Section: New Results
Algorithms and high-performance solvers
Hybrid direct/iterative solvers based on algebraic domain decomposition techniques
We have studied the parallel scalability of variants of an algebraic additive Schwarz preconditioner for the solution of large three dimensional convection diffusion problems in a non-overlapping domain decomposition framework. To alleviate the computational cost, both in terms of memory and floating-point complexity, we investigate variants based on a sparse approximation or on mixed 32- and 64-bit calculation. The robustness and the scalability of the preconditioners are investigated through extensive parallel experiments on up to two thousand processors. Their efficiency from a numerical and parallel performance view point are investigated. More detailed on this work can be found in [5] .
Parallel numerical experiments with this solver were also performed in the framework of inverse problem in geophysics. Some analysis of the its behaviour with respect to other approaches for 3D simulations are reported in [6] .
Hybrid solver based on a combination of a multigrid method and a direct method
In the context of a collaboration with the CEA/CESTA center, M. Chanaud continues a Ph.D. concerning a tight combination between multigrid methods and direct methods for the efficient solution of challenging 3D irregular finite element problems arising from the discretization of Maxwell or Helmoltz equations. A sequential prototype has been validated. A parallel solver dedicated to the ODYSSEE challenge (electromagnetism) of CEA/CESTA and the study of the numerical behaviour of this hybrid solver are ongoing activities.
Domain decomposition methods to solve neutron transport equations
This work, started with a collaboration between the EDF/SINETICS team and the former ScAlApplix project, intended to design and develop techniques to optimize the efficiency of the codes used to simulate the physics of nuclear reactors. In the context of Bruno Lathuilère PhD (in collaboration with Pierre Ramet from BACCHUS), we have completed a study to parallelize a SPn simulation code by using a domain decomposition method applied for the solution of the neutron transport equations (Boltzmann equations). The defense of the thesis is planed at the begining of February 2010.
High performance algorithms for wave propagation
A first work has been initiated during the ANR CIGC-05 NUMASIS project. The overall objective is the adaptation and the optimization of numerical methods in geophysics for large scale simulations on hierarchical and multicores architectures. Fabrice Dupros (BRGM) has started a PhD on these topics in February 2007 in the former ScAlApplix project. This work is also carried out in the framework of a collaboration with the INRIA MAGIQUE3D team (Dimitri Komatitsch) and BRGM. Several contributions can be underlined, for example the impact of the memory hierarchy for this class of simulations ([10] , [14] ). Large scale finite-elements computations for site effects in the French Riviera urban area have also been performed on the JADE GENCI/Cines platform using the PaStiX sparse parallel direct solver [3] . An ongoing topic is the evaluation of a spacetime decomposition for the time-domain finite-differences method (FDTD) and its application to the classical staggered-grid scheme [17] . The defense of this PhD is planned during the first semester of 2010.
A second work is currently carried on with TOTAL. The extraordinary challenge that the oil and gas industry must face for hydrocarbon exploration requires the development of leading edge technologies to recover an accurate representation of the subsurface. Seismic modeling and Reverse Time Migration (RTM) based on the full wave equation discretization, are tools of major importance since they give an accurate representation of complex wave propagation areas. Unfortunately, they are highly compute intensive. The recent development in GPU technologies with unified architecture and general-purpose languages coupled with the high and rapidly increasing performance throughput of these components made General Purpose Processing on Graphics Processing Units an attractive solution to speed up diverse applications. We have designed a fast parallel simulator that solves the acoustic wave equation on a GPU cluster ([1] , [15] ). Solving the acoustic wave equation in an oil exploration industrial context aims at speeding up seismic modeling and Reverse Time Migration. We consider a finite difference approach on a regular mesh, in both 2D and 3D cases. The acoustic wave equation is solved in a constant density or a variable density domain. All the computations are done in single precision, since double precision is not required in our context. We use nvidia CUDA to take advantage of the GPU computational power. We study different implementations and their impact on the application performance. We obtain a speed up of 16 for Reverse Time Migration and up to 43 for the modeling application over a sequential code running on general purpose CPU.
