Conformal modulus and planar domains with strong singularities and cusps

TY - JOUR

T1 - Conformal modulus and planar domains with strong singularities and cusps

AU - Hakula, Harri

AU - Rasila, Antti

AU - Vuorinen, Matti

N1 - Publisher Copyright: Copyright © 2018, Kent State University.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Conformal capacity

KW - Conformal modulus

KW - Hp-FEM

KW - Numerical conformal mapping

KW - Quadrilateral modulus

UR - http://www.scopus.com/inward/record.url?scp=85065389177&partnerID=8YFLogxK

U2 - 10.1553/etna_vol48s462

DO - 10.1553/etna_vol48s462

M3 - 文章

AN - SCOPUS:85065389177

SN - 1068-9613

VL - 48

SP - 462

EP - 478

JO - Electronic Transactions on Numerical Analysis

JF - Electronic Transactions on Numerical Analysis

ER -