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Low-rank approximation for partial differential equations with uncertain coefficients By Professor Olivier P. Le Maitre (Visiting Faculty at the KAUST SRI-Center for Uncertainty Quantification)

  • Class schedule:  Thursday, Oct. 2nd,  2014, 12:00 pm -13:00 pm 
  • Location: Building 9, Room 2322
  • Refreshments:  Pizza and soft drinks will be available at 11:45 am
In this talk, I will present different low-rank methods for the approximation of Stochastic Partial DifferentialEquations (SPDEs), that is PDEs with stochastic coefficients. These methods, and in particular the so called Proper Generalized Decomposition, aim at representing the dependence of the solution with respect to the stochastic coefficients through a series of functional with separated deterministic and stochastic components. The finite series is sought to minimize the approximation error in a prescribed sense (error norm, residual norm, . . .). Starting from the simple case of SPES having energy functionals e.g. elliptic equations, I will review and compare several algorithms for the approximation of the ideal decomposition. I will subsequently show that these algorithms can be successfully applied to several (moderately) non-linear problems, in particular the incompressible Navier-Stokes equations. Alternative separation formats, needed to further reduce the computational complexity of the low-rank construction algorithms, will also be discussed. Finally, I will present recent PGD results for the uncertain wave equation which requires a multi-resolution framework to effectively deal with the complicated structure of the stochastic functionals.
Olivier Le Maitre is a Research Director at the Centre National de la Recherche Scientifique (CNRS), France. He is currently visiting Professor at Duke University (North Carolina) and visiting Faculty at the KAUST SRI-center on Uncertainty Quantification. He graduated in mechanical engineering and aero-thermo-chemistry at the University du Havre in 1995; PhD in computational mechanics at the University du Havre in 1998; Habilitation Diploma at the University d'Evry in 2006. From 1998 to 2007 he was Assistant Professor at the mechanical engineering department of the University d'Evry, Paris, before being appointed as full researcher by the CNRS and joining the LIMSI (Computer and Engineering Sciences Laboratory) in Orsay. He was promoted CNRS Research Director in 2011. He has invited multiple times to the Johns Hopkins and Duke Universities and Sandia National Labs as a visiting researcher or professor. He is author of about 50 publications in international journals. His main research activities concern uncertainty quantification methods, computational fluid dynamics, and numerical approximation of PDEs, reactive and dynamical systems.