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Parallel Algorithms


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.


Main Industrial Partners : Airbus Group, CEPMMT, CNES, CNRM, EDF, IFPEN, METOFFICE, TOTAL.

Academic and Industrial Partners : Argonne National Laboratory (Etats-Unis),  CNRS, INPT, INRIA, ISAE, Rutherford Appleton Laboratory (Angleterre), Université de Namur (Belgique), Université de Coimbra (Portugal).

Joint  Laboratory :  CERFACS-IRIT.

National and International Projects : AVENUE (RTRA STAE), ERA-CLIM 2, FILAOS (RTRA STAE), LEFE (INSU-CNRS), EoCoE, PAMSIM.



Team members     ⇒        Directory

Project Leader : Ulrich Rüde

Administrative assistant : Brigitte Yzel



Patrick Amestoy

– Mario Arioli

Alfredo Buttari

– Serge Gratton

Martin J. Kühn

Daniel Ruiz

Masha Sosonkina

Sébastien Tordeux

– Fahreddin Sükrü Torun

Jean Tshimanga-Ilunga

Yin Yang



Young PhD day (JDD) – Thursday 8 October 2020

Brigitte Yzel |  24 September 2020

  Ph.D. Students' Day (JDD 2020) Thursday 8 October 2020 Virtual event open to our partners and associates   Planning   The 2020 edition of the PhD Students' Day will take place on October 8th, 2020. This year, this day of the PhD students of the Cerfacs, will take place mainly in visio in order to respect all the health safety measures relating to Covid-19. This day will be held in a virtual way through oral presentations filmed and broadcast on a private link, which we will distribute to all participants. Everyone will thus be able to discover at a distance the subjects developed by the doctoral students. At the same time, the "Posters session" will be opened on the morning of the JDD, by sending all the posters in pdf format by e-mail to all the participants for consultation, and by opening the "50-minute question session" on a channel whose links we will send you. This will allow participants to ask questions about the posters of the session. Finally, we have included in this 5th edition a great novelty, by allowing several students to present their subject in the popularised form of "My thesis in 3 minutes", guided by Matthieu Pouget, actor and theatre director. This day will end with the vote for the "Best poster" and the "Best presentation of My thesis in 3 minutes". Participation in the event is free of charge. However, for logistical reasons, registration, only by invitation, is mandatory.   Organising Committee:  Scientific committee  Nicolas Venkovic Victor Xing Inscription &  information Jade Schweiger Brigitte Yzel  Read more

Sparse Days 2020, Cerfacs

Brigitte Yzel |  24 September 2020

Sparse Days Meeting 2020  23 - 24 November 2020 Virtual Workshop   The annual Sparse Days meeting will be held this year as a virtual event, on 23 - 24 November 2020. Sadly, because of the pandemic, we will not be able to have a normal face-to-face Sparse Days at Cerfacs this year. We will be holding an online version from 3pm to 7pm on 23 and 24 November. The timing is chosen to accommodate participants from North America since, at normal Sparse Days, we have a good representation from there. A registration form  is available on this conference website where you can also submit a title and an abstract for any proposed talk. We will probably be using the Webex system and will post details about how to connect to all people who register.Read more