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.
| Original language | English |
|---|---|
| Pages (from-to) | 462-478 |
| Number of pages | 17 |
| Journal | Electronic Transactions on Numerical Analysis |
| Volume | 48 |
| DOIs | |
| Publication status | Published - 1 Jan 2018 |
| MoE publication type | A1 Journal article-refereed |
Funding
Acknowledgements. This research of the third author was supported by the Academy of Finland, Project 2600066611.
Keywords
- Conformal capacity
- Conformal modulus
- Hp-FEM
- Numerical conformal mapping
- Quadrilateral modulus
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