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by Olivier Pigaglio - published on , updated on

The group’s activities in this context have the same meaning of development models and not just of their operation. They are underpinned by two categories of objectives : improving existing numerical methods or developing methods dedicated to innovative applications.

Improvements of existing numerical methods

n continuation of work already completed before 2009 and which concerned the theoretical foundations and software, the GRE team has continued to develop tools for solving complex electromagnetic problems.

Thus, to enrich the WCIP (Wave Concept Iterative Process), a "historical" method introduced by Professor Henri Baudrand to calculate field in multilayer planar circuits. The coupling with other volumic techniques (Finite Element Method, Hybrid Discontinuous Galerkin and Finite Difference Transmission Line Method) was developed in order to easily handle heterogeneous layers of substrates. The work to expand the spectrum of the WCIP applications (such as SIW and SINRD structures) are mainly carried out in collaboration with the NACHOS team at INRIA in the framework of a thesis started in 2011.

The developed methods are compared with existing commercial, the research group is also working on the optimization of search algorithms using mainly preconditioning techniques. This work has involved:

The WCIP with the implementation of a method Krylov subspace combined with a suitable preconditioning (collaboration INRIA-CERFACS).
Integral equations for low frequency applications as part of a collaboration with the G2ELab (SEEDS project with a master thesis) and internally with GREM3 team. Our main contribution was the development of algorithms for matrices called "hierarchical".

Hierarchical matrices technique

  • Scattering from rough surfaces, as part of a thesis in collaboration with ONERA. A physical pre-conditioner for boundary integral equations was developed. As part of this thesis, conditions of impedances for periodic roughness on a dielectric interface have also been proposed.

Diffraction by a rough surface

Simulation tools dedicated to innovative applications

As part of new issues raised by the spread of telecommunications systems or radar, GRE in partnership with ONERA realized significant progress on two points:

The first concerns the temporal and spatio-temporal modeling tropospheric impairments. Original stochastic models of tropospheric propagation channel necessary for the design of future Telecommunications systems operating above 10 GHz, applicable anywhere in the world, have been developed. In addition, work was conducted on the estimation of the interannual variability and confidence intervals for statistics derived propagation measurement or model. This work is now the ITU-R P.678 recommendation of the International Telecommunication Union.
The second point concerns the modeling of the effects of tropospheric and ionospheric turbulence on the propagation of electromagnetic waves. An analytical resolution of the turbulent environment propagation equations was conducted for 2D and 3D configurations. In parallel, 3D / 2D numerical schemes based on a coupling parabolic equation / phase screens have been developed. The assembly allows the evaluation of atmospheric scintillation effects as well as analytical parameterization of the consequences of dimensional reduction 3D / 2D.

Distribution de la probabilité d'atténuation due à la pluie Modélisation de l'atténuation troposphérique sur l'Europe

Distribution of attenuation probability due to rain (left)
- Modeling of tropospheric attenuation in Europe (right)

Efforts in the modeling of waves focused through several PhD theses and internships were supported by CNES and led to a significant achievement in partnership with ENAC and ONERA. Indeed, they have lifted the latch of frequency selective surfaces to develop a usable software in the design of quasi-optical systems. Additional benefits also cover the antenna coupling / structure and propagation in inhomogeneous medium in the context of very large scenes.

In 2011, CNES has sought the expertise of the GRE team on the controversial subject of Orbital Angular Moment wave (OAM) that would be likely to increase communication skills and so break the spectral constraints. The original structure of these beams was analyzed and resulted in the completion of two significant contributions:

The first concerns the asymptotic behavior of OAM communication and proposes new concepts of gain and loss of free space.
The second demonstrates the ability to locally detect orbital orders quantified in the presence of Spin Angular Moment (SAM).

We are also involved with other local partners (CNES, ENAC, ISAE), the development of a route demonstration OAM for early 2015, the general public.