Numerical modeling and high performAnce computing for evolution problems
in Complex domains and HeterogeneOuS media

Nachos is a joint project-team between Inria, the CNRS and the University of Nice/Sophia Antipolis
via the J.A. Dieudonné Mathematics Laboratory (UMR 7351)

Our research activities are concerned with the design, analysis and high performance implementation of computational tools for modeling the interaction of waves (electromagnetic waves and elastic waves) with complex media and irregularly shaped structures.

High order discretization methods
We concentrate our efforts on finite element type methods belonging to the family of Discontinuous Galerkin (DG) methods. DG methods are at the heart of the activities of the team regarding the development of high order discretization schemes for the differential systems modeling time-domain and time-harmonic electromagnetic and elastodynamic wave propagation. We currently study three variants of DG methods: (1) nodal DG methods for time-domain problems, (2) hybridizable DG (HDG) methods for time-domain and time-harmonic problems and (3) multiscale DG methods for time-domain problems.

Efficient time integration strategies
The use of unstructured meshes (based on triangles in two space dimensions and tetrahedra in three space dimensions) is an important feature of DG methods for time-domain problems (i.e. DGTD formulations). DG methods can thus easily deal with complex geometries and heterogeneous propagation media. Moreover, DG discretization methods are naturally adapted to local, conforming as well as non-conforming, refinement of the underlying mesh. Most of the existing DGTD methods rely on explicit time integration schemes and lead to block diagonal mass matrices which is often recognized as one of the main advantages with regards to continuous finite element methods. However, explicit DGTD methods are also constrained by a stability condition that can be very restrictive on highly refined meshes and when the local approximation relies on high order polynomial interpolation. In this context, we study accurate and efficient strategies combining explicit and implicit time integration schemes.

Numerical treatment of complex material models
Towards the general aim of being able to consider concrete physical situations, we are interested in taking into account in the numerical methodologies that we study, a better description of the propagation of waves in realistic media.

High performance computing with a high order DGTD method Scattering of a plane wave by a gold nanodisk
EM wave propagation through head tissues Local Drude versus non-local hydrodynamic Drude model

From the point of view of applications, since 2012, we concentrate our efforts on problems pertaining to nanophotonics/nanoplasmonics, i.e., on the numerical modeling of light interaction with nanoscale structures. In this context, our general objective is to propose innovative numerical methodologies for the solution of the system of (time-domain and time-harmonic) Maxwell equations coupled to appropriate models of the materials/structures with which the electromagnetic wave interacts.

Scattering of a gold nanodisk by a plane wave. Comparison between local Drude and non-local hydrodynamic Drude models.

Local model modulus of Ex component Non-local model, modulus of Ex component Local model modulus of Ey component Non-local model, modulus of Ey component

Light absorption by a metal/insulator/metal structure

Recent works and related methodological contributions

L. Li, S. Lanteri and R. Perrussel
A hybridizable discontinuous Galerkin method combined to a Schwarz algorithm for the solution of 3d time-harmonic Maxwell's equations
J. Comput. Phys., Vol. 256, pp. 563–581 (2014)
Available as INRIA RR-8251 on Hyper Article Online

C. Durochat, S. Lanteri and C. Scheid
High order non-conforming multi-element Discontinuous Galerkin method for time domain electromagnetics
Appl. Math. Comput., Vol. 224, pp. 681–704 (2013)
Available as INRIA RR-8257 on Hyper Article Online

L. Moya, S. Descombes and S. Lanteri
Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations
J. Sci. Comp., Vol. 56, No. 1, pp. 190-218 (2013)
Available as INRIA RR-7983 on Hyper Article Online

L. Li, S. Lanteri and R. Perrussel
Numerical investigation of a high order hybridizable discontinuous Galerkin method for 2d time-harmonic Maxwell’s equations
COMPEL, Vol. 2, No. 3, pp. 1112-1138 (2013)
Available as INRIA RR-7649 on Hyper Article Online

M. El Bouajaji, V.Dolean, M. J. Gander and S. Lanteri
Optimized Schwarz methods for the time-harmonic Maxwell equations with damping
SIAM J. Sci. Comp., Vol. 34, No. 4, pp. A2048-A2071 (2012)
Available on Hyper Article Online

L. Moya
Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations
ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 46, pp 1225-1246 (2012)
Preprint available as INRIA RR-7533 on Hyper Article Online

T. Cabel, J. Charles and S. Lanteri
Performance evaluation of a multi-GPU enabled finite element method for computational electromagnetics
Proceedings of the Euro-Par 2011 conference, LNCS, Vol. 7156, pp. 355-364 (2012)
Preprint available as INRIA RR-7592 on Hyper Article Online

Inria, Nachos project-team
2004 Route des Lucioles, B.P. 93
06902 Sophia Antipolis Cedex, France
Contact by mail

C2S@Exa Inria Project Lab

HOSCAR CNPa-Inria project

DIOGENeS
Software suite for computational nanophotonics/nanoplasmonics

Seminars in 2015

CEA-EDF-INRIA school

Toward petaflop numerical simulation on parallel hybrid architectures, June 6-10, 2011, INRIA Sophia Antipolis-Méditerranée, France

Conferences in 2011

3rd International Conference on Finite Element Methods in Engineering and Science (FEMTEC 2011), May 9 - 13, 2011, Harvey's Casino and Resort South Lake Tahoe, USA

Postdoctoral project
Numerical modeling of the interaction of an electromagnetic field with living tissues using a discontinuous finite element method
Application deadline: March 15th

PhD project
Modélisation de la variabilité entre les individus dans le calcul électromagnétique des effets de la téléphonie mobile

Internship and PhD\\ Schémas d'intégration en temps précis et efficaces pour les équations de Maxwell discrétisées par une méthode d'éléments finis discontinus d'ordre élevé

Sujets de stages 2010 Schémas numériques performants pour la propagation d'ondes électromagnétique Méthode éléments finis hybride pour la propagation d'ondes électromagnétiques

ONERA scientific event

High accuracy numerical methods and their application to complex physics problems, December 7-8 2009, ONERA Toulouse, France

Conferences in 2010

2nd European Seminar on Coupled Problems (ESCO 2010), June 28—July 2, 2010, Pilsen, Czech Republic

CEA-EDF-INRIA school

Robust methods and algorithms for solving large algebraic systems on modern high performance computing systems, March 30-April 3 2009, INRIA Sophia Antipolis-Méditerranée, France
Slides of the lectures

Scientific activity reports

2007 to 2013

>>clip<< Seminars in 2008

Siham Layouni, CEA Saclay
April 21st 2008

Jan S. Hesthaven, Brown University, Division of Applied Mathematics
July 21st 2008


Martin J. Gander, Geneva University, Mathematics Section
August 18th 2008

Oliver Rheinbach, Universitaet Duisburg-Essen, Fachbereich Mathematik
December 2nd 2008

>>clip<< Seminars in 2007

Martin J. Gander
July 9th 2007

Sarah Delcourte
November 13th 2007

José Carcione
November 26th 2007

Numerical modeling of wave propagation in elastic media
December 11th 2007
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