Numerical conformal mapping via a boundary integral equation with the generalized Neumann kernel. (English) Zbl 1198.30009

Nasser, Mohamed M. S.

SIAM J. Sci. Comput. 31, No. 3, 1695-1715 (2009).

The main object of the paper is to present a unified boundary integral method for numerical conformal mappings of bounded (see [M. M. S. Nasser, Comput. Methods Funct. Theory 9, No. 1, 127–143 (2009; Zbl 1159.30007)]) and unbounded (see, e.g., [S. Bergman, The kernel function and conformal mapping, Mathematical Surveys. 5. Providence, R.I.: American Mathematical Society (AMS) (1950; Zbl 0040.19001) (1970; Zbl 0208.34302) (1980; Zbl 0473.30006)]) multiply connected regions onto the five classical canonical slit domains, Using this method, the approximate parameters and mapping functions onto the five canonical slit domains can be computed by solving a linear systems with a common coefficient matrix. Several numerical examples are also given to support the effectiveness of the method.

Reviewer: H. P. Dikshit (Bhopal)

MSC:

30C30	Schwarz-Christoffel-type mappings
30E25	Boundary value problems in the complex plane
65E05	General theory of numerical methods in complex analysis (potential theory, etc.)

Keywords:

numerical conformal mapping; multiply connected regions; generalized Neumann kernel