A reduced FVE formulation based on POD method and error analysis for two-dimensional viscoelastic problem

A reduced‐order extrapolated natural boundary element method based on POD for the 2D hyperbolic equation in unbounded domain

“…Theorem 6. If k+1 0 and k+1 0h are, respectively, solutions to (25) and (30), and  h (Σ) is the piecewise linear polynomial subspace. Then, when h = O( ), we have the following error estimates:…”

“…Particularly, it has been successfully applied to the Galerkin methods (see Kunisch and Volkwein 18,19 ), the FE methods (see previous studies [20][21][22] ), the FD schemes (see Luo et al 23 and Sun et al 24 ), the finite volume element (FVE) methods (see Luo, Li, et al 25 and Luo, Xie, et al 26 ), and the reduced-basis methods (see previous studies 27-29 ) for PDEs. However, the most existing POD order-reduction methods (see, eg, previous studies [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] ) are built by the POD basis formed with the classical solutions at all time nodes on [0, T], before repetitively computing the order-reduction solutions at the same time nodes. As a matter of fact, these all are some valueless repetitive calculations.…”

POD-based model order reduction with an adaptive snapshot selection for a discontinuous Galerkin approximation of the time-domain Maxwell's equations

“…The alternative approach that we consider in this work is model order reduction (MOR) [2,13,14,15]. MOR method is useful for accelerating simulations in many fields of science and engineering [16,17,18,19,20,21,22]. In particular, MOR method is also widely used in the context of electromagnetics [19,23,24,25,26,27,28,29,30,31,32].…”

A reduced-order extrapolating Crank-Nicolson finite difference scheme for the Riesz space fractional order equations with a nonlinear source function and delay

“…It has been extensively used in analysis of signal together with pattern recognition (see [5]), statistical computation (see [9]), and computational fluid dynamics (see [29]). In recent years, it also has been successfully applied to the order-reduction for the Galerkin method (see, e.g., [10,11]), the finite element method (see, e.g., [18,22]), the FD scheme (see, e.g., [24,31]), finite volume element method (see, e.g., [21,23]), and reduced basis methods (see, e.g., [1,6,28]) for PDEs. However, the most existing POD reduced order methods (see, e.g., [1, 2, 5-7, 9-11, 18, 21-25, 28-31]) are built by the POD basis formed with the classical solutions at the all time nodes on [0, T ], before repetitively computing the reduced order solutions at the same time nodes.…”