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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

NEWS

Young PhD day

Brigitte Yzel |  19 February 2020

Cerfacs organizes its 5th edition of the Cerfacs Doctoral Students Day on Monday, May 11, 2020. This day will be an opportunity for each doctoral student to present his or her research subject in front of an audience of Cerfacs researchers but also representatives of our industrial and academic partners, as well as selected external guests. Great novelty this year, 10 students have the privilege to participate in a specific training course such as "My thesis in 180 seconds", in order to present their research topic in French and in simple terms. The day will end with the selection of the : best poster, and the best MT180 presentation.Read more


A researcher of CERFACS guest during the France Culture radio show « La méthode scientifique » this week

superadmin |  20 January 2020

Mélanie Rochoux,  a researcher at Cerfacs working on wildfire spread modeling at the interface between CFD simulations and data science, is invited to the France Culture radio show « La méthode scientifique » next Wednesday to talk about megafires. Who are they? How are they formed? What are their impacts? How science can provide insights? The radio show is on Wednesday, January 22nd at 4:00 pm on the France Culture's channel.Read more

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