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Title: Multi-fidelity stochastic collocation method for computation of statistical moments

Abstract

We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.

Authors:
 [1];  [2];  [3]
  1. Department of Mathematics, University of Iowa, Iowa City, IA 52242 (United States)
  2. Department of Mathematics, University of Utah, Salt Lake City, UT 84112 (United States)
  3. Department of Mathematics, The Ohio State University, Columbus, OH 43210 (United States)
Publication Date:
OSTI Identifier:
22622309
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 341; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; ALGORITHMS; APPROXIMATIONS; COMPUTERIZED SIMULATION; CONVERGENCE; EFFICIENCY; ERRORS; STATISTICAL MODELS; STOCHASTIC PROCESSES

Citation Formats

Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu, Linebarger, Erin M., E-mail: aerinline@sci.utah.edu, and Xiu, Dongbin, E-mail: xiu.16@osu.edu. Multi-fidelity stochastic collocation method for computation of statistical moments. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2017.04.022.
Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu, Linebarger, Erin M., E-mail: aerinline@sci.utah.edu, & Xiu, Dongbin, E-mail: xiu.16@osu.edu. Multi-fidelity stochastic collocation method for computation of statistical moments. United States. doi:10.1016/J.JCP.2017.04.022.
Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu, Linebarger, Erin M., E-mail: aerinline@sci.utah.edu, and Xiu, Dongbin, E-mail: xiu.16@osu.edu. Sat . "Multi-fidelity stochastic collocation method for computation of statistical moments". United States. doi:10.1016/J.JCP.2017.04.022.
@article{osti_22622309,
title = {Multi-fidelity stochastic collocation method for computation of statistical moments},
author = {Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu and Linebarger, Erin M., E-mail: aerinline@sci.utah.edu and Xiu, Dongbin, E-mail: xiu.16@osu.edu},
abstractNote = {We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.},
doi = {10.1016/J.JCP.2017.04.022},
journal = {Journal of Computational Physics},
number = ,
volume = 341,
place = {United States},
year = {Sat Jul 15 00:00:00 EDT 2017},
month = {Sat Jul 15 00:00:00 EDT 2017}
}