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Parallel Algorithms Team

The Parallel Algorithms Project conducts a dedicated research to address the solution of problems in applied mathematics by proposing advanced numerical algorithms to be used on massively parallel computing platforms. The Parallel Algorithms Project is especially considering problems known to be out of reach of standard current numerical methods due to, e.g., the large-scale nature or the nonlinearity of the problem, the stochastic nature of the data, or the practical constraint to obtain reliable numerical results in a limited amount of computing time. This research is mostly performed in collaboration with other teams at CERFACS and the shareholders of CERFACS as outlined in this report.

This research roadmap is known to be quite ambitious and we note that the major research topics have evolved over the past years. The main current focus concerns both the design of algorithms for the solution of sparse linear systems coming from the discretization of partial differential equations and the analysis of algorithms in numerical optimization in connection with several applications including data assimilation. These research topics are often interconnected as it is the case for e.g. large-scale inverse problems (so called big data inverse problems) or the solution of nonlinear systems that require approximate solutions of linearized systems. These research developments rely on a past research expertise in numerical analysis exploiting the structure of the problem in scientific computing, especially in qualitative computing.

A strong focus is given on mathematical aspects. Indeed efficient parallel algorithms are proposed together with their mathematical analysis. Main properties such as convergence of iterative methods, scalability properties, convergence to local or global minima are theoretically investigated.

Solution methods of sparse linear systems are considered in a broad sense by tackling both sparse direct methods and projection based iterative methods. These methods can also be combined to derive hybrid algebraic methods close to domain decomposition or multiscale methods. In addition to graph theory, these activities rely on a strong expertise in software development in linear algebra and on an up-to-date knowledge of the parallel computing platforms.

Optimization methods do occur in several applications at CERFACS. Most often the main goal is to improve the performance of a given system. The Parallel Algorithms Project is mainly focussing on both differentiable optimization and derivative-free optimization. The main research topics concern the convergence to local or global minima and the efficiency of the algorithms in practice.

The Parallel Algorithms Project is also deeply involved in the design and analysis of algorithms for data assimilation. Algorithms related to differentiable optimization or derivative-free optimization are considered together with filtering techniques. All these algorithms must be adapted and improved before tackling potential applications in seismic, oceanography, atmospheric chemistry or meteorology. The Parallel Algorithms Project has notably developed a specific expertise in the field of correlation error modelling based on the iterative solution of an implicitly formulated diffusion equation.

Finally the Parallel Algorithms Project takes an active part in the Training programme at CERFACS and is also regularly organizing seminars, workshops and international conferences in numerical optimization, numerical linear algebra and data assimilation.

 

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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