PlgCirMap: A MATLAB toolbox for computing the conformal maps from polygonal multiply connected domains onto circular domains

In [1], the author has presented a method for computing the conformal mapping form a given bounded or unbounded multiply connected domains onto circular domain. The method is based on a fast numerical implementation of Koebe's iterative method using the boundary integral equation with the generalized Neumann kernel which can be solved fast and accurately with the help of FMM [2]. The method gives accurate results even when the given domain is a polygonal domain. In this talk, the method presented in [1] will be used to develop a MATLAB toolbox for computing the conformal mapping $w=f(z)$ from a given polygonal multiply connected domain $G$ onto a circular domain $D$ and its inverse $z=f^{-1}(w)$. The boundaries of the polygons are assumed to be piecewise smooth Jordan curves without cusps. The toolbox can be used even for domains with high connectivity. References. [1] M.M.S. Nasser, Fast computation of the circular map, Comput. Methods Funct. Theory 15 (2) (2015) 187-223. [2] M.M.S. Nasser, Fast solution of boundary integral equations with the generalized Neumann kernel, Electron. Trans. Numer. Anal. 44 (2015) 189-229.