A model-order reduction method based on wavelets and POD to solve nonlinear transient and steady-state continuation problems

We introduce a wavelet-based model-order reduction method (MOR) that provides an alternative subspace to Proper Orthogonal Decomposition (POD). We thus compare the wavelet and POD-based approaches for reducing high-dimensional nonlinear transient and steady-state continuation problems. We employ a global regularized Gauss-Newton (GN) algorithm for solving zero-residual problems on a reduced subspace. We rediscover that this latter is just a generalization of the Petrov-Galerkin method (PG) which retains GN's fast convergence rate. Numerical results included herein indicate that wavelet-based method is competitive with POD, for small rank systems ( ≈ 100) and compression ratios below 25% while POD achieves up to 90%. Full-order-model (FOM) results demonstrate that the proposed PGGN algorithm outperforms the standard PG method.