Differential Equations Seminar: Dr. Tengfei Su
Monday, April 22, 2019 · 11 AM - Noon
Title: Low-rank solution methods for discrete stochastic PDEs
Abstract: Stochastic PDEs are widely used to model physical problems with uncertainty. For numerical treatment, the stochastic Galerkin discretization in general gives rise to large, coupled algebraic systems that are computationally expensive to solve. In this study, we develop efficient iterative algorithms to reduce the costs, by taking advantage of the structures of the systems and computing low-rank approximations to the discrete solutions. We demonstrate this idea by exploring three types of problems: (i) the stochastic diffusion equation, in which the diffusion coefficient is a random field; (ii) stochastic eigenvalue problems arising from models of diffusion and fluid dynamics; (iii) stochastic version of the time-dependent incompressible Navier–Stokes equations with an uncertain viscosity. These problems range from a relatively straightforward linear elliptic problem for which we are able to obtain rigorous results on convergence rates for solvers, to more complex models that include eigenvalue computations and nonlinear and time-dependent computations.