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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 simelátion 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


Invited communication to the BIDS'17 conference

thual |  12 December 2017

During an invited communication to the « Big Data from Space 2017 » conference, CERFACS presented the stakes and the perspectives of its strategic axis "Data Driven Modeling" from the point of view of the valorization of satellite data. For more details, see the article:...Read more

One Cerfacs’ proposal accepted in PRACE 15th call

superadmin |  4 December 2017

This study focuses on Hall-effect thrusters, which were first invented in the 1960s. Although such systems have been extensively studied, the detailed physics of the magnetized plasmas in these thrusters is very complex and several plasma processes that have direct influence on the thruster...Read more