**Interaction of electromagnetic waves with biological tissues at microwave frequencies**

The study of the interaction between electromagnetic waves and living
tissues is of interest to several applications of societal relevance
such as the assessment of potential adverse effects of electromagnetic
fields or the utilization of electromagnetic waves for therapeutic or
diagnostic purposes. Numerical modeling of electromagnetic wave
propagation in interaction with biological tissues at microwave
frequencies requires to solve the system of Maxwell equations coupled
to appropriate models of physical dispersion in the tissues, such the
Debye and Cole-Cole models. Since the creation of the team, our works
on this topic have mainly been focussed on the study of the exposure
of humans to radiations from wireless communication systems. In the
recent years, we have studied various DGTD methods for the numerical
dosimetry analysis of the exposure of humans to electromagnetic
waves.

H. Fahs, A. Hadjem, S. Lanteri, J. Wiart and M.F. Wong

Calculation of the SAR induced in head tissues using a high order DGTD method and triangulated geometrical models

IEEE Trans. Ant. Propag., Vol. 59, No. 12, pp. 4669-4678 (2011)

C. Scheid and S. Lanteri

Convergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell's equations in dispersive media

IMA J. Numer. Anal., Vol. 33, No. 2, pp. 432-459 (2013)

Preprint available as INRIA RR-7634 on Hyper Article Online

C. Durochat, S. Lanteri and R. Léger

A non-conforming multi-element DGTD method for the simulation of human exposure to electromagnetic waves

Int. J. Numer. Model., Electron. Netw. Devices Fields, Vol. 27, No. 3, pp 614-625 (2014)

Numerical simulation of the exposure of a pregnant women to electromagnetic waves emitted by multiple localized sources, using DGTD-P1 and DGTD-P2 methods. This calculation involved an heterogeneous geometrical model of 3 tissues (body of the women, body of the foetus and brain of the foetus) consisting of an unstructured tetrahedral mesh with 5,536,852 tetrahedra (the total number of degrees of freedom for this problem is 132,884,448 for the DGTD-P1 method and 332,211,120 for the DGTD-P2 method).

The geometrical model has been built starting from MRI mdedical images provided by the FEMONUM project.

The unstructured tetrahedral mesh was generated using the TetMesh-GHS3D software developed by the Distene company and the GAMMA3 INRIA project-team.

The underlying DGTD method has been ported to a multiple GPU (Graphical Processing Unit) BULL Novascale R422 computing system.

The single precision floating point performance of the DGTD-P1 and DGTD-P2 calculation is 4.7 Tflops and 8.9 Tflops on 128 GPUs.

This work was granted access to the HPC resources of CCRT under the allocation 2010-t2010065004 made by GENCI (Grand Equipement National de Calcul Intensif).

Numerical simulation of the exposure of head tissues to an electromagnetic wave emitted by a mobile phone, using a DGTD-P1 method. This calculation involved an heterogeneous geometrical model of 4 head tissues (skin, skull, cerebro spinal fluid and brain) consisting of an unstructured tetrahedral mesh with 7,894,172 tetrahedra (the total number of degrees of freedom for this problem is 189,460,128).

The simulation was run on 512 cores of a Bull Novascale 3045 parallel system consisting of Intel Itanium 2/1.6 GHz nodes interconnected by a high performance Infiniband network.

This work was granted access to the HPC resources of CCRT under the allocation 2009-t2009065004 made by GENCI (Grand Equipement National de Calcul Intensif).

Numerical simulation of the exposure of a full body to electromagnetic waves emitted by multiple localized sources, using a DGTD-P2 method. This calculation involved a homogeneous geometrical model consisting of an unstructured tetrahedral mesh with 5,335,521 tetrahedra (the total number of degrees of freedom for this problem is 320,131,260).

The simulation was run on 512 cores of a Bull Novascale 3045 parallel system consisting of Intel Itanium 2/1.6 GHz nodes interconnected by a high performance Infiniband network.

This work was granted access to the HPC resources of CCRT under the allocation 2008-t2009065004 made by GENCI (Grand Equipement National de Calcul Intensif).

**Interaction of seismic waves with geological media**

Our research activities in this domain before all focus on the
development of numerical methodologies and simulation tools for
seismic hazard assessment. Numerical methods for the propagation of
seismic waves have been studied for many years. One of the most
popular approaches is the staggered grid finite difference time domain
(FDTD) scheme derived for the first order velocity-stress system of
elastic waves equations, which is an extension of the well-known
[[http://en.wikipedia.org/wiki/Finite-difference_time-domain_method |
FDTD]] method derived by K.S. Yee in 1966 for the solution of the
Maxwell equations. Many improvements of this method have been
proposed, in particular, higher order schemes in space or rotated
staggered-grids allowing strong fluctuations of the elastic
parameters. Despite these improvements, the use of cartesian grids is
a limitation for such numerical methods especially when it is
necessary to incorporate surface topography or curved interface.
Moreover, in presence of a non planar topography, the free surface
condition needs very fine grids (about 60 points by minimal Rayleigh
wavelength) to be approximated. In this context, our objective is to
develop high order unstructured mesh based methods for the numerical
solution of the system of elastodynamic equations for elastic media in
a first step, and then to extend these methods to a more accurate
treatment of the heterogeneities of the medium or to more complex
propagation materials such as viscoelastic media which take into
account the intrinsic attenuation.

F. Peyrusse, N. Glinsky, C. Gélis and S. Lanteri

A nodal discontinuous Galerkin method for site effects assessment in viscoelastic media—verification and validation in the Nice basin

Accepted for publication in Geophys. J. Int. (2014)

Propagation of a plane wave in a heterogeneous model of Nice area. Left figure: topography of Nice and location of the cross-section used for numerical simulations (black line). Middle figure: S-wave velocity distribution along the cross-section in the Nice basin. Right figure: amplification transfer functions for a vertically incident plane wave. This numerical simulation was performed using DGTD-P1 method for the solution of the elastodynamics equations coupled to a Generalized Maxwell Body (GMB) model of viscoelasticity (PhD thesis of Fabien Peyrusse). An unstructured triangular mesh with 107,707 elements has been used for the discretization of the heterogeneous model of the Nice area. This work is conducted in collaboration with CETE Méditerranée and IFSTTAR.

Scattering of a plane wave by an aircraft geometry. This numerical simulation was performed using a hybridized discontinuous Galerkin HDGFD-P1 method for the discretization of the frequency domain Maxwell equations in 3D combined to a domain decompositon based hybrid iterative-direct solution algorithm for the resulting system of algebraic equations. The underlying tetrahedral mesh consists of 357,038 vertices and 1,970,770 elements. Inside each element, the components of the electromagnetic field are approximated by a linear interpolation method (the total number of degrees of freedom for this problem is 47,298,480 for the hybridized DGFD-P1 method). The simulation was run on a 128 cores parallel system (Intel Xeon 2.66 GHz) and took 350 sec.

Scattering of a plane wave by a spherical cavity with a hole at one of its pole. This numerical simulation was performed using a hybrid explicit-implicit DGTD-P2 method. The elements of the underlying tetrahedral mesh are partitioned into two sets based on a geometric criterion: the set of implicit elements is composed of tetrahedra for which the geometric criterion is below a given threshold, while the explicit set is composed of the remaining elements. Numerical simulations have been conducted on 8 cores of a cluster of Intel Xeon 2.33 GHz based nodes interconnected by a high performance Myrinet network. The hybrid-explicit time stepping scheme combines a Leap-Frog scheme for time advancing the set of unknowns associated to the explicit part with a Crank-Nicolson scheme for time advancing the set of unknowns associated to the implicit part. This hybrid time integration strategy allowed to reduce the simulation time from 4 h 24 mn (fully explicit DGTD-P2 method) to 56 mn. The elements treated implicitly represent here 0.2 % of the whole set of 301,116 mesh elements. A parallel direct (sparse LU factorization) method is used for solving the implicit system at each time step.