L’objectif est de permettre à des doctorants, post-doctorants, enseignants-chercheurs ou chercheurs faisant partie d’un laboratoire du DIM RFSI ou du DIM Math Innov d’approfondir leurs connaissances sur un sujet scientifique porteur. La 1ère formation organisée par le DIM RFSI et Math Innov porte sur :

Algorithmes émergents pour le calcul scientifique à grande échelle

Document à télécharger (PDF)

La formation contiendra une présentation des concepts fondamentaux, des théories et résultats, de leur mise en œuvre, des questions ouvertes sur ce sujet, ainsi que des aspects industriels. Les enseignements seront dispensés en anglais si nécessaire. Vous trouverez ci-dessous un programme détaillé. La participation à la formation est gratuite mais l’inscription est obligatoire.

Vous pouvez vous inscrire sur le lien suivant :

https://framaforms.org/formation-dim-rfsi-1578923056

Programme prévisionnel :

Programme prévisionnel :

  1. Mardi 4 fév: Laurence Halpern & Théo Mary,
    Introduction
    09:00 – 13:00, LIP6 étage 1 - 25-26/105-(Grande Salle)

  2. Mardi 3 mars: Laura Grigori
    An overview of communication avoiding algorithms for linear algebra
    14:00 – 17:15, LIP6 étage 1 - 25-26/105-(Grande Salle)

  3. Vendredi 3 avril: Frédéric Nataf & Pierre-Henri Tournier
    Domain decomposition methods for large scale problems: from theory to practice
    9:30-12:45, LIP6 étage 1 - 25-26/105-(Grande Salle)

  4. Mercredi 22 avril: Théo Mary
    Low rank approximations for large scale linear systems
    14:00 – 18 :00, LIP6 étage 1 - 25-26/105-(Grande Salle)

  5. Lundi 4 mai : Juliette Ryan
    High performance computing in aeronautics
    9:30 à 12:45, Salle F206, F207, Institut Galilée, Université Paris 13.

  6. Mardi 19 mai: Fabienne Jézéquel et Théo Mary
    Accuracy estimation of mixed-precision algorithms and their analysis
    9:00 – 13:00, LIP6 étage 1 - 25-26/105-(Grande Salle)

-------------------

29 mai: Workshop, LIP6 étage 1 - 25-26/105-(Grande Salle)

9:30-10:30 Patrick Amestoy (Mumps Tech, Toulouse)
10:30-11:00 pause café
11:00-12:00 Nick Higham (U. Manchester)
13:30-14:30 Martin Gander (U. Genève)
14:30-15:00 pause café
15:00-16:00 Nicole Spillane (Ecole Polytechnique)

Résumé scientifique des différentes journées de formation :

L. Grigori (3 Mars)

In this lecture we will present an overview of algorithms that are able
to minimize communication and thus are efficient on current and emerging
high performance machines. These algorithms include operations as solving
a linear system of equations or computing the low rank approximation of
a matrix, through deterministic or randomized approaches.

J. Ryan (17 Mars)

Computational Fluid Dynamics applied to Aeronautics problems can be extremely time consuming : One simulation = thousand of CPU hours.
In this session will be presented a methodology to shorten the code optimization development time while getting a unified code with good performance on different targeted devices based on an efficient CPU-GPU Code Hybridization. These techniques will be illustrated on a Discontinuous Galerkin code solving the Navier-Stokes equations.

F. Nataf (3 Avril )

Domain decomposition methods are a popular way to solve large linear systems on parallel architectures.
These methods are based on a "divide and conquer" strategy. At each step, a problem is solved simultaneously
in each sub-domain, and then interface data is exchanged between neighboring sub-domains. These are
communication avoiding algorithms since they are based on local volume calculations and only surface data
transfers. Thanks to their very good computation/communication ratio, they are naturally well suited to
modern computing architectures. We will present theoretical and numerical results as well as implementation issues.

T. Mary (22 Avril)

In many applications requiring the solution of linear systems, the matrices possess a special structure that can be exploited
to reduce the computational cost of the solution. This lecture will focus on data sparse matrices, which exhibit many blocks
of low numerical rank. We will see how low-rank approximations can be used to achieve a lower asymptotic complexity. We will also
discuss how to efficiently parallelize these methods, which require careful algorithmic work to scale on modern supercomputers.
We will illustrate these challenges and the potential of these emerging algorithms on large scale, industrial applications.

F. Jézéquel & T. Mary (19 Mai)

With the recent emergence of lower precisions supported by hardware,
notably half (16-bit) precisions, new analyses and algorithms must be
developed to maintain the robustness of numerical simulations. In
this lecture we will present two important classes of such
methods. First, probabilistic methods, in particular based on the use
of stochastic rounding, can provide reliable error estimates. Second,
mixed-precision methods are based on a cleve use of both low and high
precisions to achieve an often extremely beneficial compromise between
speed and accuracy. The success of these emerging methods will be
illustrated on industrial applications.

Workshop (29 Mai)

P. Amestoy: Structural and Data Sparsity in Parallel Direct Solvers
N. Higham: Exploiting Mixed Precision Arithmetic in Numerical Linear Algebra
M. Gander: Iterative Methods for Linear Systems over two Centuries
N. Spillane: TBA

Lien vers les slides des formations/ Link to Dim RFSI and Math innov training slides :

https://drive.google.com/drive/folders/1B0GocEnvmGSNsmWDqqA51PzOlk3NgdBo?usp=sharing


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