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

Jakeman, J. D.; Wildey, T.

doi:10.1016/j.jcp.2014.09.014

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

Journal Article · Wed Dec 31 23:00:00 EST 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2014.09.014· OSTI ID:1123534

^[1]; Wildey, T. ^[1]

Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1123534

Alternate ID(s):: OSTI ID: 22382155
OSTI ID: 1247015

Report Number(s):: SAND--2013-10657J; PII: S0021999114006500

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 280; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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