On moduli of rings and quadrilaterals: algorithms and experiments

Details On moduli of rings and quadrilaterals: algorithms and experiments On moduli of rings and quadrilaterals: algorithms and experiments

2009-06-06

arxiv.org/abs/0906.1261v4

SIAM J. Sci. Comput. 33 (2011), pp. 279--302

Mathematics

Numerical Analysis

Scientific paper

10.1137/090763603

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 $hp$-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 $hp$-FEM algorithm applies to the case of non-polygonal boundary and report results with concrete error bounds.

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