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Full-Text Articles in Physical Sciences and Mathematics
Wavelet Factorization Via A Homogenization Analogy For Solutions Of Linear Systems, Andrea Van Sickle
Wavelet Factorization Via A Homogenization Analogy For Solutions Of Linear Systems, Andrea Van Sickle
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
A system of linear equations can be solved using a factorization method that produces a wavelet structure and is akin to a homogenization process used in determining the solution of differential equations. The method is dependant on the particular structure of Hadamard matrices and their implementation in a similarity transform. This paper details the development of such a method for systems of size 2n x 2n, including establishing the theoretical underpinnings necessary to define an orthogonal transform. Also, we present the development of an algorithm to implement the method for a simple 2 x 2 system, which will then be …
Using Wavelets As A Computational And Theoretical Tool For Homogenization, Laura Lee Watkins
Using Wavelets As A Computational And Theoretical Tool For Homogenization, Laura Lee Watkins
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Since the cost of petroleum fluctuates widely, it is advisable to optimize extraction of oil and other hydrocarbon products form existing oil reserves. Because of the costs involved in recovering oil from a reservoir, predicting reservoir performance can be a useful tool for determining whether continued extraction might be profitable. This can be done using computer simulations of the physical processes involved such as pressure/head, fluid velocities, and so forth. Fluid flow within a reservoir occurs at a very small scale relative to the size of the reservoir. This size difference makes performing simulations at the physically appropriate scale unfeasible. …