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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


Distinction for the book “The Human Face of Computing”

superadmin |  25 July 2017

The book "The Human Face of Computing" was selected as one of the notable books in the "21st Annual Best of Computing - Notable Books and Articles" compiled by Computing Reviews. Mrs Francoise Chatelin contributed to this book with the chapter "Qualitative Computing"Read more

Extreme CFD workshop of the SUCCESS scientific group in Toulouse, 17-21 July 2017.

superadmin |  24 July 2017

The first edition of the Extreme CFD workshop was held in Toulouse at ENSEEIHT from the 17th to the 21st of July, 2017 under the hospices of the SUCCESS scientific group (). It gathered 25 participants from CERFACS, CORIA, EM2C, IMAG, IMFT, LEGI and SAFRAN TECH grouped in 9 projects. Each project...Read more