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Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/5567
Title: Numerical Conformal Mapping Using Cross-ratios and Delaunay Triangulation
Authors: Driscoll, Tobin
Vavasis, Stephen A.
Keywords: theory center
numerical conformal mapping
Schwarz-Christoffel mapping
cross-ratios
Delaunay triangulationcrowding
Issue Date: Feb-1996
Publisher: Cornell University
Citation: http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.tc/96-233
Abstract: We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the Schwarz-Christoffel transformation. The new algorithm, CRDT, is based on cross-ratios of the prevertices, and also on cross-ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate representation of the Riemann mapping even in the presence of arbitrary long, thin regions in the polygon, unlike any previous conformal mapping algorithm. We believe that CRDT can never fail to converge to the correct Riemann mapping, but the correctness and convergence proof depend on conjectures that we have so far not been able to prove. We demonstrate convergence with computational experiments. The Riemann mapping has applications to problems in two-dimensional potential theory and to finite-difference mesh generation. We use CRDT to produce a mapping and solve a boundary value problem on long, thin regions for which no other algorithm can solve these problems.
URI: http://hdl.handle.net/1813/5567
Appears in Collections:Cornell Theory Center Technical Reports

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