The research activities of the project-team are concerned with the
formulation, analysis and evaluation of numerical methods and high performance
resolution algorithms for the computer simulation of evolution problems in
complex domains and heterogeneous media. The resulting methodologies are
applied to wave propagation problems pertaining to computational
electromagnetics and computational geoseismics.
Research themes
Discretization methods
The physical and geometrical characteristics of the applications of interest
to the project-team research activities motivate the design of accurate,
efficient and robust discretization methods for the involved systems of
PDEs. We concentrate on high-order (polynomial interpolation), non-conforming
(h-, p- and hp-adaptivity) discontinuous finite element methods, formulated on
triangulations (2D case) or tetrahedrizations (3D case) of the underlying
computational domain. Furthermore, in order to allow for the simulation of
realistic physical problems, we investigate the numerical treatment of complex
material models in the framework of these discretization methods.
Time integration schemes
Explicit time integration schemes are subjected to stability conditions that
become very restrictive when the underlying mesh is locally refined,
especially in 3D. To overcome this problem, we study locally implicit schemes
(hybrid explicit/implicit schemes) which possess advantageous stability and
accuracy properties.
Resolution algorithms
The design of high performance resolution algorithms is an important aspect of
the research activities of the project-team. In this respect, we study domain
decomposition resolution algorithms, more precisely Schwarz algorithms based
on optimized interface conditions adapted to the underlying PDE systems.
High performance computing
In view of the implementation of the resulting methodologies and the
realization of large-scale numerical simulations, we study parallelization
strategies that best exploit the characteristics of modern high performance
computing architectures, in particular hybrid shared memory/distributed memory
multi-processor/multi-core platforms.
International and industrial relations
GéoSciences Azur laboratory (UMR 6526) in Sophia Antipolis.
Ampere laboratory (UMR 5005) in Lyon.
France Telcom R&D, IOP (Interaction of electromagnetic wave with humans team),
Issy-les-Moulineaux.
CEA DAM, CESTA center, Le Barp.
