麻豆影院

Dongbin Xiu, Department of Earth And Atmospheric Sciences, Purdue University

Efficient methods for numerical simulations with uncertainty

Most of the research efforts in scientific computing so far have been in developing efficient algorithms for different applications, assuming ideal inputs with precisely defined computational domains. Recently, there has been a growing interest in verification and validation of numerical simulations and in modeling uncertainty. The more general question thus becomes how to model uncertainty and stochastic inputs, and formulate algorithms to accurately reflect the propagation of uncertainty.

In this talk we will discuss different approaches for stochastic simulations, with a focus on efficient methods suitable for computations of complex problems. In particular, we will discuss methods based Generalized Polynomial Chaos (gPC) expansions. gPC is essentially a spectral approximation of functionals in random space and can achieve fast convergence. Combined with either a stochastic Galerkin or stochastic collocation approach, the governing equations (stochastic ODEs/PDEs) are reduced to a set of deterministic equations which can be solved by conventional numerical techniques.

In addition to the mathematical framework, various applications will be presented.