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Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty

Published online by Cambridge University Press:  20 August 2015

Zhen Gao  and
Jan S. Hesthaven
Zhen Gao*
Affiliation:
Research Center for Applied Mathematics, Ocean University of China, Qingdao 266071, Shandong, China Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA
Jan S. Hesthaven*
Affiliation:
Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA
*
Email:zhengao.ouc@gmail.com
Corresponding author.Email:Jan.Hesthaven@Brown.edu
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Abstract

The important task of evaluating the impact of random parameters on the output of stochastic ordinary differential equations (SODE) can be computationally very demanding, in particular for problems with a high-dimensional parameter space. In this work we consider this problem in some detail and demonstrate that by combining several techniques one can dramatically reduce the overall cost without impacting the predictive accuracy of the output of interests. We discuss how the combination of ANOVA expansions, different sparse grid techniques, and the total sensitivity index (TSI) as a pre-selective mechanism enables the modeling of problems with hundred of parameters. We demonstrate the accuracy and efficiency of this approach on a number of challenging test cases drawn from engineering and science.

Keywords

62F1265C2065C30Sparse gridsstochastic collocation methodANOVA expansiontotal sensitivity index

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 2 , August 2011 , pp. 253 - 278
Copyright
Copyright © Global Science Press Limited 2011

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