Related papers: Heterogeneous multiscale methods for fourth-order …
Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approximations for mixed formulations. Due to the inherent…
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…
Solving time-harmonic wave propagation problems in the frequency domain within heterogeneous media poses significant mathematical and computational challenges, particularly in the high-frequency regime. Among the available numerical…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
We introduce and analyze a family of heterogeneous multiscale methods for the numerical integration of highly oscillatory systems of delay differential equations with constant delays. The methodology suggested provides algorithms of…
Microstructure reconstruction is a key enabler of process-structure-property linkages, a central topic in materials engineering. Revisiting classical optimization-based reconstruction techniques,they are recognized as a powerful framework…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
This chapter provides an introduction to Hybrid High-Order (HHO) methods. These are new generation numerical methods for PDEs with several advantageous features: the support of arbitrary approximation orders on general polyhedral meshes,…
This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…
We develop deterministic perturbation bounds for singular values and vectors of orthogonally decomposable tensors, in a spirit similar to classical results for matrices such as those due to Weyl, Davis, Kahan and Wedin. Our bounds…
A family of effective equations for wave propagation in periodic media for arbitrary timescales $\mathcal{O}(\varepsilon^{-\alpha})$, where $\varepsilon\ll1$ is the period of the tensor describing the medium, is proposed. The well-posedness…
We develop an essentially optimal numerical method for solving multiscale Maxwell wave equations in a domain $D\subset{\mathbb R}^d$. The problems depend on $n+1$ scales: one macroscopic scale and $n$ microscopic scales. Solving the…
In this paper we extend the ideas presented in Onofrei and Vernescu [\textit{Asymptotic Analysis, 54, 2007, 103-123}] and introduce suitable second order boundary layer correctors, to study the $H^1$-norm error estimate for the classical…
This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution- free also in the case…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…
Mechanical metamaterials feature engineered microstructures designed to exhibit exotic, and often counter-intuitive, effective behaviour. Such a behaviour is often achieved through instability-induced transformations of the underlying…
In this paper, we discuss a general framework for multicontinuum homogenization. Multicontinuum models are widely used in many applications and some derivations for these models are established. In these models, several macroscopic…
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…
Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…