𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Numerical conformal mapping via the Bergman kernel

✍ Scribed by M.R.M. Razali; M.Z. Nashed; A.H.M. Murid

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
813 KB
Volume
82
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

A new method to compute the Riemann mapping function via the Bergman kernel is presented. The method expresses the Bergman kernel as the solution of a second-kind integral equation involving the Neumann kernel. For symmetric regions, the integral equation can be transformed into a new one that uses only a small part of the original boundary. Numerical implementations on some test regions are also presented.

πŸ“œ SIMILAR VOLUMES

Numerical conformal mapping via the Berg
Numerical conformal mapping via the Bergman kernel using the generalized minimum residual method
✍ M.R.M. Razali; M.Z. Nashed; A.H.M. Murid πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 414 KB

The Bergman kernel function is known to satisfy a certain boundary integral equation of the second kind. For boundaries that possess symmetrical qualities, the integral equation can be transformed into another integral equation that uses only a small part of the original boundary. This paper applies

Conformal Mapping of Nonsmooth Domains v
Conformal Mapping of Nonsmooth Domains via the Kerzman–Stein Integral Equation
✍ Anthony D. Thomas πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 215 KB

The connection between the Riemann map and the Szego kernel is classical. But the fact that there is an efficient numerical procedure, based on the Kerzman᎐Stein integral equation, for computing the Szego kernel of a smoothly bounded domain in the plane is more recent. In this paper it is shown how