{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:null:10057/18800"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:null:10057/18800","repository":{"repo_id":"wichita-thes","name":"Wichita State University","base_url":"https://soar.wichita.edu/oai/request"},"display":{"title":"Numerical methods for Riemann-Hilbert problems in multiply connected circle domains","abstract":"Riemann-Hilbert problems are problems for determining functions analytic in a given domain with speci ed values on the boundary. Since the real and imaginary parts of an analytic function are related by the Cauchy-Riemann equations, both parts cannot be speci ed independently. Riemann-Hilbert problems on multiply connected regions have been studied by several authors in the past. A special kind of Riemann-Hilbert problems on circular regions is necessary for conformal mapping of multiply-connected regions. Wegmann introduced a method of successive conjugation which reduces the general conjugation problem to a sequence of Riemann-Hilbert problems on the circles. Here, we present a new method to solve Riemann-Hilbert problems on the circles. We consider the general conjugation as a Least-Squares problem and use direct and iterative methods to obtain the solution. The resulting linear system has an underlying structure of the form of the identity plus a low rank operator and can be solved e ciently by conjugate gradient-like methods. We present numerical examples and comparisons to the method of Wegmann.","abstract_html":"Riemann-Hilbert problems are problems for determining functions analytic in a given domain with speci ed values on the boundary. Since the real and imaginary parts of an analytic function are related by the Cauchy-Riemann equations, both parts cannot be speci ed independently. Riemann-Hilbert problems on multiply connected regions have been studied by several authors in the past. A special kind of Riemann-Hilbert problems on circular regions is necessary for conformal mapping of multiply-connected regions. Wegmann introduced a method of successive conjugation which reduces the general conjugation problem to a sequence of Riemann-Hilbert problems on the circles. Here, we present a new method to solve Riemann-Hilbert problems on the circles. We consider the general conjugation as a Least-Squares problem and use direct and iterative methods to obtain the solution. The resulting linear system has an underlying structure of the form of the identity plus a low rank operator and can be solved e ciently by conjugate gradient-like methods. We present numerical examples and comparisons to the method of Wegmann.","abstract_has_math":false,"creators":["Balu, Raja"],"institution":"Wichita State University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["DeLillo, Thomas K."],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-05","date_published":"2020-05","updated_at":"2026-08-21T16:50:55Z","subjects":[],"languages":["en_US"],"rights":["Copyright 2020 by Raja D. Balu All Rights Reserved"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["d20003"],"render_values":[{"text":"d20003","href":null,"code":true}]}]},"links":{"outbound_url":"https://soar.wichita.edu/handle/10057/18800","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://soar.wichita.edu/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Anull%3A10057%2F18800","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["DeLillo, Thomas K."]},{"key":"dc:creator","label":"Author","values":["Balu, Raja"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-07-14T13:37:22Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-07-14T13:37:22Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-05"]},{"key":"dc:publisher","label":"Institution","values":["Wichita State University"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 by Raja D. 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A special kind of Riemann-Hilbert problems on circular regions is necessary for conformal mapping of multiply-connected regions. Wegmann introduced a method of successive conjugation which reduces the general conjugation problem to a sequence of Riemann-Hilbert problems on the circles. Here, we present a new method to solve Riemann-Hilbert problems on the circles. We consider the general conjugation as a Least-Squares problem and use direct and iterative methods to obtain the solution. The resulting linear system has an underlying structure of the form of the identity plus a low rank operator and can be solved e ciently by conjugate gradient-like methods. We present numerical examples and comparisons to the method of Wegmann."]},{"key":"dc:title","label":"Title","values":["Numerical methods for Riemann-Hilbert problems in multiply connected circle domains"]}]}],"canonical_facts":{"dc:contributor.advisor":["DeLillo, Thomas K."],"dc:creator":["Balu, Raja"],"dc:date.accessioned":["2020-07-14T13:37:22Z"],"dc:date.available":["2020-07-14T13:37:22Z"],"dc:date.issued":["2020-05"],"dc:description":["Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics and Physics"],"dc:description.abstract":["Riemann-Hilbert problems are problems for determining functions analytic in a given domain with speci ed values on the boundary. Since the real and imaginary parts of an analytic function are related by the Cauchy-Riemann equations, both parts cannot be speci ed independently. Riemann-Hilbert problems on multiply connected regions have been studied by several authors in the past. A special kind of Riemann-Hilbert problems on circular regions is necessary for conformal mapping of multiply-connected regions. Wegmann introduced a method of successive conjugation which reduces the general conjugation problem to a sequence of Riemann-Hilbert problems on the circles. Here, we present a new method to solve Riemann-Hilbert problems on the circles. We consider the general conjugation as a Least-Squares problem and use direct and iterative methods to obtain the solution. The resulting linear system has an underlying structure of the form of the identity plus a low rank operator and can be solved e ciently by conjugate gradient-like methods. We present numerical examples and comparisons to the method of Wegmann."],"dc:identifier.other":["d20003"],"dc:identifier.uri":["https://soar.wichita.edu/handle/10057/18800"],"dc:language.iso":["en_US"],"dc:publisher":["Wichita State University"],"dc:rights":["Copyright 2020 by Raja D. Balu All Rights Reserved"],"dc:title":["Numerical methods for Riemann-Hilbert problems in multiply connected circle domains"],"dc:type":["Dissertation"]},"updated_at":"2026-08-21T16:50:55Z"}