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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



First 360-degrees Large-Eddy Simulation of a full engine

Jérôme DOMBARD |  17 June 2020

Within the PRACE project FULLEST (First fUlL engine computation with Large Eddy SimulaTion), a joint collaboration between CERFACS, SAFRAN and AKIRA technologies, Dr. C. Pérez Arroyo (post doctoral fellow at CERFACS) has carried out under the supervision of Dr. J. Dombard the first high-fidelity simulation of a part of the real engine DGEN380 (for now, from the fan to the combustion chamber). This 360-degrees integrated large-eddy simulation contains around two billion cells on the three instances, carried out with the AVBP code of CERFACS.  The CPU cost is obviously large but still within reach, performing around one turn of fan during 5 days over 14400 skylake cores. Post-treatments are in progress and already show, among other complex phenomena, a strong interaction between the high pressure compressor and the combustion chamber (see forthcoming paper GT2020-16288 C. Pérez Arroyo et al). Below a video showing: in the fan an isosurface at mid-height of the vein colored by the Mach number, in the high pressure compressor a gradient of density, in the bypass of the combustion chamber the static pressure and in the flame tube a temperature field. One of the goals of the project is to create a high-fidelity unsteady database to study interactions between modules and may help other teams to develop new lower order models and/or validate existing ones. Beyond the feasibility and the maturity of the AVBP code, this kind of calculation is an important milestone for the aeronautical industry and would allow to apprehend earlier in the design the effect of integration and installation and thus, to reduce the cycle and therefore the cost of the future aircraft engines. PRACE and GENCI CPU ressources and Safran Tech/DGAC fundings are gratefully acknowledged, along with the invaluable technical support at CERFACS: Dr. G. Staffelbach, Dr. F. Duchaine, Dr. L. Gicquel, Dr....Read more

B. Cuenot distinguished as Program Chair of international Symposium on Combustion

superadmin |  29 May 2020

B. Cuenot has been distinguished as Program Chair for the 39th International Symposium on Combustion, to be held in Vancouver (Canada) in 2022. The International Symposium on Combustion is a major event for the combustion community, where the current best research is presented.Read more