Robust Model Reduction Of Hyperbolic Problems by $L^1$-norm Minimization and Dictionary Approximation
Abstract
We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online -norm minimization of the residual. It is shown why this is a natural framework for hyperbolic problems and tested on nonlinear problems such as Burgers' equation and the one-dimensional Euler equations involving shocks and discontinuities. Efficient algorithms are presented for the computation of the -norm minimizer, both in the cases of linear and nonlinear residuals. Results indicate that the method has the potential of being accurate when involving only very few modes, generating physically acceptable, oscillation-free, solutions.
Cite
@article{arxiv.1603.02652,
title = {Robust Model Reduction Of Hyperbolic Problems by $L^1$-norm Minimization and Dictionary Approximation},
author = {Remi Abgrall and David Amsallem and Roxana Crisonovan},
journal= {arXiv preprint arXiv:1603.02652},
year = {2016}
}
Comments
submitted. arXiv admin note: text overlap with arXiv:1506.06178