A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications

摘要

A novel parameterized non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) has been developed. This P-NIROM is a generic and efficient approach for model reduction of parameterized partial differential equations (P-PDEs). Over existing parameterized reduced order models (P-ROM) (most of them are based on the reduced basis method), it is non-intrusive and independent on partial differential equations and computational codes. During the training process, the Smolyak sparse grid method is used to select a set of parameters over a specific parameterized space (ohm(p) is an element of R-P). For each selected parameter, the reduced basis functions are generated from the snapshots derived from a run of the high fidelity model. More generally, the snapshots and basis function sets for any parameters over Op can be obtained using an interpolation method. The P-NIROM can then be constructed by using our recently developed technique (Xiao et al., 2015 [ 41,42]) where either the Smolyak or radial basis function (RBF) methods are used to generate a set of hyper-surfaces representing the underlying dynamical system over the reduced space.