[Évaluation précise de lʼestimateur a posteriori dans la méthode des bases réduites]
In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this Note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and illustrated on a simple example.
Dans la méthode des bases réduites, lʼévaluation de lʼestimateur a posteriori peut sʼavérer particulièrement sensible aux erreurs dʼarrondis machine. Dans cette Note, lʼorigine de la perte de précision est révélée et une solution à ce problème est proposée et illustrée sur un exemple simple.
Accepté le :
Publié le :
Fabien Casenave 1
@article{CRMATH_2012__350_9-10_539_0, author = {Fabien Casenave}, title = {Accurate a posteriori error evaluation in the reduced basis method}, journal = {Comptes Rendus. Math\'ematique}, pages = {539--542}, publisher = {Elsevier}, volume = {350}, number = {9-10}, year = {2012}, doi = {10.1016/j.crma.2012.05.012}, language = {en}, }
Fabien Casenave. Accurate a posteriori error evaluation in the reduced basis method. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 539-542. doi : 10.1016/j.crma.2012.05.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.05.012/
[1] A posteriori error analysis of the reduced basis method for nonaffine parametrized nonlinear PDEs, SIAM J. Numer. Anal., Volume 47 (2009), pp. 2001-2022
[2] Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems, C. R. Acad. Sci. Paris, Ser. I, Volume 331 (2000) no. 2, pp. 153-158
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- Dual natural-norm a posteriori error estimators for reduced basis approximations to parametrized linear equations, M
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- Multilevel a posteriori error estimator for greedy reduced basis algorithms, SN Applied Sciences, Volume 2 (2020) no. 4 | DOI:10.1007/s42452-020-2409-9
- A robust error estimator and a residual-free error indicator for reduced basis methods, Computers Mathematics with Applications, Volume 77 (2019) no. 7, pp. 1963-1979 | DOI:10.1016/j.camwa.2018.11.032 | Zbl:1442.65351
- An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades, Mathematical and Computational Applications, Volume 24 (2019) no. 2, p. 41 | DOI:10.3390/mca24020041
- Parametric Model-Order Reduction for Accelerating the Gradient-Based Optimization of Microwave Structures Using Finite-Elements, IFAC-PapersOnLine, Volume 51 (2018) no. 2, p. 190 | DOI:10.1016/j.ifacol.2018.03.033
- A Finite-Element-Based Fast Frequency Sweep Framework Including Excitation by Frequency-Dependent Waveguide Mode Patterns, IEEE Transactions on Microwave Theory and Techniques, Volume 65 (2017) no. 7, p. 2249 | DOI:10.1109/tmtt.2017.2679181
- A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media, Computer Methods in Applied Mechanics and Engineering, Volume 307 (2016), pp. 1-31 | DOI:10.1016/j.cma.2016.03.016 | Zbl:1436.76018
- A New Method for Accurate and Efficient Residual Computation in Adaptive Model-Order Reduction, IEEE Transactions on Magnetics, Volume 51 (2015) no. 3, p. 1 | DOI:10.1109/tmag.2014.2352812
- Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method, European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis, Volume 48 (2014) no. 1, pp. 207-229 | DOI:10.1051/m2an/2013097 | Zbl:1288.65157
- A Space-Time Petrov–Galerkin Certified Reduced Basis Method: Application to the Boussinesq Equations, SIAM Journal on Scientific Computing, Volume 36 (2014) no. 1, p. A232 | DOI:10.1137/120903300
- Two-step greedy algorithm for reduced order quadratures, Journal of Scientific Computing, Volume 57 (2013) no. 3, pp. 604-637 | DOI:10.1007/s10915-013-9722-z | Zbl:1292.65024
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