TADDEI, Tommaso; ZHANG, Lei

doi:10.1051/m2an/2020073

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TADDEI, Tommaso
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]

ZHANG, Lei
Institut de Mathématiques de Bordeaux [IMB]
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]

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ESAIM: Mathematical Modelling and Numerical Analysis. 2021-01, vol. 55, n° 1, p. 99-130

EDP Sciences

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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.< Leer menos

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Model order reduction

Parameterized hyperbolic partial differential equations

Data compression

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Space-time registration-based model reduction of parameterized one-dimensional hyperbolic PDEs

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