Section: Application Domains

Numerical simulations and other intensive applications

For the research on numerical linear algebra, the final goal of the research of Marc Baboulin and Laura Grigori is to make the algorithms and software as generic and widely usable as possible. However, through our academic and industrial collaborators, our research focuses on several important application domains, that we briefly describe in the following.

• Simulation of compositional multiphase Darcy flow in heterogeneous porous media with different type of applications: simulation of reservoir models, simulation of basin models, sim- ulation of geological CO2 underground storage, simulation of underground nuclear waste disposal. This research is performed in the context of the ANR Petal and Petalh projects, in collaboration with partners from IFP and CEA.

• Data analysis in astrophysics: we focus on computationally intensif numerical algorithms arising in the data analysis of current and forthcoming Cosmic Microwave Background (CMB) experiments in astrophysics. While this application does not involve a PDE, its most complex and time consuming step is solving a generalized least squares problem, which is at the core of our research. This research is performed in the context of the ANR Midas project in collaboration with Paris 7.

• Numerical simulations of incompressible fluid flows: We address the solution of large sparse linear systems coming from the discretization of Helmholtz and Poisson equations that represent the major part of the computational time for solving the Navier-Stokes equations describing a large class of fluid flows. For this application, the objective is to develop algorithms that take advantage of current heterogeneous multicore/GPU architectures. These algorithms must minimize the amount of communication in the linear algebra kernels involved in the computation (e.g. sparse matrix-vector product) and in the choice of the preconditioners. This research is a multidisciplinary collaboration between researchers from University Paris-Sud, INRIA-Saclay and LIMSI/CNRS in the framework of the CALIFHA project (funded by DIM/Digitéo).