Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials
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We present a novel method to couple molecular dynamics with finite elements at finite temperatures using spatial filters. The mismatch in the dispersion relations between continuum and atomistic models leads, at finite temperature, to unwanted mesh vibrati ...
A class of numerical schemes is developed for the study of charged particle transport in complex stationary electromagnetic fields and tested for fields obtained from a numerical solution of the magneto-hydrodynamic equation. The performances of these sche ...
An analysis of a multiscale symmetric interior penalty discontinuous Galerkin finite element method for the numerical discretization of elliptic problems with multiple scales is proposed. This new method, first described in [A. Abdulle, C.R. Acad. Sci. Par ...
In this paper, convergence and performance properties of a sample-data continuous time model predictive control (MPC) scheme with economic performance index are developed. In particular, we provide sufficient conditions for convergence of the close loop st ...
In this work we consider the cognitive many-to-one interference network. We first extend existing coding schemes from the two-user case to this network scenario. Then we present a novel coding scheme using compute-and-forward and show it can enlarge the ac ...
Among the efficient numerical methods based on atomistic models, the quasi-continuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to mult ...
A new finite element method for the efficient discretization of elliptic homogenization problems is proposed. These problems, characterized by data varying over a wide range of scales cannot be easily solved by classical numerical methods that need mesh re ...
A new finite element heterogeneous multiscale method (FE-HMM) is proposed for the numerical solution of the wave equation over long times in a rapidly varying medium. Our FE-HMM captures long-time dispersive effects of the true solution at a cost similar t ...
The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite elemen ...