Conformal modulus on domains with strong singularities and cusps
Matti Vuorinen; Antti Rasila; Harri Hakula
Conformal modulus on domains with strong singularities and cusps
Matti Vuorinen
Antti Rasila
Harri Hakula
Kent State University * Institute of Computational Mathematics
Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2021042720331
https://urn.fi/URN:NBN:fi-fe2021042720331
Tiivistelmä
We study the problem of computing the conformal modulus of rings and quadrilaterals with strong singularities and cusps on 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, in such cases where an analytic formula for the conformal modulus can be derived. Our numerical method makes use of an hp-FEM algorithm, written for this very complicated geometry with strong singularities.
Kokoelmat
- Rinnakkaistallenteet [19207]