Lawrence Berkeley National Laboratory (USA), University of Tennessee (USA), ONERA (France).
Abstract
The numerical validation in scientific computations corresponds to a strong demand from physicists working on real-world applications. However it often suffers from a prohibitive computational cost that can be at least four times more expensive than the solution process itself. In this thesis we will develop innovative algorithms to evaluate the numerical quality of a solution at lower computational price (e.g. problem condition estimates, backward errors). These algorithms will be applied to very large linear systems arising from computational fluid dynamics.
Context
Objectives
The objective of this PhD thesis is to propose efficient tools using modern supercomputers for the numerical validation of scientific software so that it becomes affordable for large scale simulations. This thesis requires the design of fast algorithms for estimating problem condition numbers in some key linear algebra problems (namely linear systems and linear least-squares problems). These algorithms will be implemented on multicore processors possibly accelerated by GPUs. The machines targeted in our simulations are current Petascale supercomputers. For these particular linear problems, the resulting time should be much smaller than the time for the solution itself.
Work program
The software produced during this 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 and LIMSI in aerodynamics and energetics. Studying the numerical quality of such applications is essential because of the number of operations performed. In 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. For roundoff error propagation, our simulations will be compared with results obtained using numerical validation tools based on stochastic arithmetics (work in collaboration with LIP6/Université Pierre et Marie Curie).
Extra information
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Détails
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Créé
Mardi 28 février 2012 17:15:13 CET
dernière modif.
Mardi 10 avril 2012 15:53:35 CEST
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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