Wavelets and wavelet optimized-finite differences for electronic structure calculations
Rao, Vivek
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Permalink
https://hdl.handle.net/2142/30849
Description
Title
Wavelets and wavelet optimized-finite differences for electronic structure calculations
Author(s)
Rao, Vivek
Issue Date
1998
Doctoral Committee Chair(s)
Martin, Richard M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
wavelets
Daubechies wavelets
Wavelet Optimized Finite Difference Model
Language
en
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.
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