Related papers: Elements of mathematical foundations for a numeric…
We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a…
This article studies some numerical approximations of the homogenized matrix for stochastic linear elliptic partial differential equations in divergence form. We focus on the case when the underlying random field is a small perturbation of…
In this article, basing upon probabilistic methods, we discuss periodic homogenization of a class of weakly coupled systems of linear elliptic and parabolic partial differential equations. Under the assumption that the systems have rapidly…
A multiscale asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement…
We analyze a homogenization limit for the linear wave equation of second order. The spatial operator is assumed to be of divergence form with an oscillatory coefficient matrix $a^\varepsilon$ that is periodic with characteristic length…
Asymptotic homogenisation is used to systematically derive reduced-order macroscopic models of conductive behaviour in spirally-wound layered materials in which the layers have very different conductivities. The problem is motivated by the…
We develop a microscopic approach to the consistent construction of the kinetic theory of dilute weakly ionized gases of hydrogen-like atoms. The approach is based on the framework of the second quantization method in the presence of bound…
We consider a homogenization problem for the diffusion equation $-\operatorname{div}\left(a_{\varepsilon} \nabla u_{\varepsilon} \right) = f$ when the coefficient $a_{\varepsilon}$ is a non-local perturbation of a periodic coefficient. The…
This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…
We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…
A non-local dynamic homogenization technique for the analysis of a viscoelastic heterogeneous material which displays a periodic microstructure is herein proposed. The asymptotic expansion of the micro-displacement field in the transformed…
We study the behaviour of solutions to a class of nonlinear degenerate parabolic problems when the data are perturbed. The class includes the Richards equation, Stefan problem and the parabolic $p$-Laplace equation. We show that, up to a…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
A multifield asymptotic homogenization technique for periodic thermo-diffusive elastic materials is provided in the present study. Field equations for the first-order equivalent medium are derived and overall constitutive tensors are…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
In this paper a second-order homogenization approach for periodic material is derived from an appropriate representation of the down-scaling that correlates the microdisplacement field to the macro-displacement field and the macro-strain…
We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [von Pezold et al, Physical Review B 2010; Wei et…
This paper deals with the approximation and homogenization of thermoelastic wave model. First, we study the homogenization problem of a weakly coupled thermoelastic wave model with rapidly varying coefficients, using a semigroup approach,…
We outline how discrete analogues of the conservation of potential vorticity may be achieved in Finite Element numerical schemes for a variational system which has the particle relabelling symmetry, typically shallow water equations. We…