Faculty of Computing and Information Science >
Center for Advance Computing >
Cornell Theory Center Technical Reports >
Please use this identifier to cite or link to this item:
|Title: ||Numerical Conformal Mapping Using Cross-ratios and Delaunay Triangulation|
|Authors: ||Driscoll, Tobin|
Vavasis, Stephen A.
|Keywords: ||theory center|
numerical conformal mapping
|Issue Date: ||Feb-1996|
|Publisher: ||Cornell University|
|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.|
|Appears in Collections:||Cornell Theory Center Technical Reports|
Items in eCommons are protected by copyright, with all rights reserved, unless otherwise indicated.