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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.



ISAF project : To accelerate the transition to SAFs, SAFRAN and CERFACS have together obtained an allocation of 44 million CPU hours on the LUMI-C super-computer as part of the EuroHPC Regular Access call in November 2022.

CERFACS |  11 March 2023

The objective of the ISAF project is to study the impact of SAFs (Sustainable Aviation Fuels) on engine operation and pollutant emissions, using high-fidelity Large Eddy Simulations (LES). The methodology developed at CERFACS combines Analytically Reduced Chemistry (ARC) with a multi-component evaporation model to capture the effect of fuel. The target configurations range from academic burners (CRSB at CORIA, SSB at DLR Stuttgart), to isolated industrial injection systems (MICADO at ONERA, HERON at CORIA) and complete annular combustor configurations (BEARCAT at SAFRAN, NTNU test bench).Read more

A CERFACS article distinguished in Scilight (https://doi.org/10.1063/10.0017474)

CERFACS |  9 March 2023

The recently published paper in Physics of Plasma: "3D particle-in-cell study of the electron drift instability in a Hall Thruster using unstructured grids," by W. Villafana, B. Cuenot, and O. Vermorel ( attracted the attention of Scilight (), whose goal is to present the most interesting research in the physical sciences published in AIP journals."Read more