Research

The goal of this project is to propose new parallel preconditioners based on a combined ILU factorization with a tangential filtering, nested factorization, that will be validated on several complex numerical simulations. In summary, the goals are as follows:

• Development of new preconditioning techniques based on approximate factorizations. The new techniques are based on a combination of the well known incomplete LU factorization with an approximate factorization based on tangential filtering. The new algorithms are aimed for simulations involving unstructured grids, and they take into account that the matrix comes from a system of PDEs.
• Development of graph partitioning algorithms and reordering techniques necessary for the above preconditioners. The graph partitioning algorithms take into account the characteristics of the preconditioners and the irregularities of the grids involved in complex simulations.
• Development of new parallel algorithms for the proposed preconditioners targeting the architecture of future petascale machines based on hierarchical models of clusters of multi-core processors.
• Validation and assessment on challenging applications and real test cases. The new linear solvers will be tested on challenging applications. Applications from CEA and IFP involve the simulation of compositional multiphase flow in porous media and thermal-hydraulics.

The objective of the project is to develop efficient and scalable algorithms beyond the current state of the art in order to be able to use the increasing power of parallel architectures. This project will lead to the development of beta version (preliminary) codes for two new solvers, one for performing a block parallel ILU preconditioner, and one for performing a parallel tangential filtering/nested factorization preconditioner. It will also lead to the extension and integration of new algorithms in several existing codes as Scotch, HIPS, Pastix.