Related papers: Efficient multiscale algorithms for simulating non…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
In this work we introduce an effective approach to quantize the electromagnetic response of plasmonic metallic nanostructures. Their shape is arbitrary and they feature a realistic description of the frequency-dependent metal dielectric…
A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…
In this paper, we consider the frequency-domain Maxwell's equations coupled to a nonlocal Drude model which describes the nonlocal optical response in metallic nanostructures. We prove the existence and uniqueness of weak solutions to the…
In this work, we have developed a multiscale computational algorithm to couple finite element method with an open source molecular dynamics code --- the Large scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) --- to perform…
The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on macroscopic response, multiscale modeling strategies are essential.…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
We consider image denoising using a nonlinear diffusion process, where we solve unsteady partial differential equations with nonlinear coefficients. The noised image is given as an initial condition, and nonlinear coefficients are used to…
Classical multi-scale methods involving two spatial scales face significant challenges when simulating heterogeneous structures with complicated three-scale spatial configurations. This study proposes an innovative higher-order three-scale…
Plasmonic metal nanostructures are an integral part of nanophotonic device applications owing to their ability to generate strong localized electromagnetic fields when illuminated from the far-field. These nanostructures can be prepared in…
Polar dielectric nanoresonators can support hybrid photon-phonon modes termed surface phonon polaritons with lengthscales below the diffraction limit. In the deep sub-wavelength regime the optical response of these systems was recently…
Using adaptive algorithms, the design of nano-scale dielectric structures for photonic applications is explored. Widths of dielectric layers in a linear array are adjusted to match target responses of optical transmission as a function of…
This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical…
In this work, we present an efficient way to decouple the multicontinuum problems. To construct decoupled schemes, we propose Implicit-Explicit time approximation in general form and study them for the fine-scale and coarse-scale space…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
Hierarchical self-assembly arranges nanostructures at different length scales. It gradually becomes an effective method of fabricating artificial metamaterials from composite nanostructures tailored for a particular response. Hierarchical…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
Most optical systems involve a combination of lenses separated by free-space regions where light acquires the required angle-dependent phase delay for a certain functionality. Very recently, flat-optics structures have been proposed to…
In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…
Nanophotonic technologies inherently rely on tailoring light-matter interactions through the excitation and interference of deeply confined optical resonances. However, existing concepts in optical mode engineering remain heuristic and are…