Numerical Solution of Stochastic PDEs using Generalized Polynomial Chaos
主 题: Numerical Solution of Stochastic PDEs using Generalized Polynomial Chaos
报告人: George Em Karniadakis (Brown University & MIT)
时 间: 2007-10-19 下午 4:00 - 5:00
地 点: 理科一号楼 1418
Given the recent progress and maturity in numerical methods, it is timely to pose a new question and challenge for simulation science: how to model directly uncertainty associated with operating conditions, material properties, constitutive laws, etc. To this end, we propose a new stochastic modeling approach based on generalized polynomial chaos (gPC) that is many orders of magnitude faster than standard Monte Carlo methods. We will review this method and present new extensions that make the method appropriate for a relatively large number of uncertain parameters. Examples will be shown from mechanics, biology, and power systems.