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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

Continuity of activity of the Cerfacs during the Covid-19 pandemic

superadmin |  20 March 2020

On Monday 16 March 2020, in the context of the rapidly evolving COVID-19 epidemic, Cerfacs decided to reorganize its activities by implementing a Business Continuity Plan (BCP) and deploying teleworking facilities for all its employees. All staff members thus continue to carry out their full mission.Read more


A fiery wakeup call for climate science

superadmin |  26 February 2020

The extent of the recent wildfires in Australia significantly exceeded the projections of any member of the multi-model CMIP archive.  This highlights how current multi-model ensembles may be under-representing the risks of natural disasters under climate change.  Limited coupled system process representation in most models coupled with a lack of parameter uncertainty exploration means that some risks are not explored by the existing international multi-model framework.  This calls for a reassessment of how to focus climate model development on providing robust risk quantification for those impacts which most directly affect society. Sanderson, B.M., Fisher, R.A. A fiery wake-up call for climate science. Nat. Clim. Chang. (2020) nature.com Media coverage BBC Sydney Morning Herald The Guardian Wired The Daily Express YahooRead more

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