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Wavelets and wavelet optimized-finite differences for electronic structure calculations

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Title: Wavelets and wavelet optimized-finite differences for electronic structure calculations
Author(s): Rao, Vivek
Doctoral Committee Chair(s): Martin, R. M.
Department / Program: Physics
Discipline: Physics
Degree: Ph.D.
Genre: Dissertation
Subject(s): wavelets Daubechies wavelets Wavelet Optimized Finite Difference Model
Abstract: To perform electronic structure calculations on inhomogenous systems, it is desirable to use methods which adapt to the problem by using a spatially-varying level of resolution. A wavelet basis can efficiently represent a function which is rapidly varying in certain regions of space. One-dimensional calculations using Daubechies wavelets as an adaptive basis have been performed, showing that a compressed wavelet basis can determine the eigenvalues of a system with high accuracy using relatively few functions. Using the Wavelet Optimized Finite Difference Method (WOFD) [1], wavelets can also be used to determine a grid for finite difference calculations. In one dimension, starting with a guess for the wavefunction on a coarse grid with few points, an accurate solution on a nouniform grid can be evolved. In three dimensions, self-consistent total energy calculations employing density functional theory using real-space grids have been performed on atomis, molecules, and quantum dots. Calculations employing WOFD grids are much more accurate than calculations using uniform grids of the same size. Comparisons are made with other adaptive methods.
Issue Date: 1998
Genre: Dissertation / Thesis
Type: Text
Language: English
URI: http://hdl.handle.net/2142/30849
Other Identifier(s): 4120443
Rights Information: ©1998 Rao
Date Available in IDEALS: 2012-05-15
 

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