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.

[1]  Vanessa Hertzog,et al.  Computational Fluid Mechanics And Heat Transfer , 2016 .

[2]  P Kerfriden,et al.  Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. , 2011, Computer methods in applied mechanics and engineering.

[3]  Fergyanto E. Gunawan,et al.  Levenberg-Marquardt iterative regularization for the pulse-type impact-force reconstruction , 2012 .

[4]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[5]  K. Morgan,et al.  Reduced order modelling for unsteady fluid flow using proper orthogonal decomposition and radial basis functions , 2013 .

[6]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[7]  M. Paggi,et al.  Model order reduction applied to heat conduction in photovoltaic modules , 2015, 1505.05361.

[8]  Anthonio Teolis,et al.  Computational signal processing with wavelets , 1998, Applied and numerical harmonic analysis.

[9]  C. Farhat,et al.  Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations , 2011 .

[10]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[11]  A partitioning scheme and iterative solution for sparse bordered systems , 1988 .

[12]  D. Sorensen,et al.  Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media , 2011 .

[13]  J. Peraire,et al.  An efficient reduced‐order modeling approach for non‐linear parametrized partial differential equations , 2008 .

[14]  K. Kunisch,et al.  Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition , 1999 .

[15]  Charbel Farhat,et al.  Nonlinear model order reduction based on local reduced‐order bases , 2012 .

[16]  Kevin Carlberg,et al.  Adaptive h‐refinement for reduced‐order models , 2014, ArXiv.

[17]  Víctor Pereyra,et al.  Model order reduction with oblique projections for large scale wave propagation , 2016, J. Comput. Appl. Math..

[18]  J. Peraire,et al.  Balanced Model Reduction via the Proper Orthogonal Decomposition , 2002 .

[19]  David Amsallem,et al.  An adaptive and efficient greedy procedure for the optimal training of parametric reduced‐order models , 2015 .