{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/108032"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/108032","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Layer potential evaluations on distributed memory machines","abstract":"One of the main challenges of using integral equation methods (IEM) for solving partial differential equations is evaluating layer potentials with singular kernels. Quadrature by Expansion (QBX) is a quadrature method to evaluate such layer potentials accurately for targets near or on the source boundary, by forming expansions in the high-accuracy region away from the boundary, and evaluating the targets using the expansions. Recently, a new algorithm, called 'GIGAQBX', has combined QBX with the Fast Multipole Method to achieve linear complexity in terms of the number of degrees of freedom. Despite this advancement, QBX is still computationally expensive. To enable IEM on large-scale problems, this thesis investigates evaluating layer potentials on distributed-memory machines. The distributed algorithm introduced in this thesis is based on GIGAQBX and shows GIGAQBX contains plenty of parallelism. We evaluate our algorithm on the Comet supercomputer at the San Diego Supercomputer Center and show that it exhibits good strong scaling up to 1536 cores.","abstract_html":"One of the main challenges of using integral equation methods (IEM) for solving partial differential equations is evaluating layer potentials with singular kernels. Quadrature by Expansion (QBX) is a quadrature method to evaluate such layer potentials accurately for targets near or on the source boundary, by forming expansions in the high-accuracy region away from the boundary, and evaluating the targets using the expansions. Recently, a new algorithm, called 'GIGAQBX', has combined QBX with the Fast Multipole Method to achieve linear complexity in terms of the number of degrees of freedom. Despite this advancement, QBX is still computationally expensive. To enable IEM on large-scale problems, this thesis investigates evaluating layer potentials on distributed-memory machines. The distributed algorithm introduced in this thesis is based on GIGAQBX and shows GIGAQBX contains plenty of parallelism. We evaluate our algorithm on the Comet supercomputer at the San Diego Supercomputer Center and show that it exhibits good strong scaling up to 1536 cores.","abstract_has_math":false,"creators":["Gao, Hao"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Kloeckner, Andreas"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-08-26T21:58:01Z","date_published":"2020-08-26T21:58:01Z","updated_at":"2026-07-22T22:24:47Z","subjects":["Layer Potentials","Distributed Memory Parallelism","Integral Equations","Singular Integrals","Fast Multipole Method"],"languages":["en"],"rights":["Copyright 2020 Hao Gao"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/108032","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kloeckner, Andreas"]},{"key":"dc:creator","label":"Author","values":["Gao, Hao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-08-26T21:58:01Z","2020-05-12","2020-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["Layer Potentials","Distributed Memory Parallelism","Integral Equations","Singular Integrals","Fast Multipole Method"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Hao Gao"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/108032"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["One of the main challenges of using integral equation methods (IEM) for solving partial differential equations is evaluating layer potentials with singular kernels. Quadrature by Expansion (QBX) is a quadrature method to evaluate such layer potentials accurately for targets near or on the source boundary, by forming expansions in the high-accuracy region away from the boundary, and evaluating the targets using the expansions. Recently, a new algorithm, called 'GIGAQBX', has combined QBX with the Fast Multipole Method to achieve linear complexity in terms of the number of degrees of freedom. Despite this advancement, QBX is still computationally expensive. To enable IEM on large-scale problems, this thesis investigates evaluating layer potentials on distributed-memory machines. The distributed algorithm introduced in this thesis is based on GIGAQBX and shows GIGAQBX contains plenty of parallelism. We evaluate our algorithm on the Comet supercomputer at the San Diego Supercomputer Center and show that it exhibits good strong scaling up to 1536 cores.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-08-25 without embargo terms","The student, Hao Gao, accepted the attached license on 2020-05-11 at 12:11.","The student, Hao Gao, submitted this Thesis for approval on 2020-05-11 at 12:25.","This Thesis was approved for publication on 2020-05-12 at 09:03.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15321 on 2020-08-25 at 17:13:53","Made available in DSpace on 2020-08-26T21:58:01Z (GMT). No. of bitstreams: 2 GAO-THESIS-2020.pdf: 3092714 bytes, checksum: c85159141262a40b21a186a64de3d7c6 (MD5) LICENSE.txt: 4204 bytes, checksum: 8521eeb886433c80a314cca4f93a9c4b (MD5) Previous issue date: 2020-05-12"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Layer potential evaluations on distributed memory machines"]}]}],"canonical_facts":{"dc:contributor":["Kloeckner, Andreas"],"dc:creator":["Gao, Hao"],"dc:date":["2020-08-26T21:58:01Z","2020-05-12","2020-05"],"dc:description":["One of the main challenges of using integral equation methods (IEM) for solving partial differential equations is evaluating layer potentials with singular kernels. Quadrature by Expansion (QBX) is a quadrature method to evaluate such layer potentials accurately for targets near or on the source boundary, by forming expansions in the high-accuracy region away from the boundary, and evaluating the targets using the expansions. Recently, a new algorithm, called 'GIGAQBX', has combined QBX with the Fast Multipole Method to achieve linear complexity in terms of the number of degrees of freedom. Despite this advancement, QBX is still computationally expensive. To enable IEM on large-scale problems, this thesis investigates evaluating layer potentials on distributed-memory machines. The distributed algorithm introduced in this thesis is based on GIGAQBX and shows GIGAQBX contains plenty of parallelism. We evaluate our algorithm on the Comet supercomputer at the San Diego Supercomputer Center and show that it exhibits good strong scaling up to 1536 cores.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-08-25 without embargo terms","The student, Hao Gao, accepted the attached license on 2020-05-11 at 12:11.","The student, Hao Gao, submitted this Thesis for approval on 2020-05-11 at 12:25.","This Thesis was approved for publication on 2020-05-12 at 09:03.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15321 on 2020-08-25 at 17:13:53","Made available in DSpace on 2020-08-26T21:58:01Z (GMT). No. of bitstreams: 2 GAO-THESIS-2020.pdf: 3092714 bytes, checksum: c85159141262a40b21a186a64de3d7c6 (MD5) LICENSE.txt: 4204 bytes, checksum: 8521eeb886433c80a314cca4f93a9c4b (MD5) Previous issue date: 2020-05-12"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/108032"],"dc:language":["en"],"dc:rights":["Copyright 2020 Hao Gao"],"dc:subject":["Layer Potentials","Distributed Memory Parallelism","Integral Equations","Singular Integrals","Fast Multipole Method"],"dc:title":["Layer potential evaluations on distributed memory machines"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:47Z"}