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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



Tribute to Françoise Chatelin

Brigitte Yzel |  23 July 2021

  Tribute to Françoise CHATELIN   Virtual & Face to Face event @ Cerfacs 14 October 2021, CERFACS, Toulouse (France) 2 pm - 6.30 pm   Cerfacs is organizing a half scientific day on Thursday October 14, 2021 in tribute to Françoise Chatelin who left us prematurely on May 14, 2020   After graduating from the Ecole Normale Supérieure in Paris (1960-63), and her PhD in Mathematics at Grenoble University (1971) , Françoise Chatelin led with worldwide recognition her research in many areas, from spectral theory for linear operators in Banach spaces and finite precision to Dickson algebras. Professor Chatelin taught at the Universities Grenoble 2 - Pierre Mendès-France and Paris 9 - Dauphine before moving to Toulouse in 1996. She became Emeritus Professor in 2015. She was a visiting researcher at Berkeley and Stanford Universities, IBM San Jose (Ca) and Yorktown Heights (NY). For almost a decade, she was a scientific manager in Industry (in charge of intensive computing) first at the Centre Scientifique IBM France in Paris (1985 -1992) and then in the Central Research Lab of Thales (known as Thomson-CSF at that time) near Paris (1992-95). Françoise Chatelin was Head of the Qualitative Computing group at the Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (Cerfacs) in Toulouse, France. Professor Chatelin has authored four books; the first three are now classic references available from SIAM. Her second book Valeurs Propres de Matrices (Masson, Paris, 1988) has received the IBM - France prize for « Best Scientific and technical publication 1988 ». Beyond her scientific contribution, Françoise Chatelin played a structuring role on research at CERFACS through multiple thesis on innovative topics. This event is devoted to the human and scientific tribute of her life. As a faithful image of the active and passionate woman that...Read more

CERFACS is involved in the NextSim project

CERFACS |  19 July 2021

The primary objective is to increase the capabilities of Computational Fluid Dynamics tools on extreme-scale parallel computing platforms for aeronautical design. The Kick-Off Meeting took place on 12 March 2021. This project has received funding from the European High-Performance Computing Joint Undertaking (JU) under grant agreement N° 956104. The JU receives support from the European Union’s Horizon 2020 research and innovation programme and Spain, France, Germany. For more information, please visit  EuroHPC website : Project webpage :Read more