Transport Reversal for Model Reduction of Hyperbolic Partial Differential Equations

Donsub Rim, Scott Moe, Randall J. LeVeque

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.