Volume 55, Number 1, January-February 2021
|Page(s)||99 - 130|
|Published online||18 February 2021|
Space-time registration-based model reduction of parameterized one-dimensional hyperbolic PDEs
IMB, UMR 5251, Univ. Bordeaux, 33400 Talence, France
2 Inria Bordeaux Sud-Ouest, Team MEMPHIS, 33400 Talence, France
* Corresponding author: email@example.com
Accepted: 16 October 2020
We propose a model reduction procedure for rapid and reliable solution of parameterized hyperbolic partial differential equations. Due to the presence of parameter-dependent shock waves and contact discontinuities, these problems are extremely challenging for traditional model reduction approaches based on linear approximation spaces. The main ingredients of the proposed approach are (i) an adaptive space-time registration-based data compression procedure to align local features in a fixed reference domain, (ii) a space-time Petrov–Galerkin (minimum residual) formulation for the computation of the mapped solution, and (iii) a hyper-reduction procedure to speed up online computations. We present numerical results for a Burgers model problem and a shallow water model problem, to empirically demonstrate the potential of the method.
Mathematics Subject Classification: 65N30 / 41A45 / 35L02 / 90C26
Key words: Parameterized hyperbolic partial differential equations / model order reduction / data compression
© The authors. Published by EDP Sciences, SMAI 2021
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