic properties of rocks from 3D micro-computed-tomography (micro-CT) scanned images. The accurate computation of homogenized properties of rocks, archetypal random media, requires both…
Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…
We consider the homogenisation of the Stokes equations in a porous medium which is evolving in time. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables to model a…
This paper is an extension of the result by Christowiak and Kreisbeck (2017), which addresses the Gamma-convergence approach to a homogenization problem for composite materials consisting of two distinct types of parallel layers. In…
Elastic systems that are spatially heterogeneous in their mechanical response pose special challenges for molecular simulations. Standard methods for sampling thermal fluctuations of a system's size and shape proceed through a series of…
The subject of this work is a new stochastic Galerkin method for second-order elliptic partial differential equations with random diffusion coefficients. It combines operator compression in the stochastic variables with tree-based spline…
This paper is devoted to the study of tilt stability of local minimizers, which plays an important role in both theoretical and numerical aspects of optimization. This notion has been comprehensively investigated in the unconstrained…
Macroscopically heterogeneous materials, characterised mostly by comparable heterogeneity lengthscale and structural sizes, can no longer be modelled by deterministic approach instead. It is convenient to introduce stochastic approach with…
In this paper, a strain-gradient plasticity model is derived from a mesoscopic model for straight parallel edge dislocations in an infinite cylindrical crystal. The main difference to existing work is that in this work the well-separateness…
Granular materials are involved in most industrial and environmental processes, as well as many civil engineering applications. Although significant advances have been made in understanding the statics and dynamics of cohesionless grains…
In this paper we present a full discretization of the layer potentials and boundary integral operators for the elastic wave equation on a parametrizable smooth closed curve in the plane. The method can be understood as a non-conforming…
A multi-scale characterization of the field concentrations inside composite and polycrystalline media is developed. The analysis focuses on gradient fields associated with the intensive quantities given by the temperature and the electric…
This work is a natural extension of the authors previous work, Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation, theoretical fundamentals and applications, which established the foundation for…
This paper aims at developing two versions of the generalized Newton method to compute not merely arbitrary local minimizers of nonsmooth optimization problems but just those, which possess an important stability property known as tilt…
The linear response description for impurity diffusion in a granular fluid undergoing homogeneous cooling is developed in the preceeding paper. The formally exact Einstein and Green-Kubo expressions for the self-diffusion coefficient are…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
Schrodinger-type wave equations with logarithmic nonlinearity occur in hydrodynamic models of Korteweg-type materials with capillarity and surface tension, which can undergo liquid-solid or liquid-gas phase transitions. One of the…
We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely the film thickness…