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Title: Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

Abstract

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.

Authors:
ORCiD logo [1];  [1]
  1. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1123534
Alternate Identifier(s):
OSTI ID: 1247015
Report Number(s):
SAND-2013-10657J
Journal ID: ISSN 0021-9991; PII: S0021999114006500
Grant/Contract Number:
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 280; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Jakeman, J. D., and Wildey, T. Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates. United States: N. p., 2015. Web. doi:10.1016/j.jcp.2014.09.014.
Jakeman, J. D., & Wildey, T. Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates. United States. doi:10.1016/j.jcp.2014.09.014.
Jakeman, J. D., and Wildey, T. Thu . "Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates". United States. doi:10.1016/j.jcp.2014.09.014. https://www.osti.gov/servlets/purl/1123534.
@article{osti_1123534,
title = {Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates},
author = {Jakeman, J. D. and Wildey, T.},
abstractNote = {In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.},
doi = {10.1016/j.jcp.2014.09.014},
journal = {Journal of Computational Physics},
number = C,
volume = 280,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 2015},
month = {Thu Jan 01 00:00:00 EST 2015}
}

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