简介: |
Abstract: 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.
References:
1. D. Xiu and G.E. Karniadakis, “The Wiener-Askey Polynomial Chaos for stochastic differential equations", SIAM Journal of Scientic Computing, vol 24, no. 2, pp. 619-644, 2002.
2. G. Lin, C.-H. Su and G.E. Karniadakis, “The stochastic piston problem”, Proc. National Academy of Sciences, vol. 101, pp. 15840-15845, 2004.
3. G. Lin, C.-H. Su and G.E. Karniadakis, “Random roughness enhances lift in supersonic flow”, Phys. Rev. Let., vol 99, (10), 104501, 2007.
4. D. Lucor and G.E. Karniadakis, “Noisy inflows cause a shedding-mode switching in flow past an oscillating cylinder”, Phys. Rev. Lett., vol. 92(15), 154501, 2004.
Short Biography: George Em Karniadakis is Professor of Applied Mathematics at Brown University since 1994 and Senior Lecturer of Mechanical Engineering at MIT since 2000. He obtained his SM and PhD from MIT and he was postdoc at Stanford University and Assistant Professor at Princeton University. He has published three books and more than 200 research papers on computatiational mathematics, stochastic modeling, microfluidics, turbulence, biophysics, and parallel computing.
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