On moduli of rings and quadrilaterals: algorithms and experiments
Numerical Analysis
2012-01-10 v4 Complex Variables
Abstract
Moduli of rings and quadrilaterals are frequently applied in geometric function theory, see e.g. the Handbook by K\"uhnau. 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.
Cite
@article{arxiv.0906.1261,
title = {On moduli of rings and quadrilaterals: algorithms and experiments},
author = {Harri Hakula and Antti Rasila and Matti Vuorinen},
journal= {arXiv preprint arXiv:0906.1261},
year = {2012}
}