Transport Reversal for Model Reduction of Hyperbolic Partial Differential Equations
by D. Rim, S. Moe, and R. J. LeVeque SIAM/ASA Journal on Uncertainty Quantification 6(2018), pp. 118-150. doi:10.1137/17M1113679

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, Phys. D, 142 (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.

Reprint: TransportReversal2018.pdf

Journal webpage: doi:10.1137/17M1113679

Preprint: arXiv:1701.07529 (Januray, 2017)

bibtex entry:

@article{?,
  author="D. Rim and S. Moe and R. J. LeVeque",
  title="Transport Reversal for Model Reduction of Hyperbolic Partial
Differential Equations",
  journal="SIAM/ASA J. Uncertainty Quantification",
  volume="6",
  year="2018",
  pages="118-150",
  doi="10.1137/17M1113679"
}