A Laplace transform certified reduced basis method; application to the heat equation and wave equation
Author(s)Knezevic, David; Patera, Anthony T.; Huynh, Dinh Bao Phuong
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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.
DepartmentMassachusetts Institute of Technology. Department of Mechanical Engineering
Comptes Rendus Mathematique
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.
Author's final manuscript