{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/30849"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/30849","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Wavelets and wavelet optimized-finite differences for electronic structure calculations","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Rao, Vivek"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Martin, Richard M."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-15T16:48:44Z","date_published":"2012-05-15T16:48:44Z","updated_at":"2026-07-22T22:25:29Z","subjects":["wavelets","Daubechies wavelets","Wavelet Optimized Finite Difference Model"],"languages":["en"],"rights":["©1998 Rao"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["4120443"],"render_values":[{"text":"4120443","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/30849","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Martin, Richard M."]},{"key":"dc:creator","label":"Author","values":["Rao, Vivek"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-05-15T16:48:44Z","10000-01-01","1998"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["wavelets","Daubechies wavelets","Wavelet Optimized Finite Difference Model"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["©1998 Rao"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/30849","4120443"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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"]},{"key":"dc:title","label":"Title","values":["Wavelets and wavelet optimized-finite differences for electronic structure calculations"]}]}],"canonical_facts":{"dc:contributor":["Martin, Richard M."],"dc:creator":["Rao, Vivek"],"dc:date":["2012-05-15T16:48:44Z","10000-01-01","1998"],"dc:description":["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. 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