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Note: The final version of this article was published in Computers and Geosciences, Volume 206, January 2026, 106038. DOI: 10.1016/j.cageo.2025.106038. Readers should refer to the published version for the most up-to-date content.…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
We consider a nonlinear convex stochastic homogenization problem, in a stationary setting. In practice, the deterministic homogenized energy density can only be approximated by a random apparent energy density, obtained by solving the…
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…
In this paper, we present a robust and fully discretized method for solving the time fractional diffusion equation with high-contrast multiscale coefficients. We establish the homogenized equation using a multicontinuum approach and employ…
In this paper we prove convergence results for the homogenization of the Dirichlet problem with rapidly oscillating boundary data in convex polygonal domains. Our analysis is based on integral representation of solutions. Under a certain…
The paper addresses the homogenization of a micro-model of poroelasticity coupled with thermal effects for two-constituent media and with imperfect interfacial contact.The homogenized model is obtained by means of the two-scale convergence…
We prove, under some assumptions, the existence of correctors for the stochastic homoge-nization of of " viscous " possibly degenerate Hamilton-Jacobi equations in stationary ergodic media. The general claim is that, assuming knowledge of…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We determine the asymptotic behavior of the solutions to the linear elastodynamic equations in a stratified medium comprising an alternation of possibly very stiff layers with much softer ones, when the thickness of the layers tends to…
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…
This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral…
In this paper, we consider several possible ways to set up Heterogeneous Multiscale Methods for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, which can be seen as a means to modeling rapidly varying…
This paper is concerned with a family of second-order elliptic systems in divergence form with rapidly oscillating periodic coefficients. We initiate the study of homogenization and boundary layers for Neumann problems with first-order…
Numerical homogenization of multiscale equations typically requires taking an average of the solution to a microscale problem. Both the boundary conditions and domain size of the microscale problem play an important role in the accuracy of…
We develop a quantitative theory of stochastic homogenization in the more general framework of differential forms. Inspired by recent progress in the uniformly elliptic setting, the analysis relies on the study of certain subadditive…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…