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Title: Uncertainty Quantification via Random Domain Decomposition and Probabilistic Collocation on Sparse Grids

Abstract

Due to lack of knowledge or insufficient data, many physical systems are subject to uncertainty. Such uncertainty occurs on a multiplicity of scales. In this study, we conduct the uncertainty analysis of diffusion in random composites with two dominant scales of uncertainty: Large-scale uncertainty in the spatial arrangement of materials and small-scale uncertainty in the parameters within each material. A general two-scale framework that combines random domain decomposition (RDD) and probabilistic collocation method (PCM) on sparse grids to quantify the large and small scales of uncertainty, respectively. Using sparse grid points instead of standard grids based on full tensor products for both the large and small scales of uncertainty can greatly reduce the overall computational cost, especially for random process with small correlation length (large number of random dimensions). For one-dimensional random contact point problem and random inclusion problem, analytical solution and Monte Carlo simulations have been conducted respectively to verify the accuracy of the combined RDD-PCM approach. Additionally, we employed our combined RDD-PCM approach to two- and three-dimensional examples to demonstrate that our combined RDD-PCM approach provides efficient, robust and nonintrusive approximations for the statistics of diffusion in random composites.

Authors:
; ;
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
991070
Report Number(s):
PNNL-SA-67919
Journal ID: ISSN 0021-9991; JCTPAH; KJ0401000; TRN: US201020%%687
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics, 229(19-20):6995–7012
Additional Journal Information:
Journal Volume: 229; Journal Issue: 19-20; Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; ANALYTICAL SOLUTION; APPROXIMATIONS; DATA COVARIANCES; PROBABILITY; STATISTICS; RANDOMNESS; MONTE CARLO METHOD; uncertainty quantification; random composite; polynomial chaos; stochastic finite elements

Citation Formats

Lin, Guang, Tartakovsky, Alexandre M, and Tartakovsky, Daniel M. Uncertainty Quantification via Random Domain Decomposition and Probabilistic Collocation on Sparse Grids. United States: N. p., 2010. Web. doi:10.1016/j.jcp.2010.05.036.
Lin, Guang, Tartakovsky, Alexandre M, & Tartakovsky, Daniel M. Uncertainty Quantification via Random Domain Decomposition and Probabilistic Collocation on Sparse Grids. United States. https://doi.org/10.1016/j.jcp.2010.05.036
Lin, Guang, Tartakovsky, Alexandre M, and Tartakovsky, Daniel M. 2010. "Uncertainty Quantification via Random Domain Decomposition and Probabilistic Collocation on Sparse Grids". United States. https://doi.org/10.1016/j.jcp.2010.05.036.
@article{osti_991070,
title = {Uncertainty Quantification via Random Domain Decomposition and Probabilistic Collocation on Sparse Grids},
author = {Lin, Guang and Tartakovsky, Alexandre M and Tartakovsky, Daniel M},
abstractNote = {Due to lack of knowledge or insufficient data, many physical systems are subject to uncertainty. Such uncertainty occurs on a multiplicity of scales. In this study, we conduct the uncertainty analysis of diffusion in random composites with two dominant scales of uncertainty: Large-scale uncertainty in the spatial arrangement of materials and small-scale uncertainty in the parameters within each material. A general two-scale framework that combines random domain decomposition (RDD) and probabilistic collocation method (PCM) on sparse grids to quantify the large and small scales of uncertainty, respectively. Using sparse grid points instead of standard grids based on full tensor products for both the large and small scales of uncertainty can greatly reduce the overall computational cost, especially for random process with small correlation length (large number of random dimensions). For one-dimensional random contact point problem and random inclusion problem, analytical solution and Monte Carlo simulations have been conducted respectively to verify the accuracy of the combined RDD-PCM approach. Additionally, we employed our combined RDD-PCM approach to two- and three-dimensional examples to demonstrate that our combined RDD-PCM approach provides efficient, robust and nonintrusive approximations for the statistics of diffusion in random composites.},
doi = {10.1016/j.jcp.2010.05.036},
url = {https://www.osti.gov/biblio/991070}, journal = {Journal of Computational Physics, 229(19-20):6995–7012},
issn = {0021-9991},
number = 19-20,
volume = 229,
place = {United States},
year = {Wed Sep 01 00:00:00 EDT 2010},
month = {Wed Sep 01 00:00:00 EDT 2010}
}