Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals

: Nasser Mohamed, Rainio Oona, Rasila Antti, Vuorinen Matti, Wallace Terry, Yu Hang, Zhang Xiaohui

Publisher: SPRINGER

: 2022

: Advances in Computational Mathematics

: ADVANCES IN COMPUTATIONAL MATHEMATICS

: ADV COMPUT MATH

: 58

: 48

: 5

: 34

: 1019-7168

: 1572-9044

DOI: https://doi.org/10.1007/s10444-022-09975-x

: https://link.springer.com/article/10.1007/s10444-022-09975-x

: https://research.utu.fi/converis/portal/detail/Publication/176352751

We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs, also called polycircular domains, and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when possible, comparison to exact values or other methods are given. We also analyze the rate of convergence as a function of the number of degrees of freedom. The main ingredients of the computation are boundary integral equations combined with the fast multipole method.

s10444-022-09975-x.pdf