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## Publications

Publications (209)

In this work we report on a reduced-order model (ROM) based on the proper orthogonal decomposition (POD) technique for the system of 3-D time-domain Maxwell's equations coupled to a Drude dispersion model, which is employed to describe the interaction of light with nanometer scale metallic structures. By using the singular value decomposition (SVD)...

A non-intrusive model order reduction (MOR) method for solving parameterized electromagnetic scattering problems is proposed in this paper. A database collecting snapshots of high-fidelity solutions is built by solving the parameterized time-domain Maxwell equations for some values of the material parameters using a fullwave solver based on a high...

Visual perception relies on light scattering at the object's surface in the direction of observation. By engineering the surface scattering properties, it is possible to realize arbitrary visual percepts. Here, we address theoretically this problem of electromagnetic field transition conditions at conformal interfaces to achieve surface-topography-...

We present a non-intrusive model order reduction (NIMOR) approach with an offline-online decoupling for the solution of parameterized time-domain Maxwell's equations. During the offline stage, the training parameters are chosen by using Smolyak sparse grid method with an approximation level \begin{document}$ L $\end{document} (\begin{document}$ L\g...

Dynamic metasurface is an emerging concept for achieving a flexible control of electromagnetic waves. Generalized sheet transition conditions (GSTCs) can be used to model the relationship between the electromagnetic response and surface susceptibility parameters characterizing a metasurface. However, when it comes to the inverse problem of designin...

We consider finite element discretizations of Maxwell’s equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error estimation and mesh adaptivity, which is of particular interest since the electromagnetic field usually exhibits st...

The performance of metasurfaces measured experimentally often discords with expected values from numerical optimization. These discrepancies are attributed to the poor tolerance of metasurface building blocks with respect to fabrication uncertainties and nanoscale imperfections. Quantifying their efficiency drop according to geometry variation are...

We propose a controllability method for the numerical solution of time-harmonic Maxwell's equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the controllability method determines iteratively a periodic solution in the time domain. At each conjugate gradient iteration...

This paper presents a non-intrusive model order reduction (MOR) for the solution of parameterized electromagnetic scattering problems, which needs to prepare a database offline of full-order solution samples (snapshots) at some different parameter locations. The snapshot vectors are produced by a high order discontinuous Galerkin time-domain (DGTD)...

We consider finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error estimation and mesh adaptivity, which is of particular interest since the electromagnetic field usually exhibits st...

A novel computational methodology based on statistical learning multiobjective optimization is developed to optimize large-scale achromatic 3D metalenses in the visible regime. The optimized lens has a numerical aperture of 0.56 and an average focusing efficiency of 45%.

We present a novel postprocessing technique for a discontinuous Galerkin (DG) discretization of time-dependent Maxwell's equations that we couple with an explicit Runge-Kutta time-marching scheme. The postprocessed electromagnetic field converges one order faster than the unprocessed solution in the H(curl)-norm. The proposed approach is local, in...

In recent years, metasurfaces have emerged as revolutionary tools to manipulate the behavior of light at the nanoscale. These devices consist of nanostructures defined within a single layer of metal or dielectric materials, and they offer unprecedented control over the optical properties of light, leading to previously unattainable applications in...

We combine a statistical learning-based global optimization strategy with a high order 3D Discontinuous Galerkin Time-Domain (DGTD) solver to design a compact and highly efficient graded index photonic metalens. The metalens is composed of silicon (Si) strips of varying widths (in the transverse direction) and lengths (in the propagation direction)...

This work is concerned with the numerical treatment of the system of three‐dimensional frequency‐domain (or time‐harmonic) Maxwell equations using a high order hybridizable discontinuous Galerkin (HDG) approximation method combined with domain decomposition (DD) on the basis of hybrid iterative‐direct parallel solution strategies. The proposed HDG...

The discontinuous Galerkin (DG) method is a general numerical modeling approach that has been extensively studied in the last 20 years for the solution of many systems of partial differential equations in physics. Its development for the numerical treatment of the system of Maxwell equations was initiated by the applied mathematics community in the...

Plasma surrounding a hypersonic vehicle can lead to the absorption of incoming radar radiation or the interruption of communication. Therefore, the development of hypersonic vehicle relies on a clear understanding of the strong interaction between the surrounding plasma and the incident electromagnetic wave. However, because of the presence of comp...

We present an explicit hybridizable discontinuous Galerkin (HDG) method for numerically solving the system of three-dimensional (3D) time-domain Maxwell equations. The method is fully explicit similarly to classical so-called DGTD (Discontinuous Galerkin Time-Domain) methods, is also high-order accurate in both space and time and can be seen as a g...

Optimization of the performance of flat optical components, also dubbed metasurfaces, is a crucial step towards their implementation in realistic optical systems. Yet, most of the design techniques, which rely on large parameter search to calculate the optical scattering response of elementary building blocks, do not account for near-field interact...

HDG method is a new class of DG family with significantly less globally coupled unknowns, and can leverage a post-processing step to gain super-convergence. Its features make HDG a possible candidate for computational electromagnetics applications, especially in the frequency-domain. The HDG method introduces an hybrid variable, which represents an...

In this work we report a parametric reduced order model (ROM) based on proper orthogonal decomposition (POD) with Galerkin projection for solving the system of time-domain Maxwell's equations. In particular, we introduce a residual-based estimation of the error associated with the ROM. Moreover, a greedy algorithm for the snapshot selection in the...

In this work we report on a reduced-order model (ROM) for the system of time-domain Maxwell’s equations discretized by a discontinuous Galerkin (DG) method. We leverage previous results on proper orthogonal decomposition (POD) [1, 2], in particular for the wave equation [3], to propose a POD-based ROM with an adaptive snapshot selection strategy wh...

This paper is concerned with the design of a reduced-order model (ROM) based on a Krylov subspace technique for solving the time-domain Maxwell’s equations coupled to a Drude dis-persion model, which are discretized in space by a discontinuous Galerkin (DG) method. An auxiliary diﬀerential equation (ADE) method is used to represent the constitutive...

In this work, we present and study a flexible and accurate numerical solver in the context of three-dimensional computational nanophotonics. More precisely, we focus on the propagation of electromagnetic waves through metallic media described by a non-local dispersive model. For this model, we propose a discretization based on a high-order Disconti...

In this work, we address time-dependent wave propagation problems with strong multiscale features (in space and time). Our goal is to design a family of innovative high-performance numerical methods suitable for the simulation of such multiscale problems. Particularly, we extend the Multiscale Hybrid-Mixed finite element method (MHM for short) for...

In this work, a proper orthogonal decomposition (POD) method is applied to time-domain Maxwell’s equations coupled to a Drude dispersion model, which are discretized in space by a discontinuous Galerkin (DG) method. An auxiliary differential equation (ADE) method is used to represent the constitutive relation for the dispersive medium. A POD-DGTD f...

This volume entitled "European Computational Aerodynamics Research Project (ECARP)" contains the contributions of partners presented in two work shops focused on the following areas: Task 3 on Optimum Design and Task 4.2 on Navier Stokes Flow algorithms on Massively Parallel Processors. ECARP has been supported by the European Union (EU) through t...

This paper is concerned with the design of a reduced-order discontinuous Galerkin (DG) method based on proper orthogonal decomposition (POD) method for electromagnetic simulation. A centered flux approximation for surface integral and a second order leap-frog (LF2) scheme for advancing in time are applied in the classical DG method. The POD basis i...

This article has been published on IEEE Transactions on Antennas and Propagation (http://ieeexplore.ieee.org/document/8038082/).
The accurate and efficient simulation of 3D transient multiscale electromagnetic problems is extremely challenging for conventional numerical methods. Assuming a splitting of the underlying tetrahedral mesh in coarse an...

We present a time-implicit hybridizable discontinuous Galerkin (HDG) method for numerically solving the system of three-dimensional (3D) time-domain Maxwell equations. This method can be seen as a fully implicit variant of classical so-called DGTD (Discontinuous Galerkin Time-Domain) methods that have been extensively studied during the last 10 yea...

In this work, a new family of implicit-explicit (IMEX) schemes based on exponential time integration is developed for the 3D time-domain Maxwell's equations discretized by a high order discontinuous Galerkin (DG) scheme formulated on locally refined unstructured meshes. Numerical experiments demonstrate that the DGTD solver based on the proposed ti...

In this paper, we are concerned with the numerical modelling of the propagation of electromagnetic waves in dispersive materials for nanophotonics applications. We focus on a generalized model that allows for the description of a wide range of dispersive media. The underlying differential equations are recast into a generic form, and we establish a...

Discontinuous Galerkin (DG) methods are nowadays actively studied and increasingly exploited for the simulation of large-scale time-domain (i.e. unsteady) seismic wave propagation problems. Although theoretically applicable to frequency-domain problems as well, their use in this context has been hampered by the potentially large number of coupled u...

We present the Discontinuous Galerkim methods for solving Time-Domain (DGTD) Maxwell's equations coupled to the Drude model arising from nanophotonics. Model Order Reduction (MOR) techniques are employed to reduce the simulation time. We have considered a Proper Orthogonal Decomposition (POD) method, Krylov-subspace based operator exponential appro...

We propose Hybridizable Discontinuous Galerkin (HDG) methods for solving the frequency-domain Maxwell's equations coupled to the Nonlocal Hydrodynamic Drude (NHD) and Generalized Nonlocal Optical Response (GNOR) models, which are employed to describe the optical properties of nano-plasmonic scatterers and waveguides. Brief derivations for both the...

In this work, we address time dependent wave propagation problems with strong multiscale features (in space and time). Our goal is to design a family of innovative high performance numerical methods suitable to the simulation of such multiscale problems. Particularly, we extend the Multiscale Hybrid-Mixed finite element method (MHM for short) for t...

This paper is concerned with the approximation of the time domain Maxwell equations in a dispersive propagation medium by a Discontinuous Galerkin Time Domain (DGTD) method. The Debye model is used to describe the dispersive behaviour of the medium. We adapt the locally implicit time integration method from Verwer (2010) and derive a convergence an...

During the last ten years, the discontinuous Galerkin time-domain (DGTD) method has progressively emerged as a viable alternative to well established finite-difference time-domain (FDTD) and finite-element time-domain (FETD) methods for the numerical simulation of electromagnetic wave propagation problems in the time-domain. The method is now activ...

In this paper, we present a mathematical and numerical studies of the three-dimensional time-harmonic Maxwell equations. The problem is solved by a discontinuous Galerkin DG method coupled with an integral representation. This study was completed by some numerical tests to justify the effectiveness of the proposed approach. The numerical simulation...

The interaction of light with metallic nanostructures is
of increasing interest for various fields of research. When metallic
structures have sub-wavelength sizes and the illuminating
frequencies are in the regime of metal's plasma frequency, electron
interaction with the exciting fields have to be taken into account.
Due to these interactions, pla...

We study locally well-posed hybridizable discontinuous Galerkin (HDG) methods for the numerical solution of the time-harmonic Maxwell's equations. The local well-posedness is obtained by introducing another facet variable closely related to the tangential component of the magnetic field, as compared to the initial formulation. With this newly intro...

This paper is concerned with the development of a scalable high order finite element type solver for the numerical modeling of light interaction with nanometer scale structures. From the mathematical modeling point of view, one has to deal with the differential system of Maxwell equations in the time domain, coupled to an appropriate differential m...

Simulation of wave propagation through complex media relies on proper understanding of the properties of numerical methods when the wavenumber is real and complex.
Numerical methods of the Hybrid Discontinuous Galerkin (HDG) type are considered for simulating waves that satisfy the Helmholtz and Maxwell equations. It is shown that these methods, wh...

We are concerned here with the numerical simulation of electromagnetic wave propagation in biological media. Because of their water content, these media are dispersive i.e. their electromagnetic material characteristics depend of the frequency. In the time-domain, this translates in a time dependency of these parameters that can be taken into accou...

The time-harmonic Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental for the simulation of many modern devices we have become used to in everyday life. The numerical solution of these equations is hampered by two fundamental problems: first, in the high frequency regime, very fine meshes need to be use...

The system of Maxwell equations describes the evolution of
the interaction of an electromagnetic field with a propagation
medium. The different properties of the medium, such as isotropy,
homogeneity, linearity, among others, are introduced through {\it
constitutive laws} linking fields and inductions. In the present
study, we focus on nonlinear ef...

The present work is about the development of a parallel non-conforming multi-element discontinuous Galerkin time-domain (DGTD) method for the simulation of the scattering of electromagnetic waves by metallic nanoparticles. Such nanoparticles most often have curvilinear shapes, therefore we propose a numerical modeling strategy which combines the us...