Phd Position F/m Fast Solvers for Studying Light

Le descriptif de l’offre ci-dessous est en Anglais_

**Type de contrat **:CDD**Niveau de diplôme exigé **:Bac + 5 ou équivalent**Autre diplôme apprécié **:Master in applied mathematics or scientific computing**Fonction **:Doctorant**Niveau d'expérience souhaité **:De 3 à 5 ansA propos du centre ou de la direction fonctionnelle

The Inria centre at Université Côte d'Azur includes 37 research teams and 8 support services. The centre's staff (about 500 people) is made up of scientists of different nationalities, engineers, technicians and administrative staff. The teams are mainly located on the university campuses of Sophia Antipolis and Nice as well as Montpellier, in close collaboration with research and higher education laboratories and establishments (Université Côte d'Azur, CNRS, INRAE, INSERM...), but also with the regiona economic players.

With a presence in the fields of computational neuroscience and biology, data science and modeling, software engineering and certification, as well as collaborative robotics, the Inria Centre at Université Côte d'Azur is a major player in terms of scientific excellence through its results and collaborations at both European and international levels.

Contexte et atouts du poste

The exploitation of nanostructuring in order to improve the performance of CMOS imagers based on microlens grids is a very promising avenue. In this perspective, numerical modeling is a key component to accurately characterize and optimize the absorption properties of these complex imaging structures which are intrinsically multiscale (from the micrometer scale of the lenses to the nanometric characteristics of the nanostructured material layers). The present PhD project is proposed in the context of a collaboration between the Atlantis project-team of Inria research center at Université Côte d'Azur and STMicrolectronics (CMOS Imagers division of the Technology for Optical Sensors department) in Crolles. A Cifre funding will support this project.

The objectives of the project are to design (1) a fast electromagnetic simulation approach based on a model reduction technique, to characterize numerically the light trapping in digital imagers exploiting nanostructured pixels and, (2) a multi-objective optimization strategy of the geometrical characteristics of the nanostructuring in order to simultaneously maximize the light absorption in a pixel and to minimize the crosstalk phenomenon between neighboring pixels. For the first time, in addition to the rigorous methods for solving Maxwell's equations, we will be able to benefit from an alternative simulation approach based on model reduction. This new approach can be used in an optimization process and the expected gain in total computation time would be between 10 to 1000.

Mission confiée
- and frequency-domain Maxwell equations possibly coupled to differential equations modeling the behaviour of propagation media at optical frequencies. DIOGENeS is a unique numerical framework leveraging the capabilities of DG techniques for the simulation of multiscale problems relevant tonanophotonics and nanoplasmonics.

The core of the present study is concerned with reduced-order modeling for time-domain electromagnetic wave propagation problems. In short, reduced-order models (ROMs) are simplifications of high fidelity, complex models. They capture the behavior of these source models so that one can quickly study a system's dominant effects using mínimal computational resources. The starting point will consist on some preliminary works and contributions that the team has obtained during the recent years by considering a particular reduced-order modelling technique known as the proper orthogonal decomposition (POD) method.

In the POD approach, a reduced subspace with a significantly smaller dimension is constructed by a set of basis vectors extracted offline from snapshots that are extracted from simulations with a high order DGTD method. By doing so, a non-intrusive POD-based ROM has been developed for the solution of parameterized time-domain electromagnetic scattering problems. The considered parameters are the electric permittivity and the temporal variable. By using the singular value decomposition (SVD) method, the principal components of the projection coefficient matrices (also referred to as the reduced coefficient matrices) of full-order solutions onto the RB subspace are extracted. A cubic spline interpolation-based (CSI) approach is proposed to approximate the dominating time
- and parameter-modes of the reduced coefficient matrices without resorting to Galerkin projection. The generation of snapshot vectors, the construction of POD basis functions and the approximation of reduced coefficient matrices based on the CSI method are completed during the offline stage. The RB solutions for new time and parameter values can be rapidly recovered via outputs from the interpolation models in the online stage. In particular, the