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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


Two CERFACS proposals accepted in PRACE 14th call

superadmin |  4 April 2017

Two CERFACS proposals have been accepted at the last PRACE call. The two studies will be performed with the AVBP solver and will address two very different topics: "Large Eddy Simulation of the Deflagration to Detonation Transition » (in collaboration with TOTAL) will focus on explosions in...Read more

Articles of scientific mediation in the online journal “The Conversation”

thual |  31 March 2017

Among the missions of the researchers and engineers of Cerfacs is the dissemination of scientific results at all levels, from specialized scientific journals to media intended for the general public. In this spirit, Cerfacs has chosen the online journal "The Conversation" to publish several...Read more