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- Dongbin Xiu, George Em Karniadakis
- SIAM J. Scientific Computing
- 2002

We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wienerâ€™s polynomial chaos. Specifically, we represent the stochastic processesâ€¦ (More)

- Dongbin Xiu, Jan S. Hesthaven
- SIAM J. Scientific Computing
- 2005

Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methodsâ€¦ (More)

- Dongbin Xiu
- 2008

This paper presents a review of the current state-of-the-art of numerical methods for stochastic computations. The focus is on efficient high-order methods suitable for practical applications, with aâ€¦ (More)

We present a new algorithm to model the input uncertainty and its propagation in incompressible flow simulations. The stochastic input is represented spectrally by employing orthogonal polynomialâ€¦ (More)

- Dongbin Xiu
- 2006

A numerical algorithm for effective incorporation of parametric uncertainty into mathematical models is presented. The uncertain parameters are modeled as random variables, and the governingâ€¦ (More)

We present an efficient numerical strategy for the Bayesian solution of inverse problems. Stochastic collocation methods, based on generalized polynomial chaos (gPC), are used to construct aâ€¦ (More)

We present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations subject to uncertain inputs. In particular, we focus on the solution of theâ€¦ (More)

We present a semi-Lagrangian method for advectionâ€“diffusion and incompressible Navierâ€“Stokes equations. The focus is on constructing stable schemes of secondorder temporal accuracy, as this is aâ€¦ (More)

- Dongbin Xiu, Daniel M. Tartakovsky
- SIAM J. Scientific Computing
- 2006

Physical phenomena in domains with rough boundaries play an important role in a variety of applications. Often the topology of such boundaries cannot be accurately described in all of its relevantâ€¦ (More)

- Jing Li, Dongbin Xiu
- J. Comput. Physics
- 2010

Evaluation of failure probability of a given system requires sampling of the system response and can be computationally expensive. Therefore it is desirable to construct an accurate surrogate modelâ€¦ (More)