Related papers: Homogenization Method, uncovered on 2 pages
The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale…
We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…
In this paper we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media proposed in [19]. The starting point is the pore scale model in [12], which is a…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
We consider a thin heterogeneous layer consisted of the thin beams (of radius $r$) and we study the limit behaviour of this problem as the periodicity $\varepsilon$, the thickness $\delta$ and the radius $r$ of the beams tend to zero. The…
Inferring the source properties of a gravitational wave signal has traditionally been very computationally intensive and time consuming. In recent years, several techniques have been developed that can significantly reduce the computational…
A simple method to get all main characteristics of nucleation process is proposed. The advantage of this method is an applicability to situations with non-linear behavior in time of effective external source of vapor. It is important…
This work is devoted to the homogenization of elliptic equations in high-contrast media in the so-called 'double-porosity' resonant regime, for which we solve two open problems of the literature. First, we prove qualitative stochastic…
We study the homogenization problem for a system of stochastic differential equation with local time terms that models a multivariate diffusion in presence of semipermeable hyperplane interfaces with oblique penetration. We show that this…
In this article we are interested in quantitative homogenization results for linear elliptic equations in the non-stationary situation of a straight interface between two heterogenous media. This extends the previous work [Josien, 2019] to…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
In this article we provide a method for establishing operator-type error estimates between solutions to rapidly oscillating evolutionary equations and their homogenised counter parts. This method is exemplified by applications to the wave,…
We develop the viscosity method for the homogenization of an obstacle problem with highly oscillating obstacles. The associated operator, in non-divergence form, is linear and elliptic with variable coefficients. We first construct a highly…
In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a divergence-regularization in one of the cell problems. This allows…
In this paper, we find some error estimates for periodic homogenization of p-Laplace type equations under the same structure assumption on homogenized equations. The main idea is that by adjusting the size of the difference quotient of the…
This paper investigates homogenization problems for the nonlocal operators with rapidly oscillating coefficients in the cases of periodic and random statistically homogeneous micro-structures. These operators involve the fractional…
Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We…
In the first part of the paper, we propose and rigorously analyze a mixed finite element method for the approximation of the periodic strong solution to the fully nonlinear second-order Hamilton--Jacobi--Bellman equation with coefficients…
We introduce a homogenization approach to characterize the dynamical response of a generic dispersive spacetime crystal in the long-wavelength limit. The theory is applied to dispersive spacetime platforms with a travelling-wave modulation.…