{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/81713"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/81713","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Multilevel Summation for the Fast Evaluation of Forces for the Simulation of Biomolecules","abstract":"This thesis provides the most thorough investigation to date of the multilevel summation method and its use for computing electrostatic interactions. The mathematical and algorithmic details are presented along with a precise operation count. The approximation error from the method is analyzed, with error bounds formulated in terms of the fundamental method parameters. The cost and error analyses enable the determination of optimal method parameters for a desired error tolerance. Various interpolation schemes for the approximation are considered, and several alternative approaches to smoothing the electrostatic potential are examined. The use of the method with different boundary conditions is discussed, and it is shown that the application of multilevel summation to the periodic potential yields a finite sum, with the truncation expressed as bounded approximation error. The performance of multilevel summation is demonstrated to be superior to other commonly used fast methods for electrostatics, while providing comparable accuracy. The method is also shown to produce stable dynamics for cheaper, lower accuracy approximation.","abstract_html":"This thesis provides the most thorough investigation to date of the multilevel summation method and its use for computing electrostatic interactions. The mathematical and algorithmic details are presented along with a precise operation count. The approximation error from the method is analyzed, with error bounds formulated in terms of the fundamental method parameters. The cost and error analyses enable the determination of optimal method parameters for a desired error tolerance. Various interpolation schemes for the approximation are considered, and several alternative approaches to smoothing the electrostatic potential are examined. The use of the method with different boundary conditions is discussed, and it is shown that the application of multilevel summation to the periodic potential yields a finite sum, with the truncation expressed as bounded approximation error. The performance of multilevel summation is demonstrated to be superior to other commonly used fast methods for electrostatics, while providing comparable accuracy. The method is also shown to produce stable dynamics for cheaper, lower accuracy approximation.","abstract_has_math":false,"creators":["Hardy, David Joseph"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Skeel, Robert D."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:20:07Z","date_published":"2015-09-25T20:20:07Z","updated_at":"2026-07-22T22:26:16Z","subjects":["Computer Science"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3223608"],"render_values":[{"text":"(MiAaPQ)AAI3223608","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/81713","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Skeel, Robert D."]},{"key":"dc:creator","label":"Author","values":["Hardy, David Joseph"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:20:07Z","10000-01-01","2006"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/81713","(MiAaPQ)AAI3223608"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis provides the most thorough investigation to date of the multilevel summation method and its use for computing electrostatic interactions. The mathematical and algorithmic details are presented along with a precise operation count. The approximation error from the method is analyzed, with error bounds formulated in terms of the fundamental method parameters. The cost and error analyses enable the determination of optimal method parameters for a desired error tolerance. Various interpolation schemes for the approximation are considered, and several alternative approaches to smoothing the electrostatic potential are examined. The use of the method with different boundary conditions is discussed, and it is shown that the application of multilevel summation to the periodic potential yields a finite sum, with the truncation expressed as bounded approximation error. The performance of multilevel summation is demonstrated to be superior to other commonly used fast methods for electrostatics, while providing comparable accuracy. The method is also shown to produce stable dynamics for cheaper, lower accuracy approximation.","Made available in DSpace on 2015-09-25T20:20:07Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3223608.pdf: 4024534 bytes, checksum: 109f6fb7bea78c3405c35da7b530dcc8 (MD5) Previous issue date: 2006","Embargo set by: Seth Robbins for item 82994 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","152 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006."]},{"key":"dc:title","label":"Title","values":["Multilevel Summation for the Fast Evaluation of Forces for the Simulation of Biomolecules"]}]}],"canonical_facts":{"dc:contributor":["Skeel, Robert D."],"dc:creator":["Hardy, David Joseph"],"dc:date":["2015-09-25T20:20:07Z","10000-01-01","2006"],"dc:description":["This thesis provides the most thorough investigation to date of the multilevel summation method and its use for computing electrostatic interactions. The mathematical and algorithmic details are presented along with a precise operation count. The approximation error from the method is analyzed, with error bounds formulated in terms of the fundamental method parameters. The cost and error analyses enable the determination of optimal method parameters for a desired error tolerance. Various interpolation schemes for the approximation are considered, and several alternative approaches to smoothing the electrostatic potential are examined. The use of the method with different boundary conditions is discussed, and it is shown that the application of multilevel summation to the periodic potential yields a finite sum, with the truncation expressed as bounded approximation error. The performance of multilevel summation is demonstrated to be superior to other commonly used fast methods for electrostatics, while providing comparable accuracy. The method is also shown to produce stable dynamics for cheaper, lower accuracy approximation.","Made available in DSpace on 2015-09-25T20:20:07Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3223608.pdf: 4024534 bytes, checksum: 109f6fb7bea78c3405c35da7b530dcc8 (MD5) Previous issue date: 2006","Embargo set by: Seth Robbins for item 82994 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","152 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006."],"dc:identifier":["http://hdl.handle.net/2142/81713","(MiAaPQ)AAI3223608"],"dc:language":["eng"],"dc:subject":["Computer Science"],"dc:title":["Multilevel Summation for the Fast Evaluation of Forces for the Simulation of Biomolecules"],"dc:type":["text"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:16Z"}