Transport reversal for model reduction of hyperbolic partial differential equations
Numerical Analysis
2017-01-27 v1
Abstract
Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projection- based model reduction methods. To overcome this problem, we build on previous work in symmetry reduction [Rowley and Marsden, Physica D (2000), pp. 1-19] and propose an iterative algorithm that decomposes the snapshot matrix into multiple shifting profiles, each with a corresponding speed. Its applicability to typical hyperbolic problems is demonstrated through numerical examples, and other natural extensions that modify the shift operator are considered. Finally, we give a geometric interpretation of the algorithm.
Cite
@article{arxiv.1701.07529,
title = {Transport reversal for model reduction of hyperbolic partial differential equations},
author = {Donsub Rim and Scott Moe and Randall J. LeVeque},
journal= {arXiv preprint arXiv:1701.07529},
year = {2017}
}