{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:soar.wichita.edu:10057/18800"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:soar.wichita.edu: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":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-05","date_published":"2020-05","updated_at":"2026-07-24T06:05:36Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/18800"],"render_values":[{"text":"hdl:10057/18800","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2020-05"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/18800"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["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."]},{"key":"dc:title","label":"Title","values":["Numerical methods for Riemann-Hilbert problems in multiply connected circle domains"]}]}],"canonical_facts":{"dc:date.issued":["2020-05"],"dc:description.other":["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":["hdl:10057/18800"],"dc:title":["Numerical methods for Riemann-Hilbert problems in multiply connected circle domains"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T06:05:36Z"}