**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" }