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Numerical computation of Schwarz-Christoffel transformations and slit maps for multiply connected domains
Kropf, Everett
Kropf, Everett
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d12012_Kropf.pdf
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2012-05
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Dissertation
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Electronic dissertations
Electronic dissertations
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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.
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Thesis (Ph.D.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics and Physics
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Wichita State University
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Copyright Everett Kropf, 2012. All rights reserved