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Title: Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models

Abstract

Our work presents a method to adaptively refine reduced-order models a posteriori without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive h-refinement: it enriches the reduced-basis space online by ‘splitting’ a given basis vector into several vectors with disjoint support. The splitting scheme is defined by a tree structure constructed offline via recursive k-means clustering of the state variables using snapshot data. This method identifies the vectors to split online using a dual-weighted-residual approach that aims to reduce error in an output quantity of interest. The resulting method generates a hierarchy of subspaces online without requiring large-scale operations or full-order-model solves. Furthermore, it enables the reduced-order model to satisfy any prescribed error tolerance regardless of its original fidelity, as a completely refined reduced-order model is mathematically equivalent to the original full-order model. Experiments on a parameterized inviscid Burgers equation highlight the ability of the method to capture phenomena (e.g., moving shocks) not contained in the span of the original reduced basis.

Authors:
 [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1141744
Report Number(s):
SAND-2014-2732J
Journal ID: ISSN 0029-5981; 507023
Grant/Contract Number:
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 102; Journal Issue: 5; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; adaptive refinement; h-refinement; model reduction; dual-weighted residual; adjoint error estimation; clustering

Citation Formats

Carlberg, Kevin T. Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models. United States: N. p., 2014. Web. doi:10.1002/nme.4800.
Carlberg, Kevin T. Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models. United States. doi:10.1002/nme.4800.
Carlberg, Kevin T. Wed . "Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models". United States. doi:10.1002/nme.4800. https://www.osti.gov/servlets/purl/1141744.
@article{osti_1141744,
title = {Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models},
author = {Carlberg, Kevin T.},
abstractNote = {Our work presents a method to adaptively refine reduced-order models a posteriori without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive h-refinement: it enriches the reduced-basis space online by ‘splitting’ a given basis vector into several vectors with disjoint support. The splitting scheme is defined by a tree structure constructed offline via recursive k-means clustering of the state variables using snapshot data. This method identifies the vectors to split online using a dual-weighted-residual approach that aims to reduce error in an output quantity of interest. The resulting method generates a hierarchy of subspaces online without requiring large-scale operations or full-order-model solves. Furthermore, it enables the reduced-order model to satisfy any prescribed error tolerance regardless of its original fidelity, as a completely refined reduced-order model is mathematically equivalent to the original full-order model. Experiments on a parameterized inviscid Burgers equation highlight the ability of the method to capture phenomena (e.g., moving shocks) not contained in the span of the original reduced basis.},
doi = {10.1002/nme.4800},
journal = {International Journal for Numerical Methods in Engineering},
number = 5,
volume = 102,
place = {United States},
year = {Wed Nov 05 00:00:00 EST 2014},
month = {Wed Nov 05 00:00:00 EST 2014}
}

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Cited by: 15works
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