{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:soar.wichita.edu:10057/5361"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:soar.wichita.edu:10057/5361","repository":{"repo_id":"wichita-thes","name":"Wichita State University","base_url":"https://soar.wichita.edu/oai/request"},"display":{"title":"Numerical computation of Schwarz-Christoffel transformations and slit maps for multiply connected domains","abstract":"Two methods for the numerical conformal mapping of domains with m < ∞ separated circular holes to domains with m polygonal holes are presented; bounded and unbounded domains are both considered. The methods are based on extensions of the classical Schwarz- Christo el transformation to nitely connected domains. The rst method uses a truncated in nite product expressed in terms of re ections through circles, and is found to have a computational time which increases geometrically with the number of levels of re ection used. The second method uses the boundary behavior of the map to construct a linear system which gives the coe cients of a Laurent series expansion for the map. The second method has a computational time which is polynomial with the number of terms of the truncated series. Both methods require the solution of a non-linear system of equations which gives the correct parameters for the desired map. The solution to the non-linear system is achieved by a numerical continuation (homotopy) method. An application is given. Maps from the circle domains to the canonical slit domains are also computed using similar techniques.","abstract_html":"Two methods for the numerical conformal mapping of domains with m &lt; ∞ separated circular holes to domains with m polygonal holes are presented; bounded and unbounded domains are both considered. The methods are based on extensions of the classical Schwarz- Christo el transformation to nitely connected domains. The rst method uses a truncated in nite product expressed in terms of re ections through circles, and is found to have a computational time which increases geometrically with the number of levels of re ection used. The second method uses the boundary behavior of the map to construct a linear system which gives the coe cients of a Laurent series expansion for the map. The second method has a computational time which is polynomial with the number of terms of the truncated series. Both methods require the solution of a non-linear system of equations which gives the correct parameters for the desired map. The solution to the non-linear system is achieved by a numerical continuation (homotopy) method. An application is given. Maps from the circle domains to the canonical slit domains are also computed using similar techniques.","abstract_has_math":false,"creators":["Kropf, Everett"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05","date_published":"2012-05","updated_at":"2026-07-24T06:05:48Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/5361"],"render_values":[{"text":"hdl:10057/5361","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":["2012-05"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/5361"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["Two methods for the numerical conformal mapping of domains with m < ∞ separated circular holes to domains with m polygonal holes are presented; bounded and unbounded domains are both considered. The methods are based on extensions of the classical Schwarz- Christo el transformation to nitely connected domains. The rst method uses a truncated in nite product expressed in terms of re ections through circles, and is found to have a computational time which increases geometrically with the number of levels of re ection used. The second method uses the boundary behavior of the map to construct a linear system which gives the coe cients of a Laurent series expansion for the map. The second method has a computational time which is polynomial with the number of terms of the truncated series. Both methods require the solution of a non-linear system of equations which gives the correct parameters for the desired map. The solution to the non-linear system is achieved by a numerical continuation (homotopy) method. An application is given. Maps from the circle domains to the canonical slit domains are also computed using similar techniques."]},{"key":"dc:title","label":"Title","values":["Numerical computation of Schwarz-Christoffel transformations and slit maps for multiply connected domains"]}]}],"canonical_facts":{"dc:date.issued":["2012-05"],"dc:description.other":["Two methods for the numerical conformal mapping of domains with m < ∞ separated circular holes to domains with m polygonal holes are presented; bounded and unbounded domains are both considered. The methods are based on extensions of the classical Schwarz- Christo el transformation to nitely connected domains. The rst method uses a truncated in nite product expressed in terms of re ections through circles, and is found to have a computational time which increases geometrically with the number of levels of re ection used. The second method uses the boundary behavior of the map to construct a linear system which gives the coe cients of a Laurent series expansion for the map. The second method has a computational time which is polynomial with the number of terms of the truncated series. Both methods require the solution of a non-linear system of equations which gives the correct parameters for the desired map. The solution to the non-linear system is achieved by a numerical continuation (homotopy) method. An application is given. Maps from the circle domains to the canonical slit domains are also computed using similar techniques."],"dc:identifier":["hdl:10057/5361"],"dc:title":["Numerical computation of Schwarz-Christoffel transformations and slit maps for multiply connected domains"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T06:05:48Z"}