Conformal capacity and polycircular domains

Harri Hakula*, Mohamed M.S. Nasser, Matti Vuorinen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
80 Downloads (Pure)


We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by polycircular domains. Experimental error estimates are provided for the computed capacity and, when possible, the rate of convergence under refinement of discretization is analyzed. The main ingredients of the computation are two computational methods, on one hand the boundary integral equation method combined with the fast multipole method and on the other hand the hp-FEM method. The results obtained with these two methods agree with high accuracy.

Original languageEnglish
Article number114802
Pages (from-to)1-15
Number of pages15
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - 1 Mar 2023
MoE publication typeA1 Journal article-refereed


  • Capacity computation
  • Condenser capacity
  • Multiply connected domains


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