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Numerical Methods for Partial Differential Equations

Nonintrusive reduced-order modeling of parametrized time-dependent partial differential equations

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Abstract

We propose a nonintrusive reduced-order modeling method based on the notion of space-time-parameter proper orthogonal decomposition (POD) for approximating the solution of nonlinear parametrized time-dependent partial differential equations. A two-level POD method is introduced for constructing spatial and temporal basis functions with special properties such that the reduced-order model satisfies the boundary and initial conditions by construction. A radial basis function approximation method is used to estimate the undetermined coefficients in the reduced-order model without resorting to Galerkin projection. This nonintrusive approach enables the application of our approach to general problems with complicated nonlinearity terms. Numerical studies are presented for the parametrized Burgers' equation and a parametrized convection-reaction-diffusion problem. We demonstrate that our approach leads to reduced-order models that accurately capture the behavior of the field variables as a function of the spatial coordinates, the parameter vector and time. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013

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