Comptes Rendus
Partial Differential Equations/Numerical Analysis
A Laplace transform certified reduced basis method; application to the heat equation and wave equation
[Une méthode de bases réduites « certifiée » utilisant la transformation de Laplace ; Application à lʼéquation de la chaleur et à lʼéquation des ondes]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 401-405.

On introduit une méthode de bases réduites « certifiée » pour lʼéquation de la chaleur et pour lʼéquation des ondes. Les outils sont les suivants : approximation en bases réduites « certifiée » de la transformée de Laplace, transformée de Laplace inverse pour lʼapproximation de la sortie en bases réduites pour la variable temps, estimations dʼerreurs rigoureuses, filtre en temps (de Butterworth) mettant en évidence la nécessité dʼune troncature « modale », décomposition en fonctions propres en bases réduites, intégrale de contour pour la décomposition « Offline–Online ». On donne des résultats numériques pour montrer lʼéfficacité et la précision de la méthode.

We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accuracy and efficiency of the approach.

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DOI : 10.1016/j.crma.2011.02.003

D.B. Phuong Huynh 1 ; David J. Knezevic 1 ; Anthony T. Patera 1

1 Massachusetts Institute of Technology, room 3-266, Cambridge, MA 02139, USA
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D.B. Phuong Huynh; David J. Knezevic; Anthony T. Patera. A Laplace transform certified reduced basis method; application to the heat equation and wave equation. Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 401-405. doi : 10.1016/j.crma.2011.02.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.02.003/

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