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Utah State University

1. Lasisi, Abibat Adebisi. Multi-Resolution Analysis Using Wavelet Basis Conditioned on Homogenization.

Degree: PhD, Mathematics and Statistics, 2018, Utah State University

This dissertation considers an approximation strategy using a wavelet reconstruction scheme for solving elliptic problems. The foci of the work are on (1) the approximate solution of differential equations using multiresolution analysis based on wavelet transforms and (2) the homogenization process for solving one and two-dimensional problems, to understand the solutions of second order elliptic problems. We employed homogenization to compute the average formula for permeability in a porous medium. The structure of the associated multiresolution analysis allows for the reconstruction of the approximate solution of the primary variable in the elliptic equation. Using a one-dimensional wavelet reconstruction algorithm proposed in this work, we are able to numerically compute the approximations of the pressure variables. This algorithm can directly be applied to elliptic problems with discontinuous coefficients.We also implemented Java codes to solve the two dimensional elliptic problems using our methods of solutions. Furthermore, we propose homogenization wavelet reconstruction algorithm, fast transform and the inverse transform algorithms that use the results from the solutions of the local problems and the partial derivatives of the pressure variables to reconstruct the solutions. Advisors/Committee Members: Joseph V. Koebbe, ;.

Subjects/Keywords: wavelet; homogenization; fast transform; elliptic differential equations; homogenization wavelet reconstruction; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Lasisi, A. A. (2018). Multi-Resolution Analysis Using Wavelet Basis Conditioned on Homogenization. (Doctoral Dissertation). Utah State University. Retrieved from https://digitalcommons.usu.edu/etd/7313

Chicago Manual of Style (16th Edition):

Lasisi, Abibat Adebisi. “Multi-Resolution Analysis Using Wavelet Basis Conditioned on Homogenization.” 2018. Doctoral Dissertation, Utah State University. Accessed January 18, 2020. https://digitalcommons.usu.edu/etd/7313.

MLA Handbook (7th Edition):

Lasisi, Abibat Adebisi. “Multi-Resolution Analysis Using Wavelet Basis Conditioned on Homogenization.” 2018. Web. 18 Jan 2020.

Vancouver:

Lasisi AA. Multi-Resolution Analysis Using Wavelet Basis Conditioned on Homogenization. [Internet] [Doctoral dissertation]. Utah State University; 2018. [cited 2020 Jan 18]. Available from: https://digitalcommons.usu.edu/etd/7313.

Council of Science Editors:

Lasisi AA. Multi-Resolution Analysis Using Wavelet Basis Conditioned on Homogenization. [Doctoral Dissertation]. Utah State University; 2018. Available from: https://digitalcommons.usu.edu/etd/7313

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