Conformal Invariants in Simply Connected Domains



: Mohamed M. S. Nasser, Matti Vuorinen

Publisher: SPRINGER HEIDELBERG

: 2020

Computational Methods and Function Theory

COMPUTATIONAL METHODS AND FUNCTION THEORY

: COMPUT METH FUNCT TH

: 20

: 3-4

: 747

: 775

: 29

: 1617-9447

: 2195-3724

DOI: https://doi.org/10.1007/s40315-020-00351-8

: https://research.utu.fi/converis/portal/detail/Publication/50965465


This paper studies the numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The used method is based on the boundary integral equation with the generalized Neumann kernel. Several numerical examples are presented. The performance and accuracy of the presented method is validated by considering several model problems with known analytic solutions.

Last updated on 2024-26-11 at 22:42