Cerfacs Enter the world of high performance ...

Numerical Methods



The numerical simulation of physical systems based on partial differential equations plays a central role at CERFACS. Within this transverse axis we study efficient and reliable numerical methods for the numerical approximation and solution of such problems with our partners. We aim at analyzing and developing fast and accurate numerical methods and target a broad range of solution methods adapted to modern parallel platforms.


The main goal is to develop fast and accurate high-order numerical methods for the solution of time-dependent partial differential equations in fluid mechanics related to the simulation of turbulent flows on complex three-dimensional geometries.

Simultaneously, we maintain and further develop expertise on selected core problems in numerical linear algebra that are relevant for both CERFACS teams and shareholders. This includes, e.g., the solution of sparse linear systems of equations with direct, mixed direct/iterative methods or purely iterative methods, the design of preconditioners for Krylov subspace methods exploiting the structure of the system (such as systems of saddle-point type arising in PDE constrained optimization and variational methods in data assimilation), the solution of sequences of linear and nonlinear systems. This research should lead to both new algorithms of interest for the linear algebra community and software available for CERFACS teams and shareholders.

Research fields

  • Aerodynamics
  • Climate modelling
  • Combustion
  • Geophysical flows
  • Structural mechanics



CERFACS Partners

CERFACS Partners


CECI Contribution to CNRS’ “Petit Illustré” on Complex Systems (CNRS Edition)

ROGEL |  12 October 2017

CECI (Cerfacs, CNRS) and IMFT are both working on numerical modelling of the processes causing river flooding and their uncertainties. A common contribution on this subject, signed by Sophie Ricci and Hélène Roux, appears in Vol. 34 of the "Petit Illustré" collection, edited by CNRS.Read more

CERFACS was present at the European Researcher Night 2017 at Toulouse

thual |  1 October 2017

"Can we get an engine, an airplane or the entire Earth into a computer?". Such was the catchy title of the CERFACS stand  Friday September 29th, for the "European Research Night" whose theme was "Impossible". A hundred people at the "Quai des Savoirs" in Toulouse took a close interest in the...Read more