Left column: Upper and lower bounds for the relative H∞ reduction error when using balanced truncation. Middle column: Fullorder model snapshot at time t = 10 and its reconstruction error using a reduced-order model of order 10. Right column: The full-order and reduced-order models' outputs and the error.

Contexts in source publication

Context 1

... element discretization, using FEniCS, leads to a system of the form (1) with n = 12 296, m = 1, and p = 1. The top-middle plot in Figure 1 shows the state of the full-order model at t = 10 when the input is u(t) = sin( π 3 t) 2 . The average run time is about 8 seconds on a laptop (model: Vaio VJS132C11L; processor: Intel c Core TM i7-8550U CPU @ 1.80 GHz, 4 cores, 8 logical processors, hyper-threading activated; RAM: 8 GB; cache: 8 MB). ...

Context 2

... applied BT (using pyMOR 0.5) to get a ROM of order 10, with a run time of about 7 seconds. Based on Hankel singular values, we find the relative H ∞ -error lies in the interval [7.27 × 10 −5 , 1.23 × 10 −4 ], shown also in the left plot of Figure 1. The relative H 2 -error can be computed and its value is 7.37 × 10 −3 . ...

Context 3

... relative H 2 -error can be computed and its value is 7.37 × 10 −3 . In the bottom row of Figure 1, we see the state and output errors of the ROM. As expected, we see that the output is approximated better than the state. ...