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Numerical Methods

 

Background

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.

Objectives

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

Software

Partners

CERFACS Partners

CERFACS Partners

CALENDAR

Friday

24

May

2024

🎓 PhD Defense: Théo DEFONTAINE

Friday 24 May 2024From 10h00 at 13h00

  Phd Thesis       JCA room, Cerfacs, Toulouse, France    

Monday

27

May

2024

🎓 PhD Defense: Thibault GIOUD

Monday 27 May 2024From 14h00 at 18h00

  Phd Thesis       Cerfacs, Toulouse, France    

Thursday

30

May

2024

Young PhD day (JDD2024@Cerfacs) – 30/05/2024

Thursday 30 May 2024From 9h00 at 17h00

  Journée des Doctorants       CERFACS     

ALL EVENTS