Applications and comparison of model-order reduction methods based on wavelets and POD

We present a wavelet-based model-order reduction method (MOR) that provides an alternative subspace when Proper Orthogonal Decomposition (POD) is not a choice. We thus compare the wavelet- and POD-based approaches for reducing high-dimensional nonlinear transient and steady-state continuation problems. We also propose a line-search regularized Petrov-Galerkin (PG) Gauss-Newton (GN) algorithm that includes a regularization procedure and a globalization strategy. Numerical results included herein indicate that wavelet-based method is competitive with POD for compression ratios below 25% while POD achieves up to 90%. Full-order-model (FOM) results demonstrate that the proposed PGGN algorithm outperforms the standard GN method.