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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


Sparse Days Meeting 2018 at Cerfacs, Toulouse

Brigitte Yzel |  12 June 2018

The annual Sparse Days meeting will be held at CERFACS in Toulouse on 27th and 28th September 2018.

Registration for the Sparse Days is free but we ask people who are coming to register as soon as possible although the deadline is August 26th. Please complete...

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New supercomputer opened at Cerfacs

superadmin |  16 May 2018

Since the beginning of May 2018, a new supercomputer named Kraken has been setup to reinforce Cerfacs' simulation capabilities. With a peak performance of 315 Tflop / s this new computer provided by Lenovo is now available to all of Cerfacs' researchers in addition to the Nemo computer. The...Read more