Thèse en calcul scientifique : méthodes de décomposition de domaine pour des équations elliptiques incertaines
Niveau requis : MS degree or equivalent
Date de début : 1 septembre 2018
Durée de la mission : 3 years
Rémunération : 2386.29€/month (gross salary)
Uncertainty quantification (UQ) is nowadays becoming an integrated component of the numerical simulations, as their fair and complete exploitations require the assessment of the prediction quality. Uncertainty quantification studies often rely on probabilistic approaches, leading to the solution of a stochastic problem, in particular Stochastic Partial Differential Equations (SPDEs). The stochastic problems can be solved by sampling strategies, such as the Monte Carlo method, with thousands or more simulations to be performed to measure variabilities and perform sensitivity analyses. In the case of complex models having high computational cost, direct reuse of existing deterministic solvers may be insufficient to achieve acceptable computational cost and time to solution. Consequently, dedicated solvers exploiting particular structures in the stochastic problem have to be developed.
Recently, a novel domain decomposition approach was proposed for solving elliptic SPDEs. The method is based on a Schur complement approach, where polynomial chaos (PC) surrogates of the boundary-to-boundary maps are constructed in a pre-processing stage. This results in an accelerated Monte Carlo (MC) sampling of the stochastic condensed problem, where samples of the solution at the subdomain boundaries are computed.
The goal of this PhD project is to investigate two ways of making the domain decomposition method more efficient: 1) improve the efficiency and parallel scalability of the sampling stage; and 2) investigate potential dimensionality reduction of the stochastic condensed operator.
The PhD thesis funded by Cerfacs will be developed in the framework of a scientific collaboration between Paul Mycek (Cerfacs), Olivier Le Maître (LIMSI-CNRS) and Luc Giraud (Inria Bordeaux).
More information: PhD_stoch_dd
To apply: send a CV and a cover letter to firstname.lastname@example.org
Deadline for application: July 1st, 2018