A Laplace transform certified reduced basis method; application to the heat equation and wave equation
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Patera_A laplace transform.pdf
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Author(s)
Knezevic, David
Patera, Anthony T.
Huynh, Dinh Bao Phuong
Date Issued
March 2011
Journal
Comptes Rendus Mathematique
Publisher
Elsevier
Citation
Huynh, D.B. Phuong, David J. Knezevic, and Anthony T. Patera. “A Laplace Transform Certified Reduced Basis Method; Application to the Heat Equation and Wave Equation.” Comptes Rendus Mathematique 349, no. 7–8 (April 2011): 401–5.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-Noncommercial-NoDerivatives
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DOI of Published Version
https://doi.org/10.1016/j.crma.2011.02.003
