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Numerical computation of Schwarz-Christoffel transformations and slit maps for multiply connected domains

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dc.contributor.advisor DeLillo, Thomas K.
dc.contributor.author Kropf, Everett
dc.date.accessioned 2012-11-14T22:23:24Z
dc.date.available 2012-11-14T22:23:24Z
dc.date.copyright 2012
dc.date.issued 2012-05
dc.identifier.other d12012
dc.identifier.uri http://hdl.handle.net/10057/5361
dc.description Thesis (Ph.D.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics and Physics en_US
dc.description.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. en_US
dc.format.extent x, 102 p. en
dc.language.iso en_US en_US
dc.publisher Wichita State University en_US
dc.rights Copyright Everett Kropf, 2012. All rights reserved en
dc.subject.lcsh Electronic dissertations en
dc.title Numerical computation of Schwarz-Christoffel transformations and slit maps for multiply connected domains en_US
dc.type Dissertation

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