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A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space-time ROM for linear dynamical problems has been developed, which further reduces the problem size by introducing a temporal reduction in addition to a spatial reduction without much loss in accuracy....
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Context 1
... ( at which the FOM is solved. The Galerkin and Petrov-Galerkin space-time ROMs solve the Equation (7.3) with the target parameter (µ1, µ2) = (−0.7, −0.7)). Fig. 3, 4, and 5 show the relative errors, the space-time residuals, and the online speed-ups as a function of the reduced dimension ns and nt. We observe that both Galerkin and Petrov-Galerkin ROMs with ns = 5 and nt = 3 achieve a good accuracy (i.e., relative errors of 0.012% and 0.026%, respectively) and speed-up (i.e., 350.31 and 376.04, ...
Context 2
... Glaerkin (b) Petrov-Galerkin Figure 13: The comparison of the Galerkin and Petrov-Galerkin ROMs for predictive cases ...
Context 3
... ( at which the FOM is solved. The Galerkin and Petrov-Galerkin space-time ROMs solve the Equation (7.3) with the target parameter (µ1, µ2) = (−0.7, −0.7)). Fig. 3, 4, and 5 show the relative errors, the space-time residuals, and the online speed-ups as a function of the reduced dimension ns and nt. We observe that both Galerkin and Petrov-Galerkin ROMs with ns = 5 and nt = 3 achieve a good accuracy (i.e., relative errors of 0.012% and 0.026%, respectively) and speed-up (i.e., 350.31 and 376.04, ...
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