Adaptive <i>h</i> -refinement for reduced-order models [electronic resource] : ADAPTIVE <i>h</i> -refinement for reduced-order models
- Washington, D.C. : United States. National Nuclear Security Administration, 2014. and Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy
- Physical Description:
- pages 1,192-1,210 : digital, PDF file
- Additional Creators:
- Sandia National Laboratories, United States. National Nuclear Security Administration, and United States. Department of Energy. Office of Scientific and Technical Information
- Restrictions on Access:
- Free-to-read Unrestricted online access
- 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.
- Published through SciTech Connect., 11/05/2014., "sand--2014-2732j", "507023", International Journal for Numerical Methods in Engineering 102 5 ISSN 0029-5981 AM, and Kevin T. Carlberg.
- Funding Information:
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