Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals

Mohamed Nasser, Oona Rainio*, Antti Rasila, Matti Vuorinen, Terry Wallace, Hang Yu, Xiaohui Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs, also called polycircular domains, and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when possible, comparison to exact values or other methods are given. We also analyze the rate of convergence as a function of the number of degrees of freedom. The main ingredients of the computation are boundary integral equations combined with the fast multipole method.
Original languageEnglish
JournalAdvances in Computational Mathematics
StatePublished - 13 Sep 2022


  • Boundary integral equations
  • Condenser capacity
  • Numerical conformal mappings


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