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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 l’équation de la chaleur et à l’équation des ondes.) (English. Abridged French version) Zbl 1215.65156

Summary: We present a certified reduced basis (RB) method for the heat equation and the 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.

MSC:

65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35L05 Wave equation
35A22 Transform methods (e.g., integral transforms) applied to PDEs
44A10 Laplace transform
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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