Revisiting the Crowding Phenomenon in Schwarz-Christoffel Mapping

We address the problem of conformally mapping the unit disk to polygons with elongations. The elongations cause the derivative of the conformal map to be exponentially large in some regions. This crowding phenomenon creates difficulties in standard numerical methods for the computation of the conformal map. We make use of the Schwarz-Christoffel representation of the mapping and show that a simple change to the existing algorithms introduced by Trefethen [L.N. Trefethen, Numerical computation of the Schwarz-Christoffel transformation, SIAM J. Sci. Statist. Comput., 1(1):82

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: L. Banjai
• Keywords: Conformal Maps, SIAM J, SIAMSC 2008, Standard Numerical Methods