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

Tommaso Taddei (1, 2) , Lei Zhang (2, 1)

1 MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS
2 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: Model order reduction; Parameterized hyperbolic partial differential equations; Data compression

Domaines: Mathématiques [math]

Tommaso Taddei, Lei Zhang. Space-time registration-based model reduction of parameterized one-dimensional hyperbolic PDEs. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (1), pp.99-130. ⟨10.1051/m2an/2020073⟩. ⟨hal-03146217⟩