On moduli of rings and quadrilaterals: algorithms and experiments
arXiv:0906.1261 · doi:10.1137/090763603
Abstract
Moduli of rings and quadrilaterals are frequently applied in geometric function theory, see e.g. the Handbook by Kühnau. Yet their exact values are known only in a few special cases. Previously, the class of planar domains with polygonal boundary has been studied by many authors from the point of view of numerical computation. We present here a new -FEM algorithm for the computation of moduli of rings and quadrilaterals and compare its accuracy and performance with previously known methods such as the Schwarz-Christoffel Toolbox of Driscoll and Trefethen. We also demonstrate that the -FEM algorithm applies to the case of non-polygonal boundary and report results with concrete error bounds.