Projects

My research interests are on Fast Solvers, Domain Decompositions and Parallel Computing.

Fast Solvers:
Solving a linear system can be done thanks severals methods such as:

• Direct Methods with the LU decomposition,
• Krylov methods such as BICG, CG, GMRES with a preconditioner to enhance the convergence,
• Multigrid methods.

The performance of theses methods depends on the linear system, the grid size and also the architecture of the machine. That is why an interface have been developed which gathers the state of the art libraires (Lapack, Sparkit and Hypre) and it can choose the fastest solver for a given problem.

Domain Decomposition :
I use a domain decomposition method called Aitken Schwarz that is :

• numerically effcient,
• scales well on a parallel computer,
• and is tolerant to the high latency and low bandwidth of a slow network.

The main feature of this method is that it keeps the framework of Additive Schwarz algorithm which is easy to code, to parallelize, and to make it numerically efficient with an acceleration procedure.

A model is designed to handle the automatic performance tuning of the linear solver for each subdomain, each processor architecture and each applications with surface response modeling.

For more informations and results , you can read three two proceeding papers :

• Interface solver
• Aitken Schwarz with parallel performances

Parallel Hemodynamic Simulation: Presentation