Conformal modulus and planar domains with strong singularities and cusps

Harri Hakula, Antti Rasila, Matti Vuorinen

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)
237 Downloads (Pure)


We study the problem of computing the conformal modulus of rings and quadrilaterals with strong singularities and cusps at their boundary. We reduce this problem to the numerical solution of the associated Dirichlet and Dirichlet-Neumann-type boundary values problems for the Laplace equation. Several experimental results, with error estimates, are reported. In particular, we consider domains with dendrite-like boundaries where an analytic formula for the conformal modulus can be derived. The boundary value problems are solved using an hp-finite element method.

Original languageEnglish
Pages (from-to)462-478
Number of pages17
JournalElectronic Transactions on Numerical Analysis
Publication statusPublished - 1 Jan 2018
MoE publication typeA1 Journal article-refereed


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


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