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Title: Limited-memory adaptive snapshot selection for proper orthogonal decomposition: ADAPTIVE SNAPSHOT SELECTION FOR POD

Authors:
 [1];  [2];  [3];  [4]
  1. Computational Engineering Division, Lawrence Livermore National Laboratory, L-792, PO Box 808 Livermore 94550 CA USA
  2. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, L-561, PO Box 808 Livermore 94550 CA USA
  3. Applications, Simulations, and Quality, Lawrence Livermore National Laboratory, L-560, PO Box 808 Livermore 94550 CA USA
  4. Global Security Computing Applications Division, Lawrence Livermore National Laboratory, L-389, PO Box 808 Livermore 94550 CA USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1401666
Grant/Contract Number:
13-ERD-031
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 109; Journal Issue: 2; Related Information: CHORUS Timestamp: 2017-10-20 17:35:06; Journal ID: ISSN 0029-5981
Publisher:
Wiley Blackwell (John Wiley & Sons)
Country of Publication:
United Kingdom
Language:
English

Citation Formats

Oxberry, Geoffrey M., Kostova-Vassilevska, Tanya, Arrighi, William, and Chand, Kyle. Limited-memory adaptive snapshot selection for proper orthogonal decomposition: ADAPTIVE SNAPSHOT SELECTION FOR POD. United Kingdom: N. p., 2016. Web. doi:10.1002/nme.5283.
Oxberry, Geoffrey M., Kostova-Vassilevska, Tanya, Arrighi, William, & Chand, Kyle. Limited-memory adaptive snapshot selection for proper orthogonal decomposition: ADAPTIVE SNAPSHOT SELECTION FOR POD. United Kingdom. doi:10.1002/nme.5283.
Oxberry, Geoffrey M., Kostova-Vassilevska, Tanya, Arrighi, William, and Chand, Kyle. 2016. "Limited-memory adaptive snapshot selection for proper orthogonal decomposition: ADAPTIVE SNAPSHOT SELECTION FOR POD". United Kingdom. doi:10.1002/nme.5283.
@article{osti_1401666,
title = {Limited-memory adaptive snapshot selection for proper orthogonal decomposition: ADAPTIVE SNAPSHOT SELECTION FOR POD},
author = {Oxberry, Geoffrey M. and Kostova-Vassilevska, Tanya and Arrighi, William and Chand, Kyle},
abstractNote = {},
doi = {10.1002/nme.5283},
journal = {International Journal for Numerical Methods in Engineering},
number = 2,
volume = 109,
place = {United Kingdom},
year = 2016,
month = 7
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1002/nme.5283

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  • Reduced order models are useful for accelerating simulations in many-query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models can have prohibitively expensive memory and floating-point operation costs in high-performance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive time-stepping ordinary differential equation solvers. The error estimator used in this work is related to theory boundingmore » the approximation error in time of proper orthogonal decomposition-based reduced order models, and memory usage is minimized by computing the singular value decomposition using a single-pass incremental algorithm. Results for a viscous Burgers’ test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full order model is recovered to within discretization error. The resulting method can be used on supercomputers to generate proper orthogonal decomposition-based reduced order models, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space.« less
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