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Martin, Richard M. Rao, Vivek 2012-05-15T16:48:44Z 2012-05-15T16:48:44Z 10000-01-01 1998 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. Submitted by William Weathers (weathrs2@illinois.edu) on 2012-05-15T16:48:44Z No. of bitstreams: 1 1998_Rao.pdf: 2328004 bytes, checksum: 26f4fc908211ebaae550c064d23176a4 (MD5) Made available in DSpace on 2012-05-15T16:48:44Z (GMT). No. of bitstreams: 1 1998_Rao.pdf: 2328004 bytes, checksum: 26f4fc908211ebaae550c064d23176a4 (MD5) Previous issue date: 1998 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Weathers (weathrs2@illinois.edu) on 2012-05-15T16:48:44Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:10:21-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis Thesis U of I Only http://hdl.handle.net/2142/30849 4120443 en ©1998 Rao wavelets Daubechies wavelets Wavelet Optimized Finite Difference Model Wavelets and wavelet optimized-finite differences for electronic structure calculations Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.