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An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations
Abstract
We present an efficient reduced-basis discretization procedure for partial differential equations with nonaffine parameter dependence. The method replaces nonaffine coefficient functions with a collateral reduced-basis expansion which then permits an (effectively affine) offline–online computational decomposition. The essential components of the approach are (i) a good collateral reduced-basis approximation space, (ii) a stable and inexpensive interpolation procedure, and (iii) an effective a posteriori estimator to quantify the newly introduced errors. Theoretical and numerical results respectively anticipate and confirm the good behavior of the technique.
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Citations
Cited by
Nonlinear Model Reduction via Discrete Empirical Interpolation
Chaturantabut, S., & Sorensen, D. C. (2010) · SIAM Journal on Scientific Computing · doi:10.1137/090766498 · Cited by 1,925
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Brunton, S. L., & Noack, B. R. (2015) · Applied Mechanics Reviews · doi:10.1115/1.4031175 · Cited by 623
Non-intrusive reduced order modeling of nonlinear problems using neural networks
Hesthaven, J. S., & Ubbiali, S. (2018) · Journal of Computational Physics · doi:10.1016/j.jcp.2018.02.037 · Cited by 616
(2018) · IEEE Control Systems · doi:10.1109/mcs.2018.2810460 · Cited by 518
Yondo, R., Andrés, E., & Valero, E. (2018) · Progress in Aerospace Sciences · doi:10.1016/j.paerosci.2017.11.003 · Cited by 311
Metadata
- Authors
- Barrault, M., Maday, Y., Nguyen, N. C., & Patera, A. T.
- Venue
- Comptes Rendus. Mathématique
- Publisher
- MathDoc/Centre Mersenne
- Published
- 2004-10-14
- Volume
- 339
- Issue
- 9
- Pages
- 667-672
- ISSN
- 1631-073X (ISSN-L)
- 1778-3569
- OpenAlex
- W2047591100
- Cited by
- 1,530
- References
- 0
- FWCI
- 8.19
- Type
- journal article
- Language
- en
- Open access
- closed
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- Barrault, M., Maday, Y., Nguyen, N. C., & Patera, A. T. (2004). An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus. Mathématique. https://doi.org/10.1016/j.crma.2004.08.006
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