| Home > Publications > Reports > Numerical Analysis and Applied Mathematics (TW) |
TW 263
G. Uytterhoeven and D. Roose
Experiments with a Wavelet-Based Approximate Proper Orthogonal
Abstract
The Proper Orthogonal Decomposition (POD) or Karhunen-Lohve Transform (KLT) is a powerful tool to obtain low-dimensional models for large scale dynamical systems, described by partial differential equations. Starting from a set of solutions (obtained by experiment or computation), called snapshots, the method computes an ``optimal'' basis of eigenmodes for the snapshots, which can be used to construct a low-dimensional model of the dynamical system. Unfortunately the construction of a POD and also the projection of the original problem onto the eigenmodes are very expensive operations. We have done experiments with an Approximate Proper Orthogonal Decomposition, based on data compression using symmetric biorthogonal wavelets. A wavelet packet transform allows to decorrelate and compress the snapshots, after which we compute the POD of the compressed data set of much lower dimension, while we still obtain good approximations for the eigenmodes of the original system. We will present results for the computation of an Approximate POD for a system of partial differential equations (the one-dimensional Brusselator reaction-diffusion model), using symmetric wavelets (Cohen-Daubechies-Feauveau).
report.pdf / mailto: G. Uytterhoeven