research projects / scientific events / products and demonstrations

Scientific leader
Jocelyne Erhel
tél: 02 99 84 73 39 - erhel@irisa.fr

Advanced algorithms for scientific computing

Scientific context

Joint project-team with University of Rennes-1, INSA-Rennes and CNRS.

Numerical simulation of physical phenomena can be split into several steps:

• Modelisation
• Mathematical study of the underlying equations (well-posedness, regularity of the solution)
• Design of the numerical scheme (discretization, convergence, stability)
• Choice of the algorithm
• Implementation
• Visualization and validation

The research undertaken in Aladin is mainly concerned with the design of numerical schemes and algorithms

The main objective is to satisfy the two following quality criteria:

• Efficiency: run-time, memory requirements, ...
• Reliability: convergence proof, bounds on the result, ...

In order to implement these schemes and algorithms in a complete simulation process, the group conducts orthogonal projects as well:

• Application to scientific softwares
• Implementation on parallel computer

Research topics

• Nonlinear and linear problems
• Newton-Krylov methods
• Deflation
• Eigenproblems
• Arnoldi and Davidson methods
• pseudo-spectrum of a matrix
• Ordinary and algebro differential equations
• General linear methods
• Runge-Kutta methods
• Pseudo-symplectic methods
• Reliability of scientific softwares
• Interval algorithms