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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


IMFT and CERFACS win a second ERC (European Research Council) advanced grant in combustion !

superadmin |  3 April 2019

The latest results of the 2018 ERC have been announced: IMFT (Institut de Mécanique des Fluides de Toulouse) and CERFACS have won a second ERC advanced grant in the field of combustion: . This 2.5 Meuro grant will allow to study hydrogen combustion for the storage of renewable energies...Read more

Catherine Lambert, new member of National Academy of Technologies of France

nasri |  8 March 2019

Each year, the Academy recruits new  members in order to enlarge  or enhance its scope of reflection and action, this being carried out within a rigorous recruitment process which focuses on people's excellence and on the visibility of their works in Europe and...

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