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Table 1 Computational details about the high-fidelity model and the model order reduction

From: Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes

Problem number 1 2 3 4
Space dimension 2D 2D 2D 3D
IGA space dimension \((\mathcal {N}_v, \mathcal {N}_p)\) (2178, 1024) (2592, 1225) (2178, 1024) (6591, 343)
Number of geometrical parameters 2 rotations 2 rotations 4 rotations 4 = 2 rotations+ outflow variation (length and width)
Geometrical parameters range \([-75 ^\circ , 75 ^\circ ]^2\) \([-75 ^\circ , 75 ^\circ ]^2\) \([-45 ^\circ , 45 ^\circ ]^4\) \([-75 ^\circ , 75 ^\circ ]^2 \times [0,2]^2\)
Number of IGA control points 1089 1296 1089 2197
Number of FFD control points 10 10 20 40
EIM tolerance \(10^{-3}\) \(10^{-3}\) \(10^{-3}\) \(10^{-3}\)
EIM terms \(Q_K + Q_B + Q_f\) 27 + 14 + 0 89 + 22 + 0 50 + 22 + 0 104 + 44 + 0
Number of snapshots 500 500 500 500
POD tolerance I(N) \(10^{-3}\) \(10^{-2}\) \(10^{-2}\) \(2*10^{-2}\)
POD space dimension \((N_{\mathbf {u},\mathbf {s}}, N_p)\) (20, 10) (20, 10) (20, 10) (40, 20)
HF evaluation time 1.5 s 6.1 s 1.5 s 27 s
POD offline construction time 250 s 2344 s 250 s 12325 s
POD evaluation time 0.07 s 0.08 s 0.08 s 0.11 s
Computational speedup POD 20 76 18 245