On moduli of rings and quadrilaterals: Algorithms and experiments

Harri Hakula*, Antti Rasila, Matti Vuorinen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

Moduli of rings and quadrilaterals are frequently applied in geometric function theory; see, e.g., the handbook by Kühnau [Handbook of Complex Analysis: Geometric Function Theory, Vols. 1 and 2, North-Holland, Amsterdam, 2005]. 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 nonpolygonal boundary and report results with concrete error bounds.

Original languageEnglish
Pages (from-to)279-302
Number of pages24
JournalSIAM Journal of Scientific Computing
Volume33
Issue number1
DOIs
StatePublished - 2011
Externally publishedYes

Keywords

  • Conformal capacity
  • Conformal modulus
  • Hp-FEM
  • Numerical conformal mapping
  • Quadrilateral modulus

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