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Partial Differential Equations

Solving PDEs (partial differential equations) is one of the most important fundamental tasks for solving physics and engineering problems. Efficient numerical algorithms for existing and future computer architectures are one of the main targets. CERFACS performs research on the mathematical fundamentals and on application cases that are of specific interest for CERFACS shareholders, and for which the methods are developed and tested.

Research and progress in PDE methods is deeply rooted in functional analysis, but often the usefulness in practice will depend on the availability of an efficient implementation, and, in particular, the interface to numerical solvers from linear algebra, both direct and iterative. In some applications, unconventional methods, such as mesh-free and kinetic methods (such as the lattice Boltzmann method, LBM) and semistructured mesh methods combined with matrix-free techniques have shown superior potential for high performance computing. In terms of the resolution achieved and the efficiency of execution, we have demonstrated that such methods can outperform conventional techniques by several orders of magnitude. This gain in efficiency promises enormous savings  or, equivalently, a superior fidelity and improved predictive power of the simulations.

A – Legacy codes: CERFACS has successfully developed solvers for PDEs. This is the case of the LES reacting flow solver AVBP. Preparing such codes for future architectures is a continuing task at CERFACS. A related field of development for these legacy codes is fully adaptive meshing techniques to hide all meshing tasks for end users.

B – Future methods and solvers: Research in numerical PDEs is progressing rapidly. CERFACS explores promising paths for future PDE solvers. A special example is the LBM which is already studied intensively at CERFACS in coordination with leading laboratories in the field (M2P2 in Marseille, FAU Erlangen). The LBM can be implemented efficiently on certain architectures and is especially suited for manycore accelerators. In this field, the ALGO and CFD teams work together. In addition to the LBM approach, work has been carried out on another equally promising approach: SDM (Spectral Difference Method which is a family of high-oder discontinuous approach). The latter makes it possible to obtain very accurate LES simulations (up to now spatial order up to ten have been tested) with a competitive cost compared to traditional approaches. CERFACS developed its own platform called JAGUAR and since 2018 CERFACS shares the ownership and the development of this solver with ONERA.

NEWS

Catherine Lambert awarded Officer in the national order of Merit

Brigitte Yzel |  31 May 2022

Catherine LAMBERT, President of Cerfacs, has been promoted to the grade of officer in the national order of Merit, on the proposal of Mrs. Frédérique Vidal, Minister of Higher Education, Research and Innovation. Antoine PETIT, President and CEO of the CNRS, presented the insignia to Catherine LAMBERT during a ceremony that brought together many actors from the space, aeronautics, environment and digital sectors. Antoine PETIT: "Catherine's interpersonal skills, her ability to step back and understand very different environments (research, industry, politics) in order to develop a collective vision are the hallmarks of her career. Catherine is one of those people with whom you naturally feel confident, with whom you want to build something that goes beyond all of us to go further. With this honor, the Cerfacs teams are also rewarded.Read more


Sparse Days in Saint-Girons IV

Brigitte Yzel |  29 March 2022

Sparse Days Meeting 2022 🗓️  20-22 June 2022  @ Saint-Girons, France   🌐   Sparse Days 2022 will be held in Saint-Girons, Ariège, from 20-22 June. This enhanced version of Sparse Days is being co-organized by Cerfacs and ENSEEIHT/IRIT. It will be the fourth meeting in Saint- Girons following the tradition of the previous meetings held in 1994, 2003, and 2015. The tradition involves coupling our highly successful annual technical meeting with the ambience and hospitality of this wonderful Pyrenean town which encourages fruitful informal exchanges between participants.    Read more

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