Conformal modulus and planar domains with strong singularities and cusps

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2018-01-01
Major/Subject
Mcode
Degree programme
Language
en
Pages
17
462-478
Series
Electronic Transactions on Numerical Analysis, Volume 48
Abstract
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.
Description
Keywords
Conformal capacity, Conformal modulus, Hp-FEM, Numerical conformal mapping, Quadrilateral modulus
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Citation
Hakula , H , Rasila , A & Vuorinen , M 2018 , ' Conformal modulus and planar domains with strong singularities and cusps ' , Electronic Transactions on Numerical Analysis , vol. 48 , pp. 462-478 . https://doi.org/10.1553/etna_vol48s462