CERFACS CERFACS Scientific Activity Report Jan. 2010 – Dec. 2011

INTRODUCTION (S. GRATTON)
We have continued detailed discussions with EDF/SINETICS on parallel sparse direct methods for the
solution of industrial problems in structural mechanics in the framework of the ANR Solstice project
finished in June 2010.
Our work on the optimization and linear algebraic aspects of data assimilation has been of great interest
to and has been the subject of some discussions with the Climate Modeling and Global Change Group
and Météo France. In the context of this collaboration, we have also hosted visits from Kristian Mogensen
(ECMWF, UK), and from Patrick Laloyaux and Annick Sartenaer of the University of Namur, Belgium.
This collaboration on data assimilation will continue in the coming years in the framework of the RTRA
funded ADTAO project where efficient techniques for solving nonlinear least-squares problems will be
developed.
We have been working closely with TOTAL on the development of solvers on massively parallel computers
for Helmholtz problems arising in their geophysical applications (PhD of Xavier Pinel). In this context, we
have solved huge indefinite linear systems efficiently with preconditioned Krylov subspace methods. These
solvers are part of a broader project aiming at determining the velocity field of the Earth sub-surface. This
latter problem is formulated as a nonlinear least-squares problem that exhibits many local minima. The PhD
of Y. Diouane focuses on the use of appropriate techniques from global optimisation to tackle this situation.
We have also extended our collaboration with TOTAL in the direction of reservoir modeling, where we are
expected to provide efficient solvers for solving problems issued from the discretization of coupled partial
differential equations involving velocity, pressure and saturation variables.
We assist the other Projects at CERFACS at all levels from the “over-a-coffee” consultancy to more major
collaborations. These include advice on the elsA and the AVBP codes of CFD, in particular advice on the
accuracy of their computations in a parallel environment, and many aspects of numerical algorithms with
CFD and Global Change. We have also interacted with the CSG group on issues concerning new computer
chips and technologies.
S. Gratton.
6 Jan. 2010 – Dec. 2011