## Section: Other Grants and Activities

### International initiatives

#### Associated team PHyLeaS

Participants : Olivier Coulaud, Luc Giraud, Jean Roman.

**Grant:** INRIA

**Dates:** 2008-2009

**Partners:** University of Minnesota, INRIA
Sophia-Antipolis MÃ©diterranÃ©e, Institute of Computational
Mathematics Brunswick, LIMA-IRIT (UMR CNRS 5505)

**Overview:**
New advances in high performance scientific computing require
continuing the development of innovative algorithmic and numerical
techniques, their efficient implementation on modern massively
parallel computing platforms and their integration in application
software in order to perform large-scale numerical simulations
currently out of reach.
The solution of sparse linear systems is a basic kernel which appears
in many academic and industrial applications based on partial
differential equations (PDEs) modeling physical phenomena of various
nature. In most of the applications, this basic kernel is used many
times (numerical optimization procedure, implicit time integration
scheme, etc.) and often accounts for the larger part of the computing
time.
In a competitive environment where the numerical simulation tends to
replace the experiment, the modeling calls for PDEs of ever increasing
complexity. Furthermore, realistic applications involve multiple space
and time scales, and non-trivial geometrical features. In this
context, a common trend is to discretize the underlying PDE models
using arbitrary high-order finite element methods designed on
unstructured grids. As a consequence, the resulting algebraic systems
are irregularly structured and very large in size.
The aim of this project is the design and efficient implementation of
parallel hybrid linear system solvers which combine the robustness of
direct methods with the implementation flexibility of iterative
schemes. These approaches are candidate to get scalable solvers on
massively parallel computers.