On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems
The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two wellestablished and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method. Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.
 Authors:

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^{[1]};
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 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Cornell Univ., Ithaca, NY (United States)
 Publication Date:
 Report Number(s):
 SAND201520740J
Journal ID: ISSN 02668920; 558187
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 Probabilistic Engineering Mechanics
 Additional Journal Information:
 Journal Volume: 41; Journal Issue: C; Journal ID: ISSN 02668920
 Publisher:
 Elsevier
 Research Org:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org:
 ASC
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; approximation theory; Monte Carlo simulation; random variables and fields; stochastic differential equations; uncertainty propagation
 OSTI Identifier:
 1235335
Richard V. Field, Jr., Emery, John M., and Grigoriu, Mircea Dan. On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems. United States: N. p.,
Web. doi:10.1016/j.probengmech.2015.05.002.
Richard V. Field, Jr., Emery, John M., & Grigoriu, Mircea Dan. On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems. United States. doi:10.1016/j.probengmech.2015.05.002.
Richard V. Field, Jr., Emery, John M., and Grigoriu, Mircea Dan. 2015.
"On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems". United States.
doi:10.1016/j.probengmech.2015.05.002. https://www.osti.gov/servlets/purl/1235335.
@article{osti_1235335,
title = {On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems},
author = {Richard V. Field, Jr. and Emery, John M. and Grigoriu, Mircea Dan},
abstractNote = {The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two wellestablished and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method. Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.},
doi = {10.1016/j.probengmech.2015.05.002},
journal = {Probabilistic Engineering Mechanics},
number = C,
volume = 41,
place = {United States},
year = {2015},
month = {5}
}