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Title: 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 well-established 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:
;  [1] ;  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Cornell Univ., Ithaca, NY (United States)
Publication Date:
OSTI Identifier:
1235335
Report Number(s):
SAND--2015-20740J
Journal ID: ISSN 0266-8920; 558187
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
Probabilistic Engineering Mechanics
Additional Journal Information:
Journal Volume: 41; Journal Issue: C; Journal ID: ISSN 0266-8920
Publisher:
Elsevier
Research Org:
Sandia National Laboratories (SNL-NM), 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