Publications related to Simple and multi-reflections using the PE method with a complementary Kirchhoff approximation

Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales

A fully discrete analysis of the finite element heterogeneous multiscale method (FE-HMM) for elliptic problems with N+1 well-separated scales is discussed. The FE-HMM is a numerical homogenization method that relies on a macroscopic scheme (macro FEM) for ...

Oxford Univ Press2015

Optical forces in nanoplasmonic systems: how do they work, what can they be useful for?

Olivier Martin, Raziman Thottungal Valapu, Robert Julius Wolke

n this article, we share our vision for a future nanofactory, where plasmonic trapping is used to control the different manufacturing steps associated with the transformation of initial nanostructures to produce complex compounds. All the different functio ...

Royal Soc Chemistry2015

High order numerical approximation of the invariant measure of ergodic SDEs

Assyr Abdulle, Gilles Vilmart

We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then pre ...

Society for Industrial and Applied Mathematics2014

Finite element heterogeneous multiscale method for the wave equation: long-time effects

Assyr Abdulle

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 new FE-HMM-L method captures not only the short-time behavior of the wave field, well ...

Siam Publications2014

Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials

Jan Sickmann Hesthaven

In this paper, we develop a nodal discontinuous Galerkin method for solving the time-dependent Maxwell's equations when metamaterials are involved. Both semi- and fully-discrete schemes are constructed. Numerical stability and error estimate are proved for ...

Elsevier2014

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Assyr Abdulle, Gilles Vilmart

A fully discrete analysis of the finite element heterogeneous multiscale method for a class of nonlinear elliptic homogenization problems of nonmonotone type is proposed. In contrast to previous results obtained for such problems in dimension

d\leq2

for ...

Amer Mathematical Soc2014

Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

Antoine Giovanni Imboden

In this report, we first introduce operator splitting as a way to solve nonlinear reaction-diffusion PDEs. We then present a flux-limiting technique for anisotropic diffusion problems that allows to recover the discrete maximum principle. Finally, we imple ...

2014

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...

Siam Publications2013

Mechanisms of Fano Resonances in Coupled Plasmonic Systems

Olivier Martin, Andrea Lovera, Benjamin Gallinet

Fano resonances in hybridized systems formed from the interaction of bright modes only are reported. Despite precedent works, we demonstrate theoretically and experimentally that Fano resonances can be obtained by destructive interference between two brigh ...

Amer Chemical Soc2013

Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

Adrian Blumenthal, Assyr Abdulle

A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates becaus ...

Academic Press Inc Elsevier Science2013

Simple and multi-reflections using the PE method with a complementary Kirchhoff approximation

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Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales

Optical forces in nanoplasmonic systems: how do they work, what can they be useful for?

High order numerical approximation of the invariant measure of ergodic SDEs

Finite element heterogeneous multiscale method for the wave equation: long-time effects

Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Mechanisms of Fano Resonances in Coupled Plasmonic Systems

Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales

Finite element heterogeneous multiscale method for the wave equation: long-time effects

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Optical forces in nanoplasmonic systems: how do they work, what can they be useful for?

Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials

High order numerical approximation of the invariant measure of ergodic SDEs

Mechanisms of Fano Resonances in Coupled Plasmonic Systems

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Stabilized multilevel Monte Carlo method for stiff stochastic differential equations