This PhD thesis will include a collaboration with ONERA -Office National d'Études et de Recherches Aérospatiales- (Thien Hiep Lê) and LIP6/Université Paris 6 (Fabienne Jézéquel).
Abstract
Numerical quality in scientific computations corresponds to a strong demand from physicists working on real-world applications but obtaining more accurate results often generates a significant overhead in computational time.
The objective of this PhD thesis is to propose efficient tools for numerical validation using modern supercomputers so that they become affordable for large scale simulations.
Context
Objectives
This PhD thesis will be a first step toward a public domain software library for parallel computation in error analysis. It will allow the numerical validation of high-performance applications developed at ONERA in aerodynamics and energetics. Studying the numerical quality of such applications is essential because of the number of operations performed. In ONERA fluid dynamics codes, this parallel library for error analysis will enable us to control the round-off error propagation and also to optimize the convergence parameters in iterative algorithms.
Work program
This PhD thesis will require in particular the design of innovative algorithms for estimating condition numbers of problems and backward error estimates, similarly to the results obtained for some linear solvers. These algorithms will be implemented on heterogeneous parallel machines made of multicore processors accelerated by GPUs.
The models for rounding-error propagation based on stochastic arithmetic will be studied and optimized for these parallel architectures in order to reduce the overhead in time and memory space inherent to such methods. The numerical errors and their computational time will be compared with those obtained using an approach resulting from condition number/backward error analysis. This study could be extended to the numerical quality of solutions coming from nonlinear problems.
Extra information
Prerequisite
Détails
Expected funding
Institutional funding
Status of funding
Expected
Candidates
Utilisateur
marc.baboulin
Créé
Mercredi 27 mars 2013 17:40:06 CET
dernière modif.
Mercredi 27 mars 2013 17:40:06 CET
Fichiers joints
filename
créé
hits
filesize
Aucun fichier joint à cette fiche
Connexion
Ecole Doctorale Informatique Paris-Sud
Directrice
Nicole Bidoit Assistante
Stéphanie Druetta Conseiller aux thèses
Dominique Gouyou-Beauchamps
ED 427 - Université Paris-Sud
UFR Sciences Orsay
Bat 650 - aile nord - 417
Tel : 01 69 15 63 19
Fax : 01 69 15 63 87
courriel: ed-info à lri.fr