Physical Sciences and Mathematics Commons^™

A Reduced Order Parameter Estimation Technique Using Orthonormal Wavelets, Miguel Hernandez Iv

Open Access Theses & Dissertations

In this work we introduce methods for model order reduction using orthonormal wavelets. Specifically, we propose techniques and algorithms for wavelet-based reduced order parameter estimation using orthonormal wavelets for solving nonlinear least squares problems. Approaches for parameter reduction using the one dimensional and two dimensional wavelet transforms are presented using multiple levels of decomposition.

The performance of wavelet-based reduced order parameter estimation is tested using a suite of orthonormal wavelets on a groundwater hydraulics model provided by the U.S. Army Corps of Engineers. Using the hydraulics model, the goal is to find a least-squares solution of the permeability field given …