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

Understand

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.