PETALh is a research project funded by ANR (Agence Nationale de la Recherche), COSINUS Program. The objective of this project is to develop highly parallel algorithms for preconditioning used in scientific applications. This project is funded for two years from January 2011 to December 2012 and it follows the PETAL project funded from January 2009 to December 2010. It involves several research laboratories including INRIA Saclay - Île-de-France, University Paris 6, INRIA Bordeaux - Sud-Ouest, IFP Rueil-Malmaison, and CEA Saclay.
With the development of new and improved simulation techniques, and with more computational power at hand, numerical simulations have become an increasingly useful tool in industrial and environmental issues. These simulations frequently lead to solving very large sets of linear equations, often with millions of rows and columns. Solving these problems is very time consuming, and the time spent on linear solvers represents usually a dominant fraction of the overall simulation execution time.
In this collaborative effort, we propose to develop parallel preconditioning techniques for the emergent hierarchical models of clusters of multi-core processors, as used in peta-/exa-scale machines. The direction preserving preconditioners considered in this project allow to deal with the scalability problem of most of the existing preconditioners, by efficiently filtering out the low frequency modes that hinder the convergence of iterative methods. The final goal of this project is to transform these preconditioners into black box parallel preconditioners that could be as usable as standard and popular methods such as ILU. The project also focuses on developing highly efficient and communication avoiding algorithms for the considered preconditioners and their building blocks.
Numerical simulations considered
One numerical simulation on which we focus is the simulation of compositional multiphase Darcy flow in heterogeneous porous media with different type of applications from IFP and CEA: simulation of reservoir models, basin models, geological CO2 underground storage, simulation of underground nuclear waste disposal, and thermal-hydraulic simulations in nuclear cores.