MAGIQUE-3D is an INRIA Project-Team joint with University of Pau and Pays de l'Adour and CNRS (LMA, UMR 5142 and MIGP, UMR 5212)

The Magique-3D project-team is associated to two laboratories of University of Pau (Department of Applied Mathematics - LMA associated with CNRS, and Department of Modeling and Imaging in Geosciences - MIGP, also associated with CNRS). Gathering several researchers of different backgrounds in geophysics, physics, mathematics and scientific computing, MAGIQUE-3D team aims at developing sophisticated modeling tools, validating them in a rigorous way and applying them to real cases of geophysical interest. This project is intrinsically multi-disciplinary and is strongly related to the regional and national industrial environment. In particular, we develop strong collaborations with TOTAL but the topics studied can lead to applications other than petroleum engineering. During the period 2005-09, the research program of MAGIQUE-3D was mainly composed of two main topics that structured the original parts of the activities of the group. The first topic, entitled `Depth Imaging', was related to modeling of seismic wave propagation in complex geological structures, taking into account underlying physical phenomena. It has been defined jointly by working groups composed of members of MAGIQUE-3D and of its main industrial partner TOTAL in order to make sure that actual results of interest in the context of the oil industry could be reached. One usually tackles such problems by defining approximate models that either lead to less expensive numerical methods (for example by decreasing the number of unknowns by means of an approximation of the original equations), or to high-performance numerical methods applied to the full system, which leads to an accurate solution but implies a high computation cost. Both of these approaches have been considered in the project.

The second topic, that could be given the general title `Advanced modeling in wave propagation', was related to the realistic numerical simulation of complex three-dimensional geophysical phenomena and its comparison with real data recorded in the field. One of the main issues was the choice of the numerical method, which implicitly defines the subset of configurations that can be studied. Comparisons with recorded seismic data for real geological cases have been carried out and then, numerical algorithms have been optimized and implemented on parallel computers with a large number of processors and a large memory size, within the framework of message-passing programming. We have reached a maximum resolution in terms of the seismic frequencies that can be accurately simulated on currently available supercomputers.

During the period 2005-2009, MAGIQUE-3D has worked on the development of optimized software for the simulation of 3D phenomena in geophysics. The team tackled this question addressing different and complementary issues such as the development of new discretization schemes, the construction of new boundary conditions used to reduce the size of the computational domain, the porting of our softwares on GPU to speed up their performances. All the algorithms we have proposed are compatible with high resolution techniques. We now would like to continue working on the same subjects but also to apply our knowledge on the direct problem to the solution of inverse problems. It is now a natural goal for the team since we develop a significant research program with Total, in particular in the context of the research program DIP (Depth Imaging Partnership), where the solution of inverse problems has become a big challenge for oil industry.

Dimitri Komatitsch was awarded the Bull-Joseph Fourier Prize 2010 for his work on the parallelization of codes to simulate global phenomena, as well as for the impact of his research, which enables the effects of earthquakes and their aftershocks to be predicted more effectively.

**Inverse scattering problems.**The determination of
the shape of an obstacle from its effects on known
acoustic or electromagnetic waves is an important problem
in many technologies such as sonar, radar, geophysical
exploration, medical imaging and nondestructive testing.
This inverse obstacle problem (IOP) is difficult to
solve, especially from a numerical viewpoint, because it
is ill-posed and nonlinear
. Moreover the precision in
the reconstruction of the shape of an obstacle strongly
depends on the quality of the given far-field pattern
(FFP) measurements: the range of the measurements set and
the level of noise in the data. Indeed, the numerical
experiments (for example
,
,
,
) performed in the resonance
region, that is, for a wavelength that is approximately
equal to the diameter of the obstacle, tend to indicate
that in practice, and at least for simple shapes, a
unique and reasonably good solution of the IOP can be
often computed using only one incident wave and
*full aperture*far-field data (FFP measured only at
a limited range of angles), as long as the aperture is
larger than
. For smaller apertures the reconstruction of the
shape of an obstacle becomes more difficult and nearly
impossible for apertures smaller than
/4.

This plus the fact that from a
mathematical viewpoint the FFP can be determined on the
entire sphere
S1from its knowledge on a
subset of
S1because it is an
*analytic*function, we propose
,
a solution methodology to
extend the range of FFP data when measured in a limited
aperture and not on the entire sphere
S1. It is therefore possible to
solve the IOP numerically when only limited aperture
measurements are available. The objective of
Magique-3D is to extend this work to 3D
problems of acoustic scattering.

We would like also to consider electrical impedance tomography, which is a technique to recover spatial properties of the interior of an object from measurements of the potential of the boundary of the object (see by Liliana Borcea and by Martin Hanke and Martin Brühl). In shape identification problems, the measured quantities do not depend linearly on the shape of the obstacle. Most popular approaches describe the objects by appropriate parameterizations and compute the parameters by iterative schemes based on Newton-type methods which require to solve a collection of direct problems. We plan to begin with this kind of approaches since we already have an efficient solver for the direct problem and these iterative schemes are known to be very successful in many cases. Their main disadvantage is that they are expensive since they must solve a direct problem at each step. We hope that our solver will be sufficiently optimized to limit this disadvantage.

**Depth Imaging in the context of DIP.**The challenge
of seismic imaging is to obtain the best representation
of the subsurface from the solution of the full wave
equation that is the best mathematical model according to
the time reversibility of its solution. The most used
technique of imaging is RTM (Reverse Time Migration),
, which is an iterative
process based on the solution of a collection of wave
equations. The high complexity of the propagation medium
requires the use of advanced numerical methods, which
allows one to solve several wave equations quickly and
accurately. The research program DIP has been defined by
researchers of
Magique-3D and engineers of
Totaljointly.
It has been created with the aim of gathering researchers
of INRIA, with different backgrounds and the scientific
programm will be coordinated by
Magique-3D. In
this context,
Magique-3D will contribute by working on the
inverse problem and by continuing to develop new
algorithms in order to improve the RTM.

**Tomography.**Seismic tomography allows one to
describe the geometry and the physical characteristics of
the heterogeneities inside the earth by analyzing the
propagation speed of the seismic waves. The last past ten
years have known a lot of developments like the
introduction of sensitivity kernels which complete the
rai theory which is often used in short period
seismology. However the kernel sensitivity theory
introduces very large matrices and the computations which
are necessary to solve the inverse problem are very
expensive. The idea would be to represent the kernels by
a reduced number of parameters by using appropriate
methods of compression. The wavelets of Haar have been
used by Chevrot and Zhao
but they
do not seem to be optimal. We propose to address this
kind of issue by aiming at giving parcimonious
representations of kernels of sensitivity.

**Potential techniques Inversion: parallel Hybrid
local/global optimization.**In many applications,
acoustic and seismic inversion are not enough to
reconstruct multiphase component structures. Different
potential techniques like electrical capacitance,
resistivity, gravimetry and magnetometry are necessary.
As potential techniques require the resolution of Poisson
or Laplace-like equations, huge linear systems need to be
solved using very large multi-CPU/multi-GPU clusters.
Today, finite volume/conjugate gradient solvers are
running on 200 processors for electrical capacitance and
gravimetry problems at CINES/Montpellier supercomputing
center as a proof of concept. The very promising results
obtained lead us to run them on more than 2000 CPUs and
perhaps 200 or 300 GPU clusters. By developing higher
order versions we will be able to increase significantly
the accuracy of the solutions and the speed of
calculations. As the inversion process is performed
iteratively, it should be worthwhile to incorporate at
the same time local (least square methods) and global
(neighborhood/very fast simulated annealing) optimization
techniques. An acceptable model could then be taken as
the new current model and at some degree, data
compression will be used in order to compute an accurate
sensitivity matrix for this current model computed with
local/global optimization. Then, using local/global
optimization, purely sensitivy matrix based inversion
could be used to accelerate all the inversion processes.
In the case of electrical capacitance tomography, the
forward problem is accelerated by almost a factor of 100
when a GPU is preferred to a CPU. On a multiCPU/multiGPU,
an asynchronous strategy of communications between
processors and copies of informations between host (CPU)
and device (GPU) is retained and will be implemented more
properly. We plan to apply this to joint inversion at the
regional and global earth scales. A collaboration with
CAPS entreprises and GENCI has been approved in November
2009 for the multi GPU porting of a 3D finite volume code
implemented using MPI by Roland Martin. On a signe GPU an
acceleration factor of 23 has been already obtained. This
collaboration is under its way. We have the intention to
extend this to high order spectral element method in the
context of AHPI ANR project in 2010 by taking the
SPECFEM3D parallel code as a fundamental code that will
be transformed into an elliptic large system solver.

The main activities of Magique-3D in modeling are the derivation and the analysis of models that are based on mathematical physics and are suggested by geophysical problems. In particular, Magique-3D considers equations of interest for the oil industry and focus on the development and the analysis of numerical models which are well-adapted to solve quickly and accurately problems set in very large or unbounded domains as it is generally the case in geophysics.

**High-Order Schemes in Space and Time.**Using the full
wave equation for migration implies very high computational
burdens, in order to get high resolution images. Indeed, to
improve the accuracy of the numerical solution, one must
considerably reduce the space step, which is the distance
between two points of the mesh representing the
computational domain. Obviously this results in increasing
the number of unknowns of the discrete problem. Besides,
the time step, whose value fixes the number of required
iterations for solving the evolution problem, is linked to
the space step through the CFL (Courant-Friedrichs-Levy)
condition. The CFL number defines an upper bound for the
time step in such a way that the smaller the space step is,
the higher the numbers of iterations (and of
multiplications by the stiffness matrix) will be. The
method that we proposed in
allows for the use of local
time-step, adapted to the various sizes of the cells and we
recently extended it to deal with
p-
adaptivity
. However, this method can not
yet handle dissipation terms, which prevents us for using
absorbing boundary conditions or Perfectly Matched Layers
(PML). To overcome this difficulty, we will first tackle
the problem to used the modified equation technique
,
,
with dissipation terms, which
is still an open problem.

We are also considering an alternative
approach to obtain high-order schemes. The main idea is to
apply first the time discretization thanks to the modified
equation technique and after to consider the space
discretization. Our approach involves
p-harmonic operators, which can not be discretized by
classical finite elements. For the discretization of the
biharmonic operator in an homogeneous acoustic medium, both
C1 finite elements (such as the Hermite ones) and
Discontinuous Galerkin Finite Elements (DGFE) can be used
while in a discontinuous medium, or for higher-order
operators, DGFE should be preferred
. This new method seems to be
well-adapted to
p-adaptivity. Therefore, we now want to couple it to
our local time-stepping method in order to deal with
hp-adaptivity both in space and in time. We will then
carry out theoretical and numerical comparisons between
this technique and the classical modified equation
scheme.

Once we have performant
hp-adaptive techniques, it will be necessary to obtain
error-estimators. Since we consider huge domain and complex
topography, the remeshing of the domain at each time-step
is impossible. One solution would be to remesh the domain
for instance each 100 time steps, but this could also
hamper the efficiency of the computation. Another idea is
to consider only
padaptivity, since in this case there is no need to
remesh the domain.

**Mixed hybrid finite element methods for the wave
equation.**The new mixed-hybrid-like method for the
solution of Helmholtz problems at high frequency we have
built enjoys the three following important properties: (1)
unlike classical mixed and hybrid methods, the method we
proposed is not subjected to an inf-sup condition.
Therefore, it does not involve numerical instabilities like
the ones that have been observed for the DGM method
proposed by Farhat and his collaborators
,
. We can thus consider a larger
class of discretization spaces both for the primal and the
dual variables. Hence we can use unstructured meshes, which
is not possible with DGM method (2) the method requires one
to solve Helmholtz problems which are set inside the
elements of the mesh and are solved in parallel(3) the
method requires to solve a system whose unknowns are
Lagrange multipliers defined at the interfaces of the
elements of the mesh and, unlike a DGM, the system is
hermitian and positive definite. Hence we can use existing
numerical methods such as the gradient conjugate method. We
intend to continue to work on this subject and our
objectives can be described following three tasks: (1)
Follow the numerical comparison of performances of the new
methods with the ones of DGM. We aim at considering high
order elements such as R16-4, R32-8, ...; (2)Evaluate the
performance of the method in case of unstructured meshes.
This analysis is very important from a practical point of
view but also because it has been observed that the DGM
deteriorates significantly when using unstructured meshes;
(3) Extend the method to the 3D case. This is the ultimate
objective of this work since we will then be able to
consider applications.

Obviously the study we propose will contain a mathematical analysis of the method we propose. The analysis will be done in the same time and we aim at establishing a priori and a posteriori estimates, the last being very important in order to adopt a solution strategy based on adaptative meshes.

**Boundary conditions.**The construction of efficient
absorbing conditions is very important for solving wave
equations, which are generally set in unbounded or very
large domains. The efficiency of the conditions depends on
the type of waves which are absorbed. Classical conditions
absorb propagating waves but recently new conditions have
been derived for both propagating and evanescent waves in
the case of flat boundaries. MAGIQUE-3D would like to
develop new absorbing boundary conditions whose derivation
is based on the full factorization of the wave equation
using pseudodifferential calculus. By this way, we can take
the complete propagation phenomenon into account which
means that the boundary condition takes propagating,
grazing and evanescent waves into account, and then the
absorption is optimized. Moreover our approach can be
applied to arbitrarily-shaped regular surfaces.

We intend to work on the development of interface conditions that can be used to model rough interfaces. One approach, already applied in electromagnetism , consists in using homogenization methods which describes the rough surface by an equivalent transmission condition. We propose to apply it to the case of elastodynamic equations written as a first-order system. In particular, it would be very interesting to investigate if the rigorous techniques that have been used in , can be applied to the theory of elasticity. This type of investigations could be a way for MAGIQUE-3D to consider medical applications where rough interfaces are often involved. Indeed, we would like to work on the modelling and the numerical simulation of ultrasonic propagation and its interaction with partially contacting interfaces, for instance bone/titanium in the context of an application to dentures, in collaboration with G. Haiat (University of Paris 7).

**Approximation of one-way equations**Seismic migration
techniques used in petroleum field are based on the
resolution of the wave equation. We have considered the
issue of computing the solution from a one way formulation
of the wave equation. The numerical resolution of this
problem is difficult and requires the approximation of a
Fourier Integral Operator (FIO). Computing FIO is very
heavy (long time computation and big storage space). An
algorithm based on a Fourier transform representation of
FIO was proposed in
where the symbol of the FIO was
approximated by separation variables functions. Although
this approach reduces the computational cost, it does not
give good results in heterogenous media. The objective of
this study consists in developing a fast and precise
algorithm for FIO computation. Many studies have been
devoted to a fast computation of FIOs and
pseudo-differential operators. For instance, the paper of
Lamoureux, Margrave
discusses some aspects of the
computation of pseudo-differential operators. We can quote
also the work of Bao and Symes
on the expansion of the
principal symbol of the pseudo-differential operators
(homogeneous of degree 0 in
). Several techniques based on the separation of the
operator kernels have been also proposed for instance in
. A different approach to
compressing operators is the partitioned separated method
that consists in isolating off-diagonal squares of the
operator kernel, and approximating each of them by low-rank
matrix, for example: the partitioned SVD method described
in
or the H-matrix for
Hierarchical matrix
techniques. In
a method for discrete symbol
calculus was introduced. A multiscale tool which is the
curvelets
has also been proposed to speed
up the computation of FIOs. As shown in
, curvelets provide a
parsimonious representation of FIOs which can lead to a
fast computation of FIOs. Taking advantage of the
parsimonious representation of FIOs in the Curvelets
domain, curvelets have been already used in seismic
migration for instance for multiple removal
and the restoration of
migration amplitudes
. However and unfortunately,
the direct computation of the curvelet representation of
FIOs is not evident
. In
, an algorithm based on the
restriction of the FIO kernel to subsets of the temporal
and frequency domains was proposed. Indeed, unlike the
curvelets which work in the phase space (the product of the
frequency and spatial spaces), this algorithm decomposes
the FIO in the frequency domain. The FIO kernel is
decomposed into two terms: a diffeomorphism which can be
computed with a nonuniform Fast Fourier Transform FFT and a
residual factor computed with a numerical separation of the
spatial and frequency variables. The computational cost and
the storage space in this case are considerably
reduced.

**Nonlinear problems in fluid dynamics.**In order to
model heat transfers, fluid-solid interactions, in
particular landslides and tsunamis induced by earthquakes,
tremors induced by fluid motions in volcanoes, sharp
solid-to-fluid transitions in some planets, it is of
crucial importance to develop efficient parallel solvers on
multicore/multi-processor supercomputing platforms. High
order finite volumes introducing compact schemes or
spectral-like integrations as well as high order finite
elements and their related high order boundary conditions
are needed to take into account, at the same time,
discontinuities in geological structures, sharp variations
and shocks in fluid velocities and properties (density,
pressure and temperature), and the coupling between both
codes. Discrete Galerkin techniques, spectral finite
volumes or finite-volume techniques should be taken into
account in compact schemes in order to reduce drastically
the memory storage involved and compute larger models.
Viscous compressible and incompressible codes need to be
solved using non-conforming meshes between solid and fluid,
and large linear systems need to be solved on very huge
multi-CPU/multi-GPU supercomputers. Moving meshes close to
the interface between solids and fluids should be taken
into account by dynamic or adaptive remeshing. Furthermore
we developped PML for the full compressible Navier-Stokes
system of equations
using finite-differences
discretization in curvilinear coordinates and we are
planning to extend PML conditions to both compressible and
incompressible viscous flows in the context of high order
finite volumes or Discontinuous galerkin methods.

Another direction that we would like to consider would be the use of solitons in nonlinear problems. Indeed, a soliton is an interesting tool for modeling and explaining some nonlinear phenomena. For example tsumanis are sometimes explained by the emergence of solitons created by earth tremor. Strain solitons can be also used to explain the propagation of breaking in solids . Therefore it would be interesting to investigate more this issue.

A tremendous increase of the sustained power of supercomputers has occurred in the last few years, in particular with the first `petaflops' machines that have been built in the USA and also with new technology such as general-purpose computing on graphics cards (so-called `GPU computing'). Nowadays, one has access to powerful numerical methods that, when implemented on supercomputers, make it possible to simulate both forward and inverse seismic wave propagation problems in complex three-dimensional (3D) structures. Moreover, very spectacular progress in computer science and supercomputer technology is amplified by recent advances in High Performing Computing (HPC) both from a software and hardware point of view. One can in this respect say that HPC should make it possible in the near future to perform large-scale calculations and inversion of geophysical data for models and distributed data volumes with a resolution impossible to reach in the past. Our group has for instance already run simulations in parallel on 150,000 processor core, obtaining an excellent sustained performance level and almost perfect performance scaling .

We will therefore work on three HPC issues in the next few years. The first will be very large scale inversion of seismic model based on sensitivity kernels. In the context of a collaboration with TOTAL and also with Prof. Jeroen Tromp at Princeton University (USA), we will use adjoint simulations and sensitivity kernels to solve very-large scale inverse problems for seismology and for oil industry models, for instance deep offshore regions and/or complex foothills regions or sedimentary basins. The second issue is Graphics Processing Unit (GPU) computing: in the context of a collaboration with Prof. Gordon Erlebacher (Florida State University, USA) and Dr. Dominik Göddeke (Technical University of Dortmund, Germany) we have modified our existing seismic wave propagation software packages to port them to GPU computing in order to reach speedup factors of about 20x to 30x on GPU clusters (for instance at GENCI/CEA CCRT in Bruyères-le-Châtel, France). The third issue is porting our software packages to Symmetric Multi Processors (SMP) massive multicore computing to take advantage of future processors, which will have a large number of cores on petaflops or exaflops machine. In the context of a collaboration with Prof. Jesús Labarta and Prof. Rosa Badia from the Barcelona Supercomputing Center (Catalonia, Spain) we will use their 'StarSs' programming environment to take advantage of multicore architectures while keeping a flexible software package relatively simple to modify for geophysicists that may not be computer-programming experts.

The main objective of modern seismic processing is to find the best representation of the subsurface that can fit the data recorded during the seismic acquisition survey. In this context, the seismic wave equation is the most appropriate mathematical model. Numerous research programs and related publications have been devoted to this equation. An acoustic representation is suitable if the waves propagate in a fluid. But the subsurface does not contain fluids only and the acoustic representation is not sufficient in the general case. Indeed the acoustic wave equation does not take some waves into account, for instance shear waves, turning waves or the multiples that are generated after several reflections at the interfaces between the different layers of the geological model. It is then necessary to consider a mathematical model that is more complex and resolution techniques that can model such waves. The elastic or viscoelastic wave equations are then reference models, but they are much more difficult to solve, in particular in the 3D case. Hence, we need to develop new high-performance approximation methods.

Reflection seismics is an indirect measurement technique that consists in recording echoes produced by the propagation of a seismic wave in a geological model. This wave is created artificially during seismic acquisition surveys. These echoes (i.e., reflections) are generated by the heterogeneities of the model. For instance, if the seismic wave propagates from a clay layer to sand, one will observe a sharp reflected signal in the seismic data recorded in the field. One then talks about reflection seismics if the wave is reflected at the interface between the two media, or talks about seismic refraction if the wave is transmitted along the interface. The arrival time of the echo enables one to locate the position of this transition, and the amplitude of the echo gives information on some physical parameters of the two geological media that are in contact. The first petroleum exploration surveys were performed at the beginning of the 1920's and for instance, the Orchard Salt Dome in Texas (USA) was discovered in 1924 by the seismic-reflection method.

We already applied our techniques to the study of strong ground motion and associated seismic risk in the Los Angeles basin area. This region consists of a basin of great dimension (more than 100 km ×100 km) which is one of the deepest sedimentary basins in the world (the sedimentary layer has a maximum thickness of 8.5 km underneath Downtown Los Angeles), and also one of the most dangerous in the world because of the amplification and trapping of seismic waves. In the case of a small earthquake in Hollywood (September 9, 2001), well recorded by more than 140 stations of the Southern California seismic network TriNet, we managed for the first time to fit the three components of the displacement vector, most of the previous studies focusing on the vertical component only, and to obtain a good agreement until relatively short periods (2 seconds).

We wish to improve these studies of seismic risk in densely populated areas by considering other regions of the world, for example the Tokyo basin, the area of Kobe or the Mexico City region. We also plan to generalize this type of calculations to the knowledge and modeling of site effects, i.e. of the local amplification of the response of the ground to seismic excitation. The study of such effects is an important observation in urban areas to be able to anticipate the damage to constructions and, if necessary, to plan the organization of search and rescue operations. It is also a significant element of the definition of paraseismic standards. Site effects can be determined experimentally, but that requires the installation of stations for a sufficient period of time to record a few tens of seismic events. Numerical modeling makes it possible to avoid this often long and difficult experimentation, assuming of course that one has good knowledge of the geological structure of the subsurface in the studied area. We thus propose in the Magique-3Dproject to use the numerical techniques mentioned above for instance to quantify the effects of topographic variations in the structure.

The problems of seismic imaging can be related to non destructive testing, in particular medical imaging. For instance, the rheumatologist are now trying to use the propagation of ultrasounds in the body as a noninvasive way to diagnose osteoporosis. Then, the bones can be regarded as elastodynamic or poroelastic media while the muscles and the marrow can be regarded as acoustic media. Hence the computational codes we use for seismic imaging could be applied to such a problem.

The Magique-3D project is based (in part) on existing software packages, which are already validated, portable and robust. The SPECFEM3D software package, developed by Dimitri Komatitsch and his colleagues in collaboration with Jeroen Tromp and his colleagues at the California Institute of Technology and at Princeton University (USA), and which is still actively maintained by Dimitri Komatitsch and his colleagues, allows the precise modeling of seismic wave propagation in complex three-dimensional geological models. Phenomena such as anisotropy, attenuation (i.e., anelasticity), fluid-solid interfaces, rotation, self-gravitation, as well as crustal and mantle models can be taken into account. The software is written in Fortran95 with MPI message-passing on parallel machines. It won the Gordon Bell Prize for best performance of the Supercomputing'2003 conference. In 2006, Dimitri Komatitsch established a new collaboration with the Barcelona Supercomputing Center (Spain) to work on further optimizing the source code to prepare it for very large runs on future petaflops machines to solve either direct or inverse problems in seismology. Optimizations have focused on improving load balancing, reducing the number of cache misses and switching from blocking to non-blocking MPI communications to improve performance on very large systems. Because of its flexibility and portability, the code has been run successfully on a large number of platforms and is used by more than 150 academic institutions around the world. In November 2008 this software package was again among the six finalists of the pretigious Gordon Bell Prize of the SuperComputing'2008 conference in the USA for a calculation performed in parallel on 150,000 processor cores, reaching a sustained performance level of 0.16 petaflops.

This software, written in FORTRAN 90, simulates the
propagation of acoustic waves in heterogeneous 2D and 3D
media. It is based on an Interior Penalty Discontinuous
Galerkin Method (IPDGM). The 2D version of the code has been
implemented in the Reverse Time Migration (RTM) software of
Total in the
framework of the PhD. thesis of Caroline Baldassari and the
3D version should be implemented soon. The 2D code allows for
the use of meshes composed of cells of various order (
p-adaptivity in space). For the time discretization, we
used the local time stepping strategy described at
section
, item
**High-Order Schemes in Space and Time**which permits not
only the use of different time-step, but also to adapt the
order of the time-discretization to the order of each cells (
hp-adaptivity in time). These functionalities will be
soon implemented in the 3D code.

The main competitors of IPDGFEM are codes based on Finite
Differences, Spectral Element Method or other Discontinuous
Galerkin Methods (such as the ADER schemes). During her PhD.
thesis, Caroline Baldassari compared the solution obtained by
IPDGFEM to the solution obtained by a Finite Difference
Method and by a Spectral Element Method (SPECFEM). To
evaluate the accuracy of the solutions, we have compared it
to analytical solutions provided by the codes Gar6more (see
below). The results of these comparisons is: a) that IPDGFEM
outperforms the Finite Difference Methods both in terms of
accuracy and of computational burden and b) that its
performances are similar to Spectral Element Methods. Since
IPDGFEM allows for the use of meshes based on tetraedrons,
which a more appropriate to mesh complex topographies, and
for the
p-adaptivity, we decided to implement it in the RTM
code of
Total. Of course,
we also used these comparisons to validate the code. Now, it
remains to compare the performances of IPDGFEM to the ADER
schemes.

The software GAR6MORE2D and GAR6MORE3D compute the analytical solutions to problems of wave propagation in infinite bilayered media respectively in two and in three dimensions. The medium can be composed of a) two acoustic layers; b) two poroelastic layers; c) two elastodynamic layers ; d) one acoustic and one poroelastic layers; or e) one acoustic and one elastic layers. The codes can also consider the case of homogeneous medium, either infinite or semi-infinite with Neumann or Dirichlet boundary conditions. They are written in FORTRAN90 and are based on the Cagniard-de Hoop method , , , , , .

The main objective of these codes is to provide reference
solutions in order to validate numerical codes. They have
been already used by J. Tromp and C. Morency to
validate their code of poroelastic wave propagation
. They are freely distributed
under a CECILL licence and can be downloaded on the website
http://

We have proposed a solution methodology to extend the
range of FFP data when measured in a limited aperture and
not on the entire sphere
S1. Therefore it would be
possible to solve numerically the IOP when only limited
aperture measurements are available. However, due to the
analyticity nature of the FFP, the reconstruction or the
extension of the far-field pattern from limited
measurements is an inverse problem that is
*severely ill-posed*and therefore very challenging
from a numerical viewpoint. Indeed, preliminary numerical
results indicate that the reconstruction of the FFP using
the discrete
L2minimization with the standard
Tikhonov regularization is very sensitive to the noise
level in the data. The procedure is successful only when
the range of measurements is very large which is not
realistic for most applications.

We propose a multi-step procedure for
extending/reconstructing the FFP from the knowledge of
limited measurements. The proposed solution methodology
addresses the ill-posedness nature of this inverse problem
using a
*total variation*of the FFP coefficients as a penalty
term. Consequently the new cost function is no longer
differentiable. We restore the differentiability to the
cost function using a perturbation technique
which allows us to apply the
Newton algorithm for computing the minimum. The multi-step
feature of the proposed method consists in extending the
FFP at each step by an
ndegrees increment.

We investigate the effect of the frequency regime and the noise level of the performance of the proposed solution methodology. Preliminary results obtained in the case of two-dimensional sound-soft disk-shaped scatterer have been performed. They illustrate the potential of the solution methodology for enriching the FFP measurements for various frequencies and levels of noise. The solution methodology and the numerical results have been presented in a Research Report and a paper has been submitted in November.

The new method involving
p-harmonic operator described in section
has been detailed in a reseach
report
and in a submitted paper. We
have proved the convergence of the scheme and its stability
under a CFL condition. Numerical results in 1D and 2D show
that this CFL condition is slightly greater than the CFL
condition of the second-order Leap-Frog scheme. We are now
considering 3D experiments to confirm this observation. We
are also carrying out a theoretical analysis in order to
obtain an explicit expression of the CFL condition. Our
results have been presented at the peer-reviewed WONAPDE
(Concepcion, January 2010) and Congrès Français
d'Acoustique (Lyon, April 2010) conferences
,
and a poster has been presented
at the National Congress in Numerical Analysis (CANUM,
Carcans-Maubuisson, 2010)
.

The Interior Penalty Discontinuous Galerkin Method , , we use in the IPDGFEM code requires the introduction of a penalty parameter. Except for regular quadrilateral or cubic meshes, the optimal value of this parameter is not explicitely known. Moreover, the condition number of the resulting stiffness matrix is an increasing function of this parameter, but the precise behaviour has not been explicited neither. We have carried out a theoretical and numerical study of the CFL condition for quadrilateral and cubic meshes, which is the object of a research report . The numerical study of the penalization parameter and of the CFL condition on triangular meshes has been the object of the internship of Jean-Michel Bart.

The Perfectly Matched Layer (PML) absorbing technique has become popular in numerical modeling in elastic or poroelastic media because of its efficiency to absorb waves at non-grazing incidence. However, after numerical discretization, at grazing incidence large spurious oscillations are sent back from the PML into the main domain. The PML then becomes less efficient in the case of sources located close to an edge of the truncated physical domain under study, in the case of thin slices or for receivers located at large offset. In we developed a PML improved at grazing incidence for the elastic wave equation based on an unsplit convolutional formulation for the seismic wave equation written as a first-order system in velocity and stress. This so-called Convolution-PML (CPML) has a cost that is similar in terms of memory storage to that of the classical PML. In we introduced a similar technique for the two-dimensional Biot poroelastic equations and show its efficiency for both non dissipative and dissipative Biot porous models based on a fourth-order staggered finite-difference method used in a thin mesh slice. The results obtained are significantly improved compared to the classical PML. In we applied our unsplit CPML to viscoelastic media, and in we developed a variational formulation of the CPML. More recently, in we developed a version called Auxiliary Differential Equation PML (ADE-PML) that is very well suited to higher-order time schemes. In such a condition is studied for Navier-Stokes. In we develop a stable variational formulation of these improved PMLs for fluid/solid models and for sensitivity kernel calculations. This will be compared to other techniques like the Indirect Boundary Element Method (IBEM) developped by in 2011 to understand which are the fundamental modes excited in complex fluid-solid interface models. Furthermore CPML will be applied to model fluid-solid media in which fractures and salt domes are present and automatically retrieved by Hough Transform . Finally, in we developed an efficient absorbing boundary formulation for the stratified, linearized, ideal MHD equations based on an unsplit, convolutional perfectly matched layer and applied it to numerical models of the Sun.

We have investigated different approaches but unfortunately we have not obtained satisfactory results for different reasons. We have first considered the curvelets but we have not tried to implement the method for the computation of FIOs because of the lack in time and -to the best of our knowledge- the non availability of numerical studies on the subject since 2004 when the theoretical results have been published. Then we have studied the decomposition of FIOs in the frequency domain . The numerical results obtained in and the first numerical tests that have been done are promising. However, due to the randomized character of the separation algorithm a direct inclusion of the algorithm in the GSP code should not be evident for the moment. Finally, we have considered the computation of the reflection coefficient using the inversion of an Helmholtz operator. This approach is still under consideration. This method should improve the computation of the reflection coefficient but we must apply a robust numerical method for weak elliptic problems. The ideas carried out in 6.2.8 should be considered.

We have constructed a new absorbing boundary condition taking into account propagating, evanescent and grazing waves for arbitrarily-shaped convex surfaces. The condition taking into account propagating and evanescent waves has been detailed in a submitted paper, while the complete condition, which involved a fractional derivative, has been presented at the peer-reviewed conferences WONAPDE (Concepcion, January 2010), Congrès Français d'Acoustique (Lyon, April 2010) and SIAM Annual Meeting (Pittsburgh, July 2010) , , and at the National Congress in Numerical Analysis (CANUM, Carcans-Maubuisson, June 2010) . The extension of this condition to Helmholtz equation and its performance analysis has been the object of the internship of Anthony Vivier.

In order to justify the use of our code IPDGFEM for the Reverse Time Migration, we have carried out a performance analysis of the Interior Penalty Discontinuous Galerkin method and of the Spectral Element Method. This analysis has been presented in a submitted paper and at the peer-reviewed conferences WONAPDE (Concepcion, January 2010) and CANUM (Carcans-Maubuisson, Juin 2010) . The local-time stepping method we have developed to optimize our code is the object of a submitted paper and has been presented at the ISFMA Symposium (Shanghaï, 2010) .

We have proposed a new Perfectly Matched Layer for Shallow Water equations, based on a transformation proposed by Hu . The details of its construction, as well as numerical results illustrating its performances, are presented in

The computation of analytical solution of wave propagation problems in acoustic/poroelastic media has been detailed in , . These computations were implemented in Gar6more2D (for the 2D problem) and Gar6more3D (for the 3D problem).

In order to better understand the internal structure of asteroids orbiting in the Solar system, and then the response of such objects to impacts, seismic wave propagation in asteroid 433-Eros is performed numerically based on a spectral-element method at seismic frequencies from 0 Hz to 5 Hz. In the year 2000, the NEAR Shoemaker mission to Eros has provided images of the asteroid surface, which contains numerous fractures that likely extend to its interior. Our goal is to be able to propagate seismic waves resulting from an impact in such models. For that purpose we create and mesh both homogeneous and fractured models with a highly-dispersive regolith layer at the surface using the CUBIT mesh generator developed at Sandia National Laboratories (USA). The unstructured meshes are partitioned using the METIS software package in order to minimize edge-cuts and therefore optimize load balancing in our parallel non-blocking MPI implementation. In and we performed actual simulations and show that we can obtain good performance levels and good scaling when we implement overlapping of communications with calculations. Calculations were run at CINES in Montpellier, France.

In the petroleum industry, seismic data is the starting
point of many processes for the exploration for oil
reservoirs. The dimensions of these
*seismic cubes*keep increasing as the regions
undergoing exploration keep growing and have increased
spatial resolution. We have developed a new bricked cache
system suitable
for propagating seismic
horizons in such large volumes. To ensure the optimality of
such surface extraction, the propagation algorithm must
access randomly into the data volume. This lack of data
locality imposes that the volume resides entirely in the
main memory to reach decent performances. In case of
volumes larger than the memory, we showed that using a
classical brick cache strategy can also produce good
performances until a certain size. As the size of these
volumes increases very quickly, and can now reach more than
200GB, we demonstrated that the performances of the
classical algorithm are dramatically reduced when processed
on standard workstation with a limited size of memory
(currently 8GB to 16GB). In order to handle such large
volumes, we introduced a new slimming brick cache strategy
where bricks size evolves according to processed data : at
each step of the algorithm, processed data could be removed
from the cache. This new brick format allows to have a
larger number of brick loaded in memory. We further
improved the releasing mechanism by filling in priority the
holes that appear in the surface during the
propagation process. With this new cache strategy, horizons
can be extracted into volumes that are up to 75 times the
size of the available cache memory.

With the very rapid evolution of personal computers, computer clusters, and supercomputers, nowadays the seismic wave equation can be solved with very good accuracy using very precise techniques implemented based on parallel computing in the context of so-called High-Performance Computing (HPC). This has been a central part of our research activity in the last few years and increasingly more in 2008 and 2009. In particular with some colleagues from the CINES supercomputing center in Montpellier (France) we have performed some very large scale calculations that are currently being published.

Using the high-order finite-element method implemented in our SPECFEM3D software package , we for instance studied the influence of topography modeled at very high resolution on seismic wave propagation in the region of Taipei in Taiwan , .

We also applied the technique to model seismic wave propagation at very high frequency in the whole Earth , . In November 2008 our SPECFEM3D software package was again among the six finalists of the pretigious Gordon Bell Prize of the SuperComputing'2008 conference in the USA for a calculation performed in parallel on 150,000 processor cores, reaching a sustained performance level of 0.16 petaflops. And in June 2010 Dimitri Komatitsch won the first BULL Joseph Fourier Prize with it.

In the context of a collaboration with Gordon Erlebacher from Florida State University (USA) who visited us for a month in May-June 2010 and we ported our modeling algorithm to a NVIDIA graphics video card (Graphical Processing Units – GPU) using the CUDA language on top of a C implementation of our code. This technique is known as General-purpose Processing on Graphical Processing Units (GPGPU) and had never been used before for a high-order finite-element technique, which induces significant technical problems in particular regarding memory accesses. regarding memory accesses. In several recent articles , , we used it to improve the speed of our code by a factor of 20 to 30 on large GPU clusters. In we accelerated a 3D finite-difference wave propagation code by a factor between 20x and 60x using GPU graphics cards. In we solved a very large problem on 6144 processor cores to study the splitting of shear waves at the bottom of the Earth's mantle. In we used large scale 3D simulations to study the effects of 3D models of viscoelasticity in the full Earth, and in we showed how such simulations can be performed in quasi-real time after a real earthquake and stored online in a catalog of seismograms for all large earthquakes worldwide.

Depth Imaging Partnership (DIP)

Period: 2010 January - 2012 december, Management: INRIA Bordeaux Sud-Ouest, Amount: 3600000 euros. 50 000 euros have been devoted to hire an associate engineer (from Oct. 2010 to Sept. 2011).

Propagation automatique de Surface nD Filtrage et traitement de la sismique avant stack Period: 2008 January - 2010 december, Management: INRIA Bordeaux Sud-Ouest, Amount: 45000 euros.

Analyse méthodologique pour la génération de maillages irréguliers et de leur décomposition en sous-domaines sur calculateurs parallèles pour la propagation d'ondes sismiques en milieu géologiques complexes Period: 2009 May - 2010 April, Management: INRIA Bordeaux Sud-Ouest, Amount: 50000 euros

Optimisation de codes pour la migration terrestre d'ondes élastiques.

Period: 2009 January - 2010 December, Management: INRIA Bordeaux Sud-Ouest, Amount: 60000 euros.

Schémas en temps d'ordre élevé pour la simulation d'ondes élastiques en milieux fortement hétérogènes par des méthodes DG.

Period: 2010 November - 2013 October, Management: INRIA Bordeaux Sud-Ouest, Amount: 150000 euros.

In the context of the Associate Team MAGIC.

Period: 2009 January - 2011 December, Total Amount: 15000 USD

The PhD fellowship of Elodie Estecahandy is partially (50%) financed by the Conseil Régional d'Aquitaine.

Joint project with BCAM (Basque Center of Applied Mathematics) funded by the Conseil Régional d'Aquitaine and the Basque Government in the framework of the Aquitaine-Euskadi Call. Total Amount: 14 000 euros.

Magique-3D maintains active collaborations with Total . In
the context of depth imaging and with the collaboration of
Henri Calandra from Total , Magique-3D coordinates research
activities dealing with the development of high-performance
numerical methods for solving wave equations in complex
media. This project involves French academic researchers in
mathematics, computing and in geophysics, and is funded by
Total . At the end of 2009, two PhD students working in
Magique-3D from 2007, have defended their PhD dealing with
new numerical imaging methods that are based on the solution
of the full wave equation. Two Ph.D students advised by J.
Roman and S. Petiton respectively started to work in january
2008 on computing aspects for optimizing the computational
performances of our numerical methods. They will defend their
thesis in march 2011. A Ph.D. student has been hired in
Magique-3D and a Master student will start working with
Nachos in April. To our knowledge, this network is the first
in the French research community to establish links between
industrial and academic researchers in the context of a
long-term research program managed by an INRIA team. A
workshop has been organized in December, gathering INRIA
teams, engineers from TOTAL and academic researchers (see
http://

The endeavour of this project is to develop some methodology for modelling and solving certain inverse problems using tools from harmonic and complex analysis. These problems pertain to deconvolution issues, identification of fractal dimension for Gaussian fields, and free boundary problems for propagation and diffusion phenomena. The target applications concern radar detection, clinical investigation of the human body (e.g. to diagnose osteoporosis from X-rays or epileptic foci from electro/magneto encephalography), seismology, and the computation of free boundaries of plasmas subject to magnetic confinement in a tokamak. Such applications share as a common feature that they can be modeled through measurements of some transform (Fourier, Fourier-Wigner, Riesz) of an initial signal. Its non-local character generates various uncertainty principles that make all of these problems ill-posed. The techniques of harmonic analysis, as developed in each case below, form the thread and the mathematical core of the proposal. They are intended, by and large, to regularize the inverse issues under consideration and to set up constructive algorithms on structured models. These should be used to initialize numerical techniques based on optimization, which are more flexible for modelling but computationally heavy and whose convergence often require a good initial guess. In this context, the development of wavelet analysis in electrical engineering, as well as signal and image processing or singularity detection, during the last twenty years, may serve as an example. However, many other aspects of Fourier analysis are at work in various scientific fields. We believe there is a strong need to develop this interaction that will enrich both Fourier analysis itself and its fields of application, all the more than in France the scientific communities may be more separate than in some other countries.

The project was created in july 2007. A first meeting took place to Pau in october 2007 and a second one to Orléans in september 2008. Collaborations have began with the Bordeaux team on the use of bandelet formalism for the seismic inversion and a post-doc, hired in october 2008, had in charge to analyze with us the feasibility of this apporach. We have worked on the approximation of seismic propagators involving Fourier integral operators by considering different approaches. In November 2010, we have hired an associate engineer who will work with us on the development of a software for the gravimetric inversion.

Dimitri Komatitsch, Pieyre Le Loher and Roland Martin spent two weeks at the Barcelona Supercomputing Center of the “Universitat Politecnica de Catalunya” in June 2010;

Abal-Kassim Cheikh spent two weeks at Florida State University in July 2010.

Mounir Tlemcani spent two weeks in July 2010 in Magique-3D.

Chokri Bekkey spent two weeks in Magique-3D in April 2010.

Rabia Djellouli spent one month in Magique-3D in May 2010.

Julien Diaz spent two weeks at CSUN in November 2010.

Emiljana Gorgji spent one week at the Barcelona Supercomputing Center of the “Universitat Politecnica de Catalunya” in November 2010.

Gordon Erlebacher spent two weeks in Magique-3Din May 2010.

Roland Martin spent one month at “Laboratorio de Flujos Complejos, Instituto de Ingenieria en Ciencias de Materiales, Universidad Nacional Autonoma de Mexico” in July 2010

Roland Martin spent one month at `Laboratorio de Paleomagnetismo, Instituto de Geofisica (UNAM)” in Mexico in August 2010.

Since january 2006, the team is associated to a team
located at CSUN (California State University at Northridge)
which is managed by R. Djellouli. Our common programm
research takes part of the activities we develop in
modeling essentially (see
http://

Collaboration with BCAM (Basque Center of Applied Mathematics) in the framework of the Aquitaine Euskadi Call

In collaboration with the INRIA multimedia department, we realized a movie describing an example of the applications considered in the team. This movie, entitled "Sonder l'invisible: du seisme au modèle", focuses on the numerical simulation of earthquakes and is designed for the general public. It was played for the first time at "Fête de la Science" event which was held on October 20th, 2010 at Pau university. About thirty persons attended the event, a large part of them were students. Three conferences were also given during the event by Julien Diaz, Céline Blitz and Meriem Laleg about respectively: “seismic imaging”, “simulation of wave propagation in the Asteroid Eros” and “modelling and analysis of the blood pressure for clinical diagnosis”.

Following our collaboration with the BCAM (Basque Center for Applied Mathematics), Hélène Barucq was one of the main organizers of the Workshop INRIA-BCAM, gathering researchers from BCAM and INRIA Bordeaux Sud-Ouest Research Center.

Hélène Barucq coorganized a session at CFA 2010 (Congrès Français d'Acoustique, April 12-16 2010, Lyon, France) with Salah Naili (Professeur, Laboratoire de Mécanique Physique, Paris 12).

Lecture/course to Master students (64 hours) at University of Pau, France, on "Calcul Parallèle et Modélisation en Géophysique" ("Parallel computing and geophysical modeling")

Lecture/course to Master students (46 hours) at University of Pau, France, on "Propagation d'ondes et imagerie" ("Waves propagation and Imaging")

Lecture/course (36 hours) to fourth-year engineering students at EISTI (Ecole Internationale des Sciences du Traitement de l'Information)

Lecture/course (24 hours) to fourth-year engineering students at ESTIA (Ecole Supérieure des Technologies Industrielles Avancées).

Cyril Agut

C. Agut, J. Diaz and A. Ezziani
*A new modified equation approach for high-order space
and time discretizations of the wave equation*, Third
Chilean Workshop on Numerical Analysis of Partial
Differential Equations, WONAPDE 2010, 11th 15th
January 2010, Concepcion (Chile),
http://

C. Agut and J. Diaz
*High-order discretizations for the wave equation based
on the modified equation technique*, 10ème Congrès
Français d'Acoustique, CFA 2010, 12th 16th April
2010, Lyon (France),
http://

C. Agut, J. Diaz and A. Ezziani
*Une nouvelle approche de type équation modifiée pour
des discrétisations d'ordre élevé en espace et en temps
de l'équation des ondes*, 40ème Congrès National
d'Analyse Numérique, CANUM 2010, 31st May 4th June
2010, Carcans-Maubuisson (France),
http://

C. Agut, J. Diaz and A. Ezziani
*High-order discretizations for the wave equation based
on the modified equation technique*, XIV
Spanish-French Jacques-Louis Lions School, 6th
10th September 2010, A Coruna (Spain),
http://

Hélène Barucq

H. Barucq, C. Bekkey and R. Djellouli,
*An efficient multi-step procedure for enriching
limited two-dimensional far-field pattern
measurements*, V International Conference on Inverse
Problems, Control and Shape Optimization, PICOF 2010,
Cartagena (Spain), April 7-9 2010 (
http://

H. Barucq, J. Diaz and V. Duprat
*Conditions aux limites artificielles enrichies pour
l'équation des ondes acoustiques*, Séminaire du
Laboratoire Jacques-Louis Lions, Paris, France, Apr. 9,
2010.

H. Barucq,
*Conditions aux limites modélisant la propagation
d ondes acoustiques et électromagnétiques au
voisinage de surfaces régulières arbitraires:
construction et analyse mathématique*. Séminaire de
l'EPI NACHOS, Sophia Antipolis, France, Aug. 27,
2010.

H. Barucq, C. Bekkey and R. Djellouli,
*An efficient multi-step procedure for enriching
limited two-dimensional far-field pattern
measurements*, IV European Conference on Computational
Mechanics, ECCM 2010, Paris (France), May 16-21 2010 (
http://

Julien Diaz

C. Baldassari, H. Barucq and J. Diaz
*An hp-adaptive energy conserving time scheme for the
wave equation*, Third Chilean Workshop on Numerical
Analysis of Partial Differential Equations, WONAPDE 2010,
Jan. 11, 2010, Concepcion, Chile,
http://

H. Barucq, J. Diaz and V. Duprat
*Absorbing Boundary Condition Taking into Account the
Grazing Modes*, 2010 SIAM Annual Meeting (AN10), Jul.
12, 2010, Pittsburgh, USA,
http://

H. Barucq, C. Baldassari and J. Diaz
*High-Order Schemes with Local Time Stepping for
Solving the Wave Equation in a Reverse Time Migration
Algorithm*, 2010 ISFMA Symposium & Shanghai Summer
School on Maxwell' equations: Theoretical and Numerical
Issues with Applications, Jul. 25, 2010, Shanghaï,
China.

H. Barucq, C. Baldassari and J. Diaz
*Schémas d'ordre élevé à pas de temps local pour la
résolution de l'équation des ondes*, Séminaire du
Groupe de Modélisation Mathématiques Mécanique et
Numérique (GM3N), Caen, France, Oct. 11 2010.

Véronique Duprat

H. Barucq, J. Diaz and V. Duprat
*Enriched absorbing boundary conditions for the
acoustic wave equation involving a fractional
derivative*, WONAPDE 2010, 11th 15th January
2010, Concepcion (Chile),
http://

H. Barucq, J. Diaz and V. Duprat
*Approximate boundary conditions based on a complete
transparent condition for the acoustic wave equation*,
CFA 2010, 12th 16th April 2010, Lyon,
http://

H. Barucq, J. Diaz and V. Duprat
*Factorisation complète de l'équation des ondes pour la
construction de conditions aux limites absorbantes*,
CANUM 2010, 31st May 4th June 2010,
Carcans-Maubuisson,
http://

H. Barucq, J. Diaz and V. Duprat
*Development and optimization of absorbing boundary
conditions for acoustic wave problems in complex
media*, XIV Jacques-Louis Lions Spanish-French school
on numerical simulation in physics and engineering, 6th
10th September 2010, A Coruna (Spain),
http://

Jonathan Gallon

J. Gallon, S. Guillon, B. Jobard, H
Barucq and N. Keskes
*Slimming Brick Cache Strategies for Seismic Horizon
Propagation Algorithms*, Eurographics/IEEE VGTC on
Volume Graphics, 2th - 3th may 2010, Norrköping
(Sweden),

Dimitri Komatitsch

F. Magnoni, E. Casarotti, A. Michelini, A. Piersanti, D. Komatitsch and J. Tromp, Spectral-element simulations of seismic waves and coseismic deformations generated by the 2009 L'Aquila earthquake, AGU Fall Meeting, San Francisco, USA, December 13-17, 2010.

D. Komatitsch, Invited talk, Modélisation de la propagation des ondes sismiques en multi-GPUs, Groupe de travail du GDR Ondes, Lyon, France, November 9, 2010.

D. Komatitsch, Invited talk, Eléments finis d'ordre élevé sur un réseau de cartes graphiques GPU pour la modélisation numérique des ondes sismiques, Académie des Sciences, Institut de France, Paris, November 2, 2010.

D. Komatitsch, UNESCO ICTP Center in Trieste (Italy), Invited teaching class, The spectral-element method and three-dimensional seismology for the "Tenth Workshop on three-dimensional modeling of seismic wave generation, propagation and their inversion", September 27 - October 8, 2010.

D. Komatitsch, Invited talk, A spectral-element seismic wave propagation algorithm on a large cluster of GPUs, University of Munich, Germany, July 2, 2010.

D. Komatitsch, G. Erlebacher, D. Göddeke and D. Michéa, A spectral-element seismic wave propagation algorithm on a cluster of 192 GPUs, Invited talk, 6th International Workshop on Parallel Matrix Algorithms and Applications (PMAA'10), Basel, Switzerland, June 30 - July 2, 2010.

D. Komatitsch, Simulation d'un tremblement de terre à l'échelle planétaire, Invited talk, Académie des Sciences, Institut de France, Paris, June 29, 2010.

D. Komatitsch, D. Michéa, G. Erlebacher and D. Göddeke, Running 3D finite-difference or spectral-element wave propagation codes faster using a GPU cluster, 72nd European Association of Geoscientists & Engineers (EAGE) conference, Barcelona, Spain, June 14-17, 2010.

D. Komatitsch, G. Erlebacher, D. Göddeke and D. Michéa, Modeling of seismic wave propagation using high-order finite elements with MPI on a cluster of 192 GPUs, Invited talk, 4th European Congress on Computational Mechanics (ECCM/ECCOMAS'2010), Paris, France, May 16-21, 2010.

D. Komatitsch, D. Michéa, G. Erlebacher and D. Göddeke, Invited talk, Accelerating a 3D finite-difference wave propagation code and a spectral-element code using a cluster of GPU graphics cards, Annual meeting of the European Geophysical Union, Vienna, Austria, May 2-7, 2010.

D. Komatitsch, Invited talk, Portage d'une application de propagation d'ondes sismiques en multi-GPUs, Aristote/OpenGPU workshop, Ecole Polytechnique, Paris, France, March 25, 2010.

D. Komatitsch, Invited talk, Le calcul parallèle haute performance sur des clusters de cartes graphiques (NVIDIA GPUs) et certaines applications en sismique, sismologie et industrie pétrolière, Groupe Thématique Mathématiques Appliquées, Informatique, Réseaux, Calcul, Industrie de la Société de Mathématiques Appliquées et Industrielles (SMAI), France Télécom Orange Labs, Paris, France, March 19, 2010.

Taous-Meriem LALEG-KIRATI

T.M. Laleg-Kirati, C. Médigue, B.
Helffer, E. Crépeau and M. Sorine
*Nouvelle technique d'analyse de la forme des signaux
de pression artérielle basée sur une approche
semi-classique*, Une demi-journée sur le
cœur-Séminaire au laboratoire de mathématiques appliquées
de l'université de Versailles Saint Quentin en Yvelines,
31 mars 2010.

H. Barucq, J. Diaz and T.M.
Laleg-Kirati,
*Approximation des opérateurs one-way*, Réunion
projet ANR Analyse Harmonique et Problèmes Inverses
(AHPI), Université de Bordeaux, 19 janvier 2010

T.M. Laleg-Kirati, E. Crépeau and M.
Sorine
*Analyse des signaux par quantication semi-classique.
Application à l'analyse des signaux de pression
artérielle*, Séminaire de l'Institut de Mathématiques
de Bordeaux, Université de Bordeaux, 04 janvier 2010.

Pieyre Le Loher

D. Komatitsch, P. Le Loher, D. Michéa,
G. Erlebacher, D. Göddeke
*Modeling of seismic wave propagation using high-order
finite elements with MPI on a cluster of 192
GPUs*,ECCM European Conference on Computational
Mechanics 2010, Paris, 17 mai 2010.

D. Komatitsch, P. Le Loher, D. Michéa,
G. Erlebacher, D. Göddeke
*Running 3D Finite-difference or Spectral-element Wave
Propagation Codes Faster Using a GPU Cluster*,EAGE
European Association of Geoscientists and Engineers 2010,
Barcelone, Espagnes, 16 juin 2010.

D. Komatitsch, P. Le Loher, D. Michéa,
G. Erlebacher, D. Göddeke
*Running 3D Finite-difference or Spectral-element Wave
Propagation Codes Faster Using a GPU Cluster*, QUEST
workshop, Alghero, Italie, 23 septembre 2010.

Roland Martin

R. Martin, D. Komatitsch, S. D. Gedney
and E. Bruthiaux,
*Convolution and non convolution Perfectly Matched
Layer techniques optimized at grazing incidence*, 72nd
European Association of Geoscientists & Engineers
(EAGE) conference, Barcelona, Spain, June 14-17,
2010.

R. Martin, D. Komatitsch, S. D. Gedney
and E. Bruthiaux,
*Convolution and non convolution Perfectly Matched
Layer techniques optimized at grazing incidence for
anisotropic, poroelastic or viscoelastic high-order wave
propagation modelling*, 4th European Congress on
Computational Mechanics (ECCM/ECCOMAS'2010), Paris,
France, May 16-21, 2010.

R. Martin, D. Komatitsch, E. Bruthiaux
and S.D. Gedney.
*Convolution and non convolution Perfectly Matched
Layer techniques optimized at grazing incidence for
high-order wave propagation modelling*. Vol. 12, EGU
General Assembly 2010, Vienna, Austria.

R. Martin,
*Portage d'un code de volumes finis pour la gravimétrie
sur GPU*, Aristote/OpenGPU workshop, École
Polytechnique, Paris, France, March 25, 2010.

Victor Peron

V. Péron
*On the Influence of the Geometry on Skin Effect in
Electromagnetism*, Rencontres de Mathématiques
UPPA-UPV, Sep. 30 Oct. 1, 2010, Anglet
(France).