Mixed accuracies for preconditioned iterative methods applied to sparse systems

Currently, most numerical simulations performed at IFPEN are carried out in double precision. However, computing in mixed or reduced precision allows an acceleration of the execution, a decrease in energy consumption, and optimal use of the memory. 
This PhD aims to exploit mixed precision arithmetic (involving half, single and double precision) for preconditioned iterative sparse linear solvers based on Krylov methods. More precisely, the aim is to design mixed precision algorithms for both the construction of the preconditioner (such as SPAI, incomplete LU) and the iterative solution of the sparse linear system (computed using BiCGStab for instance), by limiting the error propagation related to low precision computation.
Iterative methods based on Krylov subspaces suffer from high operational complexity and memory consumption. They therefore have limited parallel scalability on supercomputers. Using mixed precision instead of double precision can be beneficial for direct methods. However, the use of an iterative preconditioned solver in mixed or reduced precision will require careful consideration of error propagation and numerical aspects. Indeed, the blind use of low precision in an iterative solver degrades in most cases either the achievable level of accuracy or the convergence speed, or both.
During this PhD, new approaches will be proposed to take advantage of mixed precision when computing the iterative solution of large sparse linear systems on supercomputers. The results of this work will be used in various applications at IFPEN where such numerical computation is crucial.

Keywords: High performance computing, numerical algorithms, floating point arithmetc, linear algebra

• Academic supervisor    Dr, JEZEQUEL Fabienne, Laboratoire Lip6, ORCID
• Doctoral School    ED 130: Ecole Doctorale Informatique, Télécommunications et Electronique (EDITE), https://www.edite-de-paris.fr/
• IFPEN supervisor     Encadrant IFPEN
• Dr, ANCIAUX-SEDRAKIAN Ani, éventuellement fonction, Sciences et Technologies du Numérique, ani.anciaux-sedrakian@ifpen.fr, 0000-0001-6084-5652
• PhD location    IFP Energies nouvelle, Rueil, France
• Duration and start date    3 years, starting in fourth quarter 2023
• Employer    IFP Energies nouvelle, Rueil, France
• Academic requirements    University Master degree in   mathematics and computer science
• Language requirements    Fluency in French or English, willingness to learn French 
• Other requirements     High performance computing, numerical algorithms, linear algebra