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

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 non-linearity 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. (C) 2013 Wiley Periodicals, Inc.