Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
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.
- Research Organization:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1141744
- Report Number(s):
- SAND-2014-2732J; 507023
- Journal Information:
- International Journal for Numerical Methods in Engineering, Vol. 102, Issue 5; ISSN 0029-5981
- Publisher:
- WileyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
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